The analysis of these groups can then determine how likely a population cluster is to purchase products or services. If these groups are defined clearly, a marketing team can then target varying cluster with tailored, targeted communication. Marketers commonly use cluster analysis to develop market segments, which allow for better positioning of products and messaging.
Insurance companies often leverage cluster analysis if there are a high number of claims in a given region. This enables them to learn exactly what is driving this increase in claims. For cities on fault lines, geologists use cluster analysis to evaluate seismic risk and the potential weaknesses of earthquake-prone regions. By considering the results of this research, residents can do their best to prepare mitigate potential damage.
Whether we realize it or not, we deal with clustering in practically every aspect of our day-to-day lives. For example, a group of friends sitting at the same table in a restaurant can be considered a cluster. In grocery stores, goods of a similar nature are grouped together in order to make shopping more convenient and efficient.
This list of events during which we use clustering in our everyday lives could go on forever, but perhaps it makes more sense to consider a more classic, archetypal example. In biology, humans belong to the following clusters: primates, mammals, amniotes, vertebrates, and animals.
In this example, note that as we move down the chain of clusters, humans show less and less similarities to the other members of the group.
Humans have more in common with primates than they do with other mammals, and more in common with mammals than they do with all animals in general.
Classification models segment data by assigning it to classes that are previously defined and specified in a goal. Cluster analysis is intended to detect natural object partitioning. In other words, it groups similar observations into homogeneous sub-sets. Such subclasses can reveal patterns associated with the phenomenon being studied. A distance function is used to determine whether there is overlap between artifacts and a wide range of clustering algorithms based on different concepts.
Clustering is useful in data research. Brand Experience. Employee Experience. Product Experience. Design Experience. XM Services. Platform Security. Survey Tool. What is Experience Management Learn More. We're hiring! View careers. Partnerships Become a Partner. What is XM? What is Experience Management? Explore our XM Guides. Back Partnerships Overview Become a Partner.
Back Resources What is XM? Back What is XM? Experience Management. Try Qualtrics for free Free account. What is cluster analysis and when should you use it? Cluster analysis definition Cluster analysis is a statistical method for processing data. How is cluster analysis used? Clustering is measured using intracluster and intercluster distance. Intracluster distance is the distance between the data points inside the cluster.
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.
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