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Cluster analysis research paper

Objects in sparse areas — that are required to separate clusters — are usually considered to be noise and border points. Similar to linkage based clustering, it is based on connecting points within certain distance thresholds. However, it only connects points that satisfy a density criterion, in the original variant defined as a minimum number of other objects within this radius.

A cluster consists of all density-connected objects which can form a cluster of an arbitrary shape, in contrast to many other methods plus all objects that are within these objects' range. Another interesting property of DBSCAN is that its complexity is fairly low — it requires a linear number of range queries on the database — and that it will discover essentially the same results it is deterministic for core and noise points, but not for border points in each run, therefore there is no need to run it multiple times.

On data sets with, for example, overlapping Gaussian distributions — a common use case in artificial data — the cluster borders produced by these algorithms will often look arbitrary, because the cluster density decreases continuously.

On a data set consisting of mixtures of Gaussians, these algorithms are nearly always outperformed by methods such as EM clustering that are able to precisely model this kind of data. Mean-shift is a clustering approach where each object is moved to the densest area in its vicinity, based on kernel density estimation. Eventually, objects converge to local maxima of density.

Similar to k-means clustering, these "density attractors" can serve as representatives for the data set, but mean-shift can detect arbitrary-shaped clusters similar to DBSCAN. Besides that, the applicability of the mean-shift algorithm to multidimensional data is hindered by the unsmooth behaviour of the kernel density estimate, which results in over-fragmentation of cluster tails.

The grid-based technique is used for a multi-dimensional data set. The grid-based technique is fast and has low computational complexity. Steps involved in grid-based clustering algorithm are:. In recent years, considerable effort has been put into improving the performance of existing algorithms. This led to the development of pre-clustering methods such as canopy clustering , which can process huge data sets efficiently, but the resulting "clusters" are merely a rough pre-partitioning of the data set to then analyze the partitions with existing slower methods such as k-means clustering.

For high-dimensional data , many of the existing methods fail due to the curse of dimensionality , which renders particular distance functions problematic in high-dimensional spaces. This led to new clustering algorithms for high-dimensional data that focus on subspace clustering where only some attributes are used, and cluster models include the relevant attributes for the cluster and correlation clustering that also looks for arbitrary rotated "correlated" subspace clusters that can be modeled by giving a correlation of their attributes.

Several different clustering systems based on mutual information have been proposed. Evaluation or "validation" of clustering results is as difficult as the clustering itself. Internal evaluation measures suffer from the problem that they represent functions that themselves can be seen as a clustering objective.

For example, one could cluster the data set by the Silhouette coefficient; except that there is no known efficient algorithm for this. By using such an internal measure for evaluation, one rather compares the similarity of the optimization problems, [34] and not necessarily how useful the clustering is. External evaluation has similar problems: if we have such "ground truth" labels, then we would not need to cluster; and in practical applications we usually do not have such labels.

On the other hand, the labels only reflect one possible partitioning of the data set, which does not imply that there does not exist a different, and maybe even better, clustering. Neither of these approaches can therefore ultimately judge the actual quality of a clustering, but this needs human evaluation, [34] which is highly subjective. Nevertheless, such statistics can be quite informative in identifying bad clusterings, [35] but one should not dismiss subjective human evaluation.

When a clustering result is evaluated based on the data that was clustered itself, this is called internal evaluation. These methods usually assign the best score to the algorithm that produces clusters with high similarity within a cluster and low similarity between clusters.

One drawback of using internal criteria in cluster evaluation is that high scores on an internal measure do not necessarily result in effective information retrieval applications. For example, k-means clustering naturally optimizes object distances, and a distance-based internal criterion will likely overrate the resulting clustering. Therefore, the internal evaluation measures are best suited to get some insight into situations where one algorithm performs better than another, but this shall not imply that one algorithm produces more valid results than another.

An algorithm designed for some kind of models has no chance if the data set contains a radically different set of models, or if the evaluation measures a radically different criterion. On a data set with non-convex clusters neither the use of k -means, nor of an evaluation criterion that assumes convexity, is sound. More than a dozen of internal evaluation measures exist, usually based on the intuition that items in the same cluster should be more similar than items in different clusters.

In external evaluation, clustering results are evaluated based on data that was not used for clustering, such as known class labels and external benchmarks. Such benchmarks consist of a set of pre-classified items, and these sets are often created by expert humans.

Thus, the benchmark sets can be thought of as a gold standard for evaluation. However, it has recently been discussed whether this is adequate for real data, or only on synthetic data sets with a factual ground truth, since classes can contain internal structure, the attributes present may not allow separation of clusters or the classes may contain anomalies.

A number of measures are adapted from variants used to evaluate classification tasks. In place of counting the number of times a class was correctly assigned to a single data point known as true positives , such pair counting metrics assess whether each pair of data points that is truly in the same cluster is predicted to be in the same cluster.

As with internal evaluation, several external evaluation measures exist, [37] : — for example:. One issue with the Rand index is that false positives and false negatives are equally weighted. This may be an undesirable characteristic for some clustering applications.

The F-measure addresses this concern, [ citation needed ] as does the chance-corrected adjusted Rand index. To measure cluster tendency is to measure to what degree clusters exist in the data to be clustered, and may be performed as an initial test, before attempting clustering. One way to do this is to compare the data against random data. On average, random data should not have clusters. From Wikipedia, the free encyclopedia. Task of grouping a set of objects so that objects in the same group or cluster are more similar to each other than to those in other clusters.

Main category: Cluster analysis algorithms. Main article: Hierarchical clustering. Main article: k-means clustering. Density-based clusters cannot be modeled using Gaussian distributions. See also: Determining the number of clusters in a data set. This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.

November Learn how and when to remove this template message. See also: Distance matrices in phylogeny. The Journal of Abnormal and Social Psychology. ISSN X. Edwards Brothers. Journal of Abnormal and Social Psychology. S2CID Cluster analysis.

Chichester, West Sussex, U. K: Wiley. ISBN The Computer Journal. British Computer Society. AAAI Press. ACM Press. CiteSeerX Advances in Knowledge Discovery and Data Mining. Lecture Notes in Computer Science. Reddy, Chandan K. Data Clustering : Algorithms and Applications.

OCLC Web-scale k-means clustering. Data Mining and Knowledge Discovery. Ng and J. Int'l Conf. In: Proc. SIAM Int. Advances in Databases: Concepts, Systems and Applications. Learning Theory and Kernel Machines. Bibcode : q. July 18—23, Wcci Cec. Bibcode : Sci PMID Knowledge and Information Systems. Cambridge Univ. Introduction to Information Retrieval. Cambridge University Press. Journal of Cybernetics. In Fern, Xiaoli Z.

Journal of the American Statistical Association. American Statistical Association. JSTOR Recall and Precision versus the Bookmaker. International Conference on Cognitive Science. Journal of Classification. The Problem with Kappa. European Chapter of the Association for Computational Linguistics.

Annals of Botany. Annals Botany Co. ISSN Information Processing Letters. Journal of Classification, 2 , — Hudson, H. Classifying social data. San Francisco: Jossey-Bass. Judd, C. Estimating the effects of social interventions. New York: Cambridge University Press. Knoke, D. Network analysis. Beverly Hills: Sage. Lathrop, R. The reliability of inverse scree tests for cluster analysis.

Educational and Psychological Measurement, 47 , — The validity of the inverse scree test for cluster analysis. Educational and Psychological Measurement, 50 , — Lorr, M. Cluster analysis for social scientists. Washington, DC: Jossey-Bass. Luke, D. The assessment of change in a mutual help context. Unpublished dissertation, University of Illinois, Urbana-Champaign. Setting phenotypes in a mutual help organization: Expanding behavior setting theory.

American Journal of Community Psychology, 19 , — PubMed Google Scholar. Milligan, G. Methodology review: Clustering methods. Applied Psychological Measurement, 11 , — A study of standardization of variables in cluster analysis. Ortiz, B. Transculturation as a determinant of sexual risk behavior in Latina immigrants to New York City.

Popper, K. Corroboration, or how a theory stands up to tests. Popper, The logic of scientific discovery. New York: Harper. Price, R. Explorations in the taxonomy of behavior settings. American Journal of Community Psychology, 3 , — Toward a taxonomy of inpatient treatment environments.

Journal of Abnormal Psychology, 84 , — Rapkin, B. Framing the construct of life satisfaction in terms of older adults' personal goals. Psychology and Aging, 7 1. Rand, W. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66 , — Rogosa, D.

Demonstrating the reliability of the difference score in the measurement of change. Journal of Educational Measurement, 20 , — SAS Institute, Inc. SAS user's guides: Version 5 edition. Cary, NC: Author. Shinn, M. Cross-level research without cross-ups in community psychology.

Seidman Eds. Shepard, R. Additive clustering: Representation of similarities as combination of discrete, overlapping properties. Psychological Review, 86 , 87— Skinner, H. Dimensions and clusters: A hybrid approach to classification. Applied Psychological Measurement, 3 , — SPSS Inc. SPSSsupx user's guide 3rd Ed. Chicago: Author. Tabachnick, B. Using multivariale statistics 2nd ed.

New York: Harper and Row. Ward, J. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58 , — Wilkinson, L. Evanston, IL: Systat, Inc. Willett, J. Questions and answers in the measurement of change. Review of Research in Education. Download references. You can also search for this author in PubMed Google Scholar. Editor's note : Dr. Edward Seidman served as action editor for this article while serving as Associate Editor for Methodology.

Reprints and Permissions. Cluster analysis in community research: Epistemology and practice. Am J Commun Psychol 21, — Download citation. Issue Date : April Search SpringerLink Search. Abstract Cluster analysis refers to a family of methods for identifying cases with distinctive characteristics in heterogeneous samples and combining them into homogeneous groups.

References Aldenderfer, M. Google Scholar Anderberg, M. Google Scholar Altman, I. Google Scholar Blashfield, R. Google Scholar Borgen, F. Google Scholar Breckenridge, J. Google Scholar Cronbach, L. Google Scholar Dillon, W. Google Scholar Dixon, W.

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A key question is the extent to which life has been shortened. Internet and search engines are increasingly the relevant tools for searching for jobs and possible training and education opportunities. In this sense, the approach In this sense, the approach is to understand how to vary the online job-search strategies over the Italian territory.

In this sense, the statistical question in this research is how to vary the different strategies of internet job search. In order to answer the question, a strategy that uses big social data is necessary. Clustering is the most well-known data mining method used for classifying the data into clusters based on distance measures.

The appearance growth of high dimensional data like microarray gene appearance data and clustering high The appearance growth of high dimensional data like microarray gene appearance data and clustering high dimensional data into groups will find the similarity between the objects in the full-dimensional space is usually wrong because it includes various types of data.

We propose a new set of clustering algorithm called CURE Clustering Using Representatives which is more robust for outliers and recognises clusters with non-spherical shapes and wide variations in size. CURE achieves this by representing each group by a positive fixed number of factors created by selecting well-dispersed factors from the group and then shrinking them near the group's centre by a given ratio.

Having two representative factors by group allows CURE to fit well into the geometry of non-spherical shapes, and shrinkage allows us to extract from the effects of outliers. To manage large databases, CURE uses a combination of random sampling and segmentation. The random pattern derived from the set of facts is split first, and each section is partially grouped.

The subsets are then grouped into a two-dimensional path to produce the desired groups. Our experimental results confirm that the number of clusters produced by CURE is significantly better than that observed with the current algorithms. The experimental results demonstrate that the proposed algorithm gets better accuracy compared with the previous algorithm.

Social capital as the substantial concept of social network research. A methodology for a systematic literature review. The book provides a synthesis of the very heterogeneous social network literature. In doing so, it proposes a research methodology for a systematic literature review: Content Analysis in conjunction with Multiple Correspondence Analysis In doing so, it proposes a research methodology for a systematic literature review: Content Analysis in conjunction with Multiple Correspondence Analysis and Cluster Analysis.

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A sample of competitive athletes Comparing the sample as a whole, cluster analyses revealed two emotional profiles: a High unpleasant emotions and low pleasant emotions; and b moderately high pleasant emotions and low unpleasant emotions. Therefore, results suggested that an emotion profile approach offered a robust heuristic for examining emotions in a more holistic method to unpack their complex associations with key outcomes coping, burnout and they have implications fo The West African sub-region is indisputably the region of greatest diversity of Okra Abelmoschus spp L.

These are These are largely uncharacterised, making it practically impossible to ascribe specific attributes to known accessions to facilitate breeding for further improvement to meet specific demands by end-users or industrial-scale production. Twenty six 26 local accessions and three 3 exotic lines of Okra were collected from eight geographic regions of Ghana.

Their agro-morphological traits were evaluated under field conditions on the research farm of the Biotechnology and Nuclear Agriculture Research Institute. Hierarchical cluster analysis of results grouped the accessions into two major clusters and subsequently into five sub-clusters based on the qualitative characters studied.

The pattern of clustering did not indicate any relationship with geographic orig Quantum clustering QC , is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential.

This is an outstanding task because normally such expressions are impossible to solve analytically. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach "per block". This technique decreases the number of particles by approximating some groups of particles to weighted particles. These findings are not only useful to the quantum clustering problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics and other applications.

Tony Scott. Correspondent Banking in Euro: bank clustering via self-organizing maps. The goal of this paper is to shed light on a key business in Europe that surpasses — in value of transactions — many European payment The goal of this paper is to shed light on a key business in Europe that surpasses — in value of transactions — many European payment systems and that, due to the nature of the data collected, has not been the subject of any in-depth study before.

This study builds upon the findings of the Eighth Survey on Correspondent Banking in Euro by adopting a finer clustering methodology. The main findings include the discovery of two additional clusters, and a more detailed understanding of the inner market dynamics over time, tying the discussion within the relevant literature. It is assumed here that the reader is already familiar with the main findings of the survey. In mid, Scientific Reports, which is part of the publishing ecosystem of Nature scientific journal, published an article on the results of an international study of the concentration of polycyclic aromatic hydrocarbons In mid, Scientific Reports, which is part of the publishing ecosystem of Nature scientific journal, published an article on the results of an international study of the concentration of polycyclic aromatic hydrocarbons and fragrances in glacial cores of Elbrus.

The structure of the study can be conditionally separated into empirical and interpretive parts. Methodologically, the study follows the general direction of research within the framework of the macroecological and biogeographic concept referred to as Great Acceleration. The concept substantiates the prepositional geochronological framework of the Great Acceleration of the s, when the human impact on the Earths ecosystem became dominant and began to determine its further development Anthropocene.

This is one of the first studies on the territory of Russia devoted to a comprehensive analysis of the impact of the Great Acceleration on the environment. The results of the study confirm the key provisions of the concept, while drawing attention to two large periods of decline stagnation of polluting factors in the second half of the 20th century. The periods were — and the s. Meanwhile, the empirical part of the study is based on the logical positivism, and the interpretational part uses the comparative method.

Results and Discussion. The article analyses the findings of a study that establishes a correlation between a decrease stagnation in the level of PAHs concentration in the period — and the general sociopolitical characteristics of the period classified as 'the era of stagnation'. In the course of the comparative chronological analysis, structural contradictions between the obtained research results and the author's interpretation model were revealed. Thus, to create a scientifically grounded interpretive research model, it is proposed to use a multi-factor model based on the principles of maintaining a balance between the biochemical and macroeconomic components of the study; defining the role of infrastructure, innovative technological and other components.

As for the relevant research methodology for the analysis of the matrix panel of variables with the establishment of appropriate relationships, the principal component method and the systemic and structural method are proposed for creating a multivariate analytical model.

A conclusion has been made about the structural inconsistency of the obtained results of the empirical study and the presented interpretation model. Attention is drawn to the need to adjust approaches within the research space of the Great Acceleration concept in relation to countries that were not members of the Organisation for Economic Cooperation and Development OECD in the given economic and historical period. Divergence was revealed in the representation of the hyper-acceleration period in comparison with the existing chronological reference to the s.

It is proposed to use the systemic and structural method and factor analysis in order to create a grounded and internally consistent interpretive model for the results of scientific research. Our planet is abundant with raw data and to monitor the available data properly, processing of the enormous raw data is very vital.

One of the key things in development of mankind and the nature is to acquire as much data as possible and One of the key things in development of mankind and the nature is to acquire as much data as possible and to react appropriately in accordance with the studied data. It's nothing but diagnosis of the physical world by studying the data acquired from them in order to take proper measures that can help in treating them better. Large volume of data incurs high energy consumption for its transmission and thus results in decrease of overall network lifetime.

Wireless Sensor Network WSN is a collection of multiple sensor nodes that all together forms a network for transmitting data acquired by each sensor node to sink known as Base Station BS. In hierarchical routing acquired data are sent via relay agents like Cluster Heads CH. The Cluster Heads must be customised with computations and formulations, which will help in aggregating the gathered data, in order to reduce energy consumption while transmitting the data further in the network while maintaining the data integrity to withhold the significance of every single value in a data set.

Related Topics. Mixed Effects Models. Follow Following.

Although traditional clustering methods e.

Cluster analysis research paper Fuzzy clustering provides one such technique as it provides more professional paper proofreading sites ca in the modeling and interpretation of cluster solutions. Fuzzy clustering enabled us and other studies i. Nonuse and dropout attrition for a web-based mental health intervention delivered in a post-disaster context. The membership exponent chosen by the researcher will depend on how much cluster overlap the researcher expects in their data. On data sets with, for example, overlapping Gaussian distributions — a common use case in artificial data — the cluster borders produced by these algorithms will often look arbitrary, because the cluster density decreases conjugaison essayer au present. These findings align with a previous investigation conducted by Matthews et al [ 15 ].
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Cluster analysis research paper Price, R. In the second analysis, the super users reported the lowest PHQ-9 and GAD-7 scores at sign-up, contrasting with the symptom pattern observed in the first analysis. This will essentially create a different, yet meaningful alternative solution to that produced by K-means. Based upon these studies, it appears that fuzzy clustering can be a useful clustering method due to its ability to produce both hard and soft clusters, show the relationship of cluster analysis research paper to one another, and deal effectively with outliers Goktepe et al. The novelty of this approach was our attempt to identify actual user engagement behaviors, as opposed to employing engagement benchmarks derived from a trial protocol.
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Cluster analysis research paper The following overview will only list the most prominent examples of clustering algorithms, as there are possibly over published clustering algorithms. Use of this web site signifies your agreement to the terms and conditions. As can be seen in Table 2the cluster means for the 4-cluster K-means solution and the 4 cluster fuzzy clustering solution show similar patterns indicating similar cluster interpretation. The purpose of this paper is to provide an illustration of the utility of fuzzy clustering to a research question from the social sciences. The current salt iodization strategy in Kyrgyzstan ensures sufficient iodine nutrition among school-age children but not pregnant women.

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While the items and eventual factor structure for each scale differ, the underlying conclusions of the research in the field confirms essentially similar patterns of responses, with both positive e. The FMPS has been perhaps the most commonly studied set of perfectionism items and originally identified a six-factor solution to the item scale.

While several studies have used the FMPS and provided strong validation for the scale and a multidimensional nature for perfectionism, there have been multiple alternative representations for the construct Stoeber, ; Purdon et al. The various factor solutions for the FMPS provide ample opportunity to analyze a pattern of performances in the normal population.

Their reconceptualization of the item scale produced the following four factors a Negative Projections—items addressing the tendency to make social comparisons and hold self-doubt over competence; b Achievement Expectations—items addressing holding high personal standards and ego involvement goal orientation; c Parental Influences—items addressing parental influences and reactions to performance; and d Organization—consistently identified in other factor solutions for the FMPS that identify tendencies toward organization and neatness.

Their analysis for this new factor structure showed theoretical similarity to Stoeber's four-factor structure, but demonstrated a better fit to the data and strong construct validity with the original six-factor solution Frost et al. An alternative approach to examining perfectionism in learners has been to adopt a group-based or individualistic orientation, where the focus is on constructing perfectionism profiles based on responses to one of the primary assessment tools Stoeber and Otto, The predominant approach to reviewing perfectionism through a group-based orientation has been to use cluster analysis to generate the profiles of perfectionism identified in the response data e.

Stoeber and Otto's review of the extant research revealed the bulk of group-based perfectionism research can be summarized rather effectively by reviewing the presence of two dimensions of perfectionism: evaluative concerns and personal standards. In their proposed tripartite framework to explain the various research, non-perfectionists were identified as those with low levels of personal standards perfectionism regardless of evaluative concerns.

Two key questions arise when reviewing the debate regarding the Gaudreau and Thompson and Stoeber and Otto representations for dispositional perfectionism. The first is whether the individuals with characteristically low levels of personal standards perfectionism can be split into two groups Gaudreau, The second is a fundamental issue of whether each cluster is a distinct group with clear differentiation. As demonstrated above, research into group-based orientation is commonly assessed using K-means clustering.

While this clustering method has been shown to be useful and effective it does not allow researchers to account for overlap among the clusters. In order to address the issue of overlap, we propose the use of fuzzy clustering. The following section provides descriptions of both the K-means and fuzzy clustering algorithms, highlighting their similarities and differences.

K-means clustering is a common centroid based clustering method that identifies a specified number of non-overlapping clusters within data Gan et al. It requires the researcher to pre-specify the number of clusters and then places each individual into one of them.

It should be noted that the actual profile i. The K-means clustering algorithm is based on the following steps. The ESS is calculated for each iteration of the process described above, until all reassignments are completed, and ESS itself is minimized. When such convergence is reached, the researcher then examines the resultant clusters in order to determine whether they are substantively meaningful and clearly distinct based upon the pattern of means on the variables used to cluster, as well as other variables that are hypothesized to differ among the clusters.

By definition this latter step in the clustering process involves subjective judgment on the part of the researcher. Fuzzy clustering is an extension of the traditional K-means algorithm. However, unlike K-means clustering, fuzzy clustering focuses on cluster membership based on fuzzy set theory Everitt et al.

Given this paradigm, fuzzy clustering allows individuals to have multiple cluster memberships, thereby providing useful information about the degree of cluster overlap in the population, as well as information about the relative membership of each individual within each cluster. Thus, in fuzzy clustering each case is allowed but not required to have partial membership in multiple clusters.

As implied in this example, the degree to which a case belongs to a certain cluster is indicated by its membership share, which ranges from 0 to 1 i. The algorithm for fuzzy clustering is based on minimizing the following objective function, as described by Kaufman and Rousseeuw :.

Here, k is as defined above. In addition, u ik is a membership coefficient reflecting the membership share for observation i in cluster k. The value d ij is a measure of dissimilarity for observations i and j , across the variables used in the clustering. For continuous data, the Euclidean distance measure d ij is expressed as:. Thus, fuzzy clustering makes use of an iterative algorithm in which the function in 2 is minimized through altering the values of u ik.

The membership coefficients are in turn calculated as Kaufman and Rousseeuw, :. In the context of fuzzy clustering, the amount of overlap among clusters across the sample is referred to as the degree of fuzziness. The degree of fuzziness allowed in a particular analysis can be controlled by the researcher through manipulation of a quantity known as the membership exponent ME. This value ranges from 1 minimal fuzziness and equal to K-means to infinity, where larger values are associated with a greater degree of fuzziness Gan et al.

Previous studies have recommended setting the membership exponent to 2 in many applications in practice Lekova, ; Maharaj and D'Urso, The membership exponent chosen by the researcher will depend on how much cluster overlap the researcher expects in their data.

Researchers in fields such as medicine, technology e. Specifically, fuzzy clustering has been used in gene research for cancer prediction Alshalalfah and Alhajj, , tumor classification Wang et al. Several studies using existing and simulated data have been conducted to compare the performance of traditional hard clustering methods to fuzzy clustering.

Based upon these studies, it appears that fuzzy clustering can be a useful clustering method due to its ability to produce both hard and soft clusters, show the relationship of clusters to one another, and deal effectively with outliers Goktepe et al. The ability to handle outliers is an especially important feature of fuzzy clustering given that outliers can be a serious problem for other clustering algorithms such as K-means Grubesic, In the context of fuzzy clustering, the outlier's membership is distributed throughout the clusters, instead of the outlier being placed into one cluster.

Unlike fuzzy clustering, K-means clustering would have the outlier belong to one cluster, which can skew the structure of the clusters Grubesic, Additionally, fuzzy clustering has been shown to accurately group cases into clusters with real and simulated data Schreer et al. Schreer et al.

While fuzzy clustering has been shown to produce similar clusters to K-means on simulated data, fuzzy clustering was able to show the strength of membership for each cluster as well Schreer et al. Despite the demonstrated benefits, fuzzy clustering has yet to be fully utilized throughout the social and behavioral sciences. It does appear, however, that researchers in the social and behavioral sciences are aware that not all clusters are discrete.

Although graphical representations can be quite informative, it is also important to be able to quantify the degree of such overlap. The utilization of fuzzy clustering could be considered a more natural approach in many applications, because behavioral clusters are not always distinct, and there will be some overlap due to the abstract nature of human behavior. In order to demonstrate the utility of fuzzy clustering, a comparison of traditional K-means clustering and fuzzy clustering was made using a previously analyzed data set from a study on perfectionism.

Data were collected over the course of three academic years, where participation in data collection satisfied a course requirement. Collectively, students females, males participated in the study. A total of 30 cases had to be deleted due to missing data bringing the final sample size to As only a small number of cases had missing information, simple listwise deletion was used. The average age of the participant was As mentioned earlier, in a systematic comparison of the factor representations of the FMPS, Harvey et al.

In order to compare and demonstrate the performance of hard and fuzzy clustering methods, a cluster solution generated by K-means, and a cluster fuzzy clustering of the four FMPS Harvey factors were run using R statistical software, version 2.

For both the fuzzy clustering and K-means solutions, the default R settings were used. By default, the K-means clustering algorithm in R uses the Hartigan-Wong algorithm Hartigan and Wong, , and for fuzzy clustering R uses a Euclidian dissimilarity measure with a measurement exponent of 2.

First, the default fuzzy clustering solution was compared to the K-means clustering solution in terms of similarity of cluster structure, cluster solution fit, and cluster interpretation. Following this comparison, the membership exponent for fuzzy clustering was manipulated to demonstrate differences in cluster interpretation between fuzzier and crisper cluster solutions for the same data.

To accomplish this comparison, the membership exponent was changed to 1. The purpose of changing the membership exponents is to show how manipulating the degree of fuzziness can provide different but meaningful cluster solutions. Prior to clustering, multicollinearity was assessed through use of zero order correlations and VIF statistics. Together, these results indicate that multicollinearity was not a concern, and the clustering proceeded as planned.

Originally, two different K-means cluster solutions were created: one solution based on the raw subscales and one solution using standardized subscales. Because the FMPS Harvey subscales have differing numbers of items, it was important to ensure that the differential weighting of the variables did not impact the interpretation of the cluster solution. After comparing the standardized and unstandardized solutions, it was determined that both solutions supported the same conceptual profiles, thus the cluster solution based on the unstandardized variables was chosen for ease of interpretation.

As K-means clustering is the standard approach, it was performed first. Initially, however, a hierarchical cluster analysis was performed in order to determine the number of clusters for the K-means approach. Based on the visual information from the dendrogram, three and four cluster solutions were created using K-means cluster analysis.

Comparison of the two different K-means solutions revealed that the four-cluster solution was more consistent with the current theoretical models of perfectionism. Cluster means for the four-cluster solution appear in Table 2. Within-cluster R 2 was calculated for each cluster as a measure of cluster similarity, ranging from 0. The clusters listed in Table 2 were tentatively named based on the relationships observed among the four Harvey factors and are described briefly.

First, Externalized Perfectionists K-means cluster 1 were characterized primarily by having low organization and achievement expectations with moderate levels of parental influence and negative projections. The term Externalized Perfectionism was selected as it depicts the profile of an individual with moderately elevated perfectionism, driven primarily by external influences similar to notions of socially prescribed perfectionism. Second, the Mixed Perfectionists K-means cluster 2 reported high overall levels of perfectionism, with heightened negative projections, achievement expectations and parental influence, but reported moderate levels of organization.

Internalized Perfectionism K-means cluster 3 included individuals with moderate overall perfectionist tendencies who demonstrated heightened levels of organization and personally-prescribed achievement expectations. Finally, Non-Perfectionists K-means cluster 4 were those individuals in the sample who did not demonstrate an elevated degree of any of the Harvey perfectionism factors — as such those in the sample with no clear perfectionist tendencies.

Tables 2 , 3 provide information regarding the similarity of the K-means and fuzzy clustering solutions. As already discussed above, Table 2 presents the cluster means for the original 4 cluster K-means solution and the default 4 cluster fuzzy clustering solution.

Also presented are a 3 cluster fuzzy clustering solution and the 4 cluster fuzzy clustering solution using a membership exponent of 1. Table 3. Percentage of fuzzy cluster solutions that belong to corresponding k-means clustering solutions with a membership exponent of 2. As can be seen in Table 2 , the cluster means for the 4-cluster K-means solution and the 4 cluster fuzzy clustering solution show similar patterns indicating similar cluster interpretation.

K-means cluster 1 externalized perfectionists and K-means cluster 3 internalized perfectionists are related closest to cluster 1 of the 4-cluster fuzzy cluster solution. According to Table 3 , fuzzy cluster 1 has the highest percent of participants belonging to the externalized perfectionists as defined by K-means The second K-means cluster mixed-perfectionists was most closely associated with fuzzy cluster 2.

Fuzzy cluster 2 had the highest percent of participants classified by K-means as mixed perfectionists K-means cluster 4 non-perfectionists relates most strongly to fuzzy cluster 4, with Thinking about the big picture provided by the 4 cluster fuzzy solution, although the clusters roughly follow the same pattern of means as the K-means solution, it is evident that fuzzy clusters 3 and 4 are very similar indicating that possibly one of the clusters is redundant. This prompted investigation into a 3 cluster fuzzy clustering solution shown in Table 2 and depicted in Figure 1.

Looking at the 3 cluster fuzzy clustering solution it seems that fuzzy cluster 3 is very similar in interpretation to clusters 3 and 4 of the 4 cluster fuzzy clustering solution. The remaining two clusters of the 3 cluster fuzzy solution appear to map onto the K-means clusters 1 and 2.

Figure 1. Visual representation of the 3 cluster fuzzy clustering solution. Axes are standardized representations of the principal components of the cluster solution. Although Table 2 indicates a similar interpretation for the K-means and fuzzy clustering solutions, the cluster similarity is not absolute. Table 3 presents the percentage of overlap between the four K-means clusters and their corresponding fuzzy clusters. As can be seen, in general each K-means cluster has a clear match to a fuzzy cluster with which it shares a majority of cases.

However, clusters 1 and 3 do not map onto the K-means clusters as cleanly. Regarding K-means cluster 1, the highest correspondence can be seen with fuzzy cluster 1, however, they only share K-means cluster 1 also shares K-means Cluster 3 shows even less consistency with An additional In summary, the 4 cluster solutions obtained from the K-means and the fuzzy clustering methods were similar in interpretation. However, when a moderate degree of cluster overlap was modeled into the clusters as is the default in fuzzy clustering two of the clusters appeared nearly indistinguishable to the point that a 3-cluster solution gave nearly the same information.

This finding is emphasized in Table 3 with the considerable overlap of fuzzy cluster 3 with multiple K-means clusters. Conceptually speaking, this speaks to potential group similarity of the individuals in these clusters. Focusing more fully on the fuzzy clustering solution, relationships between the fuzzy clusters can be investigated by looking at the cluster membership.

In fuzzy clustering, cluster membership refers to the degree to which a fuzzy cluster overlaps with another fuzzy cluster. The cluster membership of the 4 cluster fuzzy solution appears in Table 4. According to Table 4 , as would be expected, the individuals in each fuzzy cluster belong most strongly to their own cluster than to any other cluster. Consistent with the findings from above, fuzzy clusters 2 and 4 appear to be more distinct than clusters 1 and 3 belonging to their own clusters more strongly Further information can be gained by examining which clusters overlap.

Thinking theoretically about these results, conceptual similarities can be seen between clusters 3 most closely mapping to Internalized Perfectionists and 4 most closely mapping to Non-Perfectionists. Thus, the conceptual relationship between fuzzy clusters 3 and 4, can be seen through both the cluster membership and the cluster means. Along the same lines, fuzzy cluster 4, shows no practical similarities with fuzzy clusters 1 most closely mapping to externalized perfectionists and 2 most closely mapping to mixed perfectionists as evidenced by both the small percentages of overlap in the cluster membership 4.

As previously mentioned, the membership exponent used in fuzzy clustering can be changed to increase or decrease the preferred amount of cluster overlap in order to model the hypothesized amount of cluster overlap. In order to investigate the impact of the membership exponent on fuzzy clustering solution, a comparison of the K-means cluster and fuzzy cluster solutions with a membership exponent of 1. The purpose of using a membership exponent of 1. Results of this comparison appear in Tables 2 , 5.

Whereas previously, there were differences between the K-means and fuzzy clusters, when the membership exponent was decreased it created crisper clusters with nearly identical results to the K-means solution. Fuzzy clusters 2 and 4, which were already identified as corresponding reasonably well with the K-means solution when the membership exponent was 2. Fuzzy clusters 1 and 3 which exhibited a large degree of overlap with the other clusters in the ME 2.

Thus, the manipulation of the membership exponent to model more distinct clusters with little cluster overlap resulted in a solution nearly identical to the original K-means solution. Table 5. Percentage of fuzzy cluster solutions that belong to corresponding k-means clustering solutions with a membership exponent of 1. While hard clustering methods are dominant in the behavioral sciences, there is also great worth in investigating the utility of more flexible clustering algorithms.

Fuzzy clustering provides one such technique as it provides more flexibility in the modeling and interpretation of cluster solutions. This study demonstrated that fuzzy clustering is also able to show a different perspective to the cluster solutions, perhaps, better illuminating the nature of relationships between clusters. Through the first comparison of the four-cluster K-means and fuzzy solutions, we found two unique yet similar cluster solutions.

The K-means cluster solution created four distinct, non-overlapping clusters, whereas, fuzzy clustering created two clearly distinct clusters and two clearly overlapping clusters. One potential reason for the difference in cluster solutions between the two methods is due to the way fuzzy clustering handles ambiguity in clusters.

Unlike K-means clustering, fuzzy clustering allows observations to belong to multiple clusters, with the primary cluster being the one for which the individual has the largest membership coefficient. In this study, the fuzzy clustering solution included one cluster with moderate means on all factors, one cluster with higher means on all factor, especially negative projections, and two clusters with low means on all factors.

This will essentially create a different, yet meaningful alternative solution to that produced by K-means. The allowance for overlap among the clusters increases the potential utility of fuzzy clustering for gaining insights into the nature of the subgroups present in the population, by demonstrating more clearly than do K-means solutions the proximity and interrelatedness of these groups. From the overlapping clusters in not only the current study, but in other studies as well e.

Like most areas in psychology, perfectionism profiles can be seen as abstract since the profiles will naturally have similar attributes in certain areas. Without the use of fuzzy clustering we could only speculate how the means impact the relationship between the clusters.

Fuzzy clustering enabled us and other studies i. In addition to demonstrating the potential for finding different clustering solutions using the K-means and fuzzy approaches, this study also showed how similar results can also be identified by the two clustering methods through manipulation of the membership exponent in the fuzzy clustering algorithm. When using a very low membership exponent 1. Since the 's, there has been universal agreement that perfectionism is a multidimensional construct, with multiple measures constructed to assess these factors, including the Multidimensional Perfectionism Scale Hewitt and Flett, , Almost Perfect Scale Slaney et al.

While the items and eventual factor structure for each scale differ, the underlying conclusions of the research in the field confirms essentially similar patterns of responses, with both positive e. The FMPS has been perhaps the most commonly studied set of perfectionism items and originally identified a six-factor solution to the item scale.

While several studies have used the FMPS and provided strong validation for the scale and a multidimensional nature for perfectionism, there have been multiple alternative representations for the construct Stoeber, ; Purdon et al. The various factor solutions for the FMPS provide ample opportunity to analyze a pattern of performances in the normal population.

Their reconceptualization of the item scale produced the following four factors a Negative Projections—items addressing the tendency to make social comparisons and hold self-doubt over competence; b Achievement Expectations—items addressing holding high personal standards and ego involvement goal orientation; c Parental Influences—items addressing parental influences and reactions to performance; and d Organization—consistently identified in other factor solutions for the FMPS that identify tendencies toward organization and neatness.

Their analysis for this new factor structure showed theoretical similarity to Stoeber's four-factor structure, but demonstrated a better fit to the data and strong construct validity with the original six-factor solution Frost et al.

An alternative approach to examining perfectionism in learners has been to adopt a group-based or individualistic orientation, where the focus is on constructing perfectionism profiles based on responses to one of the primary assessment tools Stoeber and Otto, The predominant approach to reviewing perfectionism through a group-based orientation has been to use cluster analysis to generate the profiles of perfectionism identified in the response data e.

Stoeber and Otto's review of the extant research revealed the bulk of group-based perfectionism research can be summarized rather effectively by reviewing the presence of two dimensions of perfectionism: evaluative concerns and personal standards. In their proposed tripartite framework to explain the various research, non-perfectionists were identified as those with low levels of personal standards perfectionism regardless of evaluative concerns.

Two key questions arise when reviewing the debate regarding the Gaudreau and Thompson and Stoeber and Otto representations for dispositional perfectionism. The first is whether the individuals with characteristically low levels of personal standards perfectionism can be split into two groups Gaudreau, The second is a fundamental issue of whether each cluster is a distinct group with clear differentiation.

As demonstrated above, research into group-based orientation is commonly assessed using K-means clustering. While this clustering method has been shown to be useful and effective it does not allow researchers to account for overlap among the clusters. In order to address the issue of overlap, we propose the use of fuzzy clustering. The following section provides descriptions of both the K-means and fuzzy clustering algorithms, highlighting their similarities and differences. K-means clustering is a common centroid based clustering method that identifies a specified number of non-overlapping clusters within data Gan et al.

It requires the researcher to pre-specify the number of clusters and then places each individual into one of them. It should be noted that the actual profile i. The K-means clustering algorithm is based on the following steps.

The ESS is calculated for each iteration of the process described above, until all reassignments are completed, and ESS itself is minimized. When such convergence is reached, the researcher then examines the resultant clusters in order to determine whether they are substantively meaningful and clearly distinct based upon the pattern of means on the variables used to cluster, as well as other variables that are hypothesized to differ among the clusters.

By definition this latter step in the clustering process involves subjective judgment on the part of the researcher. Fuzzy clustering is an extension of the traditional K-means algorithm. However, unlike K-means clustering, fuzzy clustering focuses on cluster membership based on fuzzy set theory Everitt et al.

Given this paradigm, fuzzy clustering allows individuals to have multiple cluster memberships, thereby providing useful information about the degree of cluster overlap in the population, as well as information about the relative membership of each individual within each cluster. Thus, in fuzzy clustering each case is allowed but not required to have partial membership in multiple clusters. As implied in this example, the degree to which a case belongs to a certain cluster is indicated by its membership share, which ranges from 0 to 1 i.

The algorithm for fuzzy clustering is based on minimizing the following objective function, as described by Kaufman and Rousseeuw :. Here, k is as defined above. In addition, u ik is a membership coefficient reflecting the membership share for observation i in cluster k. The value d ij is a measure of dissimilarity for observations i and j , across the variables used in the clustering.

For continuous data, the Euclidean distance measure d ij is expressed as:. Thus, fuzzy clustering makes use of an iterative algorithm in which the function in 2 is minimized through altering the values of u ik. The membership coefficients are in turn calculated as Kaufman and Rousseeuw, :. In the context of fuzzy clustering, the amount of overlap among clusters across the sample is referred to as the degree of fuzziness.

The degree of fuzziness allowed in a particular analysis can be controlled by the researcher through manipulation of a quantity known as the membership exponent ME. This value ranges from 1 minimal fuzziness and equal to K-means to infinity, where larger values are associated with a greater degree of fuzziness Gan et al. Previous studies have recommended setting the membership exponent to 2 in many applications in practice Lekova, ; Maharaj and D'Urso, The membership exponent chosen by the researcher will depend on how much cluster overlap the researcher expects in their data.

Researchers in fields such as medicine, technology e. Specifically, fuzzy clustering has been used in gene research for cancer prediction Alshalalfah and Alhajj, , tumor classification Wang et al. Several studies using existing and simulated data have been conducted to compare the performance of traditional hard clustering methods to fuzzy clustering.

Based upon these studies, it appears that fuzzy clustering can be a useful clustering method due to its ability to produce both hard and soft clusters, show the relationship of clusters to one another, and deal effectively with outliers Goktepe et al.

The ability to handle outliers is an especially important feature of fuzzy clustering given that outliers can be a serious problem for other clustering algorithms such as K-means Grubesic, In the context of fuzzy clustering, the outlier's membership is distributed throughout the clusters, instead of the outlier being placed into one cluster. Unlike fuzzy clustering, K-means clustering would have the outlier belong to one cluster, which can skew the structure of the clusters Grubesic, Additionally, fuzzy clustering has been shown to accurately group cases into clusters with real and simulated data Schreer et al.

Schreer et al. While fuzzy clustering has been shown to produce similar clusters to K-means on simulated data, fuzzy clustering was able to show the strength of membership for each cluster as well Schreer et al. Despite the demonstrated benefits, fuzzy clustering has yet to be fully utilized throughout the social and behavioral sciences. It does appear, however, that researchers in the social and behavioral sciences are aware that not all clusters are discrete.

Although graphical representations can be quite informative, it is also important to be able to quantify the degree of such overlap. The utilization of fuzzy clustering could be considered a more natural approach in many applications, because behavioral clusters are not always distinct, and there will be some overlap due to the abstract nature of human behavior.

In order to demonstrate the utility of fuzzy clustering, a comparison of traditional K-means clustering and fuzzy clustering was made using a previously analyzed data set from a study on perfectionism. Data were collected over the course of three academic years, where participation in data collection satisfied a course requirement.

Collectively, students females, males participated in the study. A total of 30 cases had to be deleted due to missing data bringing the final sample size to As only a small number of cases had missing information, simple listwise deletion was used. The average age of the participant was As mentioned earlier, in a systematic comparison of the factor representations of the FMPS, Harvey et al.

In order to compare and demonstrate the performance of hard and fuzzy clustering methods, a cluster solution generated by K-means, and a cluster fuzzy clustering of the four FMPS Harvey factors were run using R statistical software, version 2. For both the fuzzy clustering and K-means solutions, the default R settings were used.

By default, the K-means clustering algorithm in R uses the Hartigan-Wong algorithm Hartigan and Wong, , and for fuzzy clustering R uses a Euclidian dissimilarity measure with a measurement exponent of 2. First, the default fuzzy clustering solution was compared to the K-means clustering solution in terms of similarity of cluster structure, cluster solution fit, and cluster interpretation.

Following this comparison, the membership exponent for fuzzy clustering was manipulated to demonstrate differences in cluster interpretation between fuzzier and crisper cluster solutions for the same data. To accomplish this comparison, the membership exponent was changed to 1.

The purpose of changing the membership exponents is to show how manipulating the degree of fuzziness can provide different but meaningful cluster solutions. Prior to clustering, multicollinearity was assessed through use of zero order correlations and VIF statistics. Together, these results indicate that multicollinearity was not a concern, and the clustering proceeded as planned. Originally, two different K-means cluster solutions were created: one solution based on the raw subscales and one solution using standardized subscales.

Because the FMPS Harvey subscales have differing numbers of items, it was important to ensure that the differential weighting of the variables did not impact the interpretation of the cluster solution. After comparing the standardized and unstandardized solutions, it was determined that both solutions supported the same conceptual profiles, thus the cluster solution based on the unstandardized variables was chosen for ease of interpretation.

As K-means clustering is the standard approach, it was performed first. Initially, however, a hierarchical cluster analysis was performed in order to determine the number of clusters for the K-means approach. Based on the visual information from the dendrogram, three and four cluster solutions were created using K-means cluster analysis.

Comparison of the two different K-means solutions revealed that the four-cluster solution was more consistent with the current theoretical models of perfectionism. Cluster means for the four-cluster solution appear in Table 2. Within-cluster R 2 was calculated for each cluster as a measure of cluster similarity, ranging from 0. The clusters listed in Table 2 were tentatively named based on the relationships observed among the four Harvey factors and are described briefly.

First, Externalized Perfectionists K-means cluster 1 were characterized primarily by having low organization and achievement expectations with moderate levels of parental influence and negative projections. The term Externalized Perfectionism was selected as it depicts the profile of an individual with moderately elevated perfectionism, driven primarily by external influences similar to notions of socially prescribed perfectionism.

Second, the Mixed Perfectionists K-means cluster 2 reported high overall levels of perfectionism, with heightened negative projections, achievement expectations and parental influence, but reported moderate levels of organization. Internalized Perfectionism K-means cluster 3 included individuals with moderate overall perfectionist tendencies who demonstrated heightened levels of organization and personally-prescribed achievement expectations. Finally, Non-Perfectionists K-means cluster 4 were those individuals in the sample who did not demonstrate an elevated degree of any of the Harvey perfectionism factors — as such those in the sample with no clear perfectionist tendencies.

Tables 2 , 3 provide information regarding the similarity of the K-means and fuzzy clustering solutions. As already discussed above, Table 2 presents the cluster means for the original 4 cluster K-means solution and the default 4 cluster fuzzy clustering solution.

Also presented are a 3 cluster fuzzy clustering solution and the 4 cluster fuzzy clustering solution using a membership exponent of 1. Table 3. Percentage of fuzzy cluster solutions that belong to corresponding k-means clustering solutions with a membership exponent of 2. As can be seen in Table 2 , the cluster means for the 4-cluster K-means solution and the 4 cluster fuzzy clustering solution show similar patterns indicating similar cluster interpretation. K-means cluster 1 externalized perfectionists and K-means cluster 3 internalized perfectionists are related closest to cluster 1 of the 4-cluster fuzzy cluster solution.

According to Table 3 , fuzzy cluster 1 has the highest percent of participants belonging to the externalized perfectionists as defined by K-means The second K-means cluster mixed-perfectionists was most closely associated with fuzzy cluster 2.

Fuzzy cluster 2 had the highest percent of participants classified by K-means as mixed perfectionists K-means cluster 4 non-perfectionists relates most strongly to fuzzy cluster 4, with Thinking about the big picture provided by the 4 cluster fuzzy solution, although the clusters roughly follow the same pattern of means as the K-means solution, it is evident that fuzzy clusters 3 and 4 are very similar indicating that possibly one of the clusters is redundant.

This prompted investigation into a 3 cluster fuzzy clustering solution shown in Table 2 and depicted in Figure 1. Looking at the 3 cluster fuzzy clustering solution it seems that fuzzy cluster 3 is very similar in interpretation to clusters 3 and 4 of the 4 cluster fuzzy clustering solution. The remaining two clusters of the 3 cluster fuzzy solution appear to map onto the K-means clusters 1 and 2. Figure 1. Visual representation of the 3 cluster fuzzy clustering solution.

Axes are standardized representations of the principal components of the cluster solution. Although Table 2 indicates a similar interpretation for the K-means and fuzzy clustering solutions, the cluster similarity is not absolute. Table 3 presents the percentage of overlap between the four K-means clusters and their corresponding fuzzy clusters.

As can be seen, in general each K-means cluster has a clear match to a fuzzy cluster with which it shares a majority of cases. However, clusters 1 and 3 do not map onto the K-means clusters as cleanly. Regarding K-means cluster 1, the highest correspondence can be seen with fuzzy cluster 1, however, they only share K-means cluster 1 also shares K-means Cluster 3 shows even less consistency with An additional In summary, the 4 cluster solutions obtained from the K-means and the fuzzy clustering methods were similar in interpretation.

However, when a moderate degree of cluster overlap was modeled into the clusters as is the default in fuzzy clustering two of the clusters appeared nearly indistinguishable to the point that a 3-cluster solution gave nearly the same information. This finding is emphasized in Table 3 with the considerable overlap of fuzzy cluster 3 with multiple K-means clusters. Conceptually speaking, this speaks to potential group similarity of the individuals in these clusters.

Focusing more fully on the fuzzy clustering solution, relationships between the fuzzy clusters can be investigated by looking at the cluster membership. In fuzzy clustering, cluster membership refers to the degree to which a fuzzy cluster overlaps with another fuzzy cluster. The cluster membership of the 4 cluster fuzzy solution appears in Table 4.

According to Table 4 , as would be expected, the individuals in each fuzzy cluster belong most strongly to their own cluster than to any other cluster. Consistent with the findings from above, fuzzy clusters 2 and 4 appear to be more distinct than clusters 1 and 3 belonging to their own clusters more strongly Further information can be gained by examining which clusters overlap. Thinking theoretically about these results, conceptual similarities can be seen between clusters 3 most closely mapping to Internalized Perfectionists and 4 most closely mapping to Non-Perfectionists.

Thus, the conceptual relationship between fuzzy clusters 3 and 4, can be seen through both the cluster membership and the cluster means. Along the same lines, fuzzy cluster 4, shows no practical similarities with fuzzy clusters 1 most closely mapping to externalized perfectionists and 2 most closely mapping to mixed perfectionists as evidenced by both the small percentages of overlap in the cluster membership 4. As previously mentioned, the membership exponent used in fuzzy clustering can be changed to increase or decrease the preferred amount of cluster overlap in order to model the hypothesized amount of cluster overlap.

In order to investigate the impact of the membership exponent on fuzzy clustering solution, a comparison of the K-means cluster and fuzzy cluster solutions with a membership exponent of 1. The purpose of using a membership exponent of 1. Results of this comparison appear in Tables 2 , 5. Whereas previously, there were differences between the K-means and fuzzy clusters, when the membership exponent was decreased it created crisper clusters with nearly identical results to the K-means solution.

Fuzzy clusters 2 and 4, which were already identified as corresponding reasonably well with the K-means solution when the membership exponent was 2. Fuzzy clusters 1 and 3 which exhibited a large degree of overlap with the other clusters in the ME 2.

Thus, the manipulation of the membership exponent to model more distinct clusters with little cluster overlap resulted in a solution nearly identical to the original K-means solution. Table 5. Percentage of fuzzy cluster solutions that belong to corresponding k-means clustering solutions with a membership exponent of 1. While hard clustering methods are dominant in the behavioral sciences, there is also great worth in investigating the utility of more flexible clustering algorithms.

Fuzzy clustering provides one such technique as it provides more flexibility in the modeling and interpretation of cluster solutions. This study demonstrated that fuzzy clustering is also able to show a different perspective to the cluster solutions, perhaps, better illuminating the nature of relationships between clusters. Through the first comparison of the four-cluster K-means and fuzzy solutions, we found two unique yet similar cluster solutions.

The K-means cluster solution created four distinct, non-overlapping clusters, whereas, fuzzy clustering created two clearly distinct clusters and two clearly overlapping clusters. One potential reason for the difference in cluster solutions between the two methods is due to the way fuzzy clustering handles ambiguity in clusters.

Unlike K-means clustering, fuzzy clustering allows observations to belong to multiple clusters, with the primary cluster being the one for which the individual has the largest membership coefficient. In this study, the fuzzy clustering solution included one cluster with moderate means on all factors, one cluster with higher means on all factor, especially negative projections, and two clusters with low means on all factors.

This will essentially create a different, yet meaningful alternative solution to that produced by K-means. The allowance for overlap among the clusters increases the potential utility of fuzzy clustering for gaining insights into the nature of the subgroups present in the population, by demonstrating more clearly than do K-means solutions the proximity and interrelatedness of these groups.

From the overlapping clusters in not only the current study, but in other studies as well e. Like most areas in psychology, perfectionism profiles can be seen as abstract since the profiles will naturally have similar attributes in certain areas. Without the use of fuzzy clustering we could only speculate how the means impact the relationship between the clusters.

Fuzzy clustering enabled us and other studies i. In addition to demonstrating the potential for finding different clustering solutions using the K-means and fuzzy approaches, this study also showed how similar results can also be identified by the two clustering methods through manipulation of the membership exponent in the fuzzy clustering algorithm.

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