{"id":8079,"date":"2018-10-25T02:07:59","date_gmt":"2018-10-25T00:07:59","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&p=8079"},"modified":"2018-10-25T02:07:59","modified_gmt":"2018-10-25T00:07:59","slug":"fuzzy-clustering-essentials","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/lessons\/fuzzy-clustering-essentials\/","title":{"rendered":"Fuzzy Clustering Essentials"},"content":{"rendered":"
\n

The fuzzy clustering<\/strong> is considered as soft clustering, in which each element has a probability of belonging to each cluster. In other words, each element has a set of membership coefficients corresponding to the degree of being in a given cluster.<\/p>\n

This is different from k-means and k-medoid clustering, where each object is affected exactly to one cluster. K-means and k-medoids clustering are known as hard or non-fuzzy clustering.<\/p>\n

In fuzzy clustering, points close to the center of a cluster, may be in the cluster to a higher degree than points in the edge of a cluster. The degree, to which an element belongs to a given cluster, is a numerical value varying from 0 to 1.<\/p>\n

The fuzzy c-means<\/strong> (FCM) algorithm is one of the most widely used fuzzy clustering algorithms. The centroid of a cluster is calculated as the mean of all points, weighted by their degree of belonging to the cluster:<\/p>\n

\n

\nIn this article, we\u2019ll describe how to compute fuzzy clustering using the R software.\n<\/p>\n<\/div>\n

<\/div>\n
<\/span><\/a><\/div>

Related Book <\/a><\/h4>Practical Guide to Cluster Analysis in R<\/div>\n
<\/div>\n
\n

Required R packages<\/h2>\n

We\u2019ll use the following R packages: 1) cluster<\/em> for computing fuzzy clustering and 2) factoextra<\/em> for visualizing clusters.<\/p>\n<\/div>\n

\n

Computing fuzzy clustering<\/h2>\n

The function fanny<\/em>() [cluster<\/em> R package] can be used to compute fuzzy clustering. FANNY<\/strong> stands for fuzzy analysis clustering<\/strong>. A simplified format is:<\/p>\n

fanny(x, k, metric = "euclidean", stand = FALSE)<\/code><\/pre>\n
\n
    \n
  • \nx<\/strong>: A data matrix or data frame or dissimilarity matrix\n<\/li>\n
  • \nk<\/strong>: The desired number of clusters to be generated\n<\/li>\n
  • \nmetric<\/strong>: Metric for calculating dissimilarities between observations\n<\/li>\n
  • \nstand<\/strong>: If TRUE, variables are standardized before calculating the dissimilarities\n<\/li>\n<\/ul>\n<\/div>\n
    The function fanny<\/em>() returns an object including the following components:<\/p>\n
      \n
    • membership<\/strong>: matrix containing the degree to which each observation belongs to a given cluster. Column names are the clusters and rows are observations<\/li>\n
    • coeff<\/strong>: Dunn\u2019s partition coefficient F(k) of the clustering, where k is the number of clusters. F(k) is the sum of all squared membership coefficients, divided by the number of observations. Its value is between 1\/k and 1. The normalized form of the coefficient is also given. It is defined as \\((F(k) - 1\/k) \/ (1 - 1\/k)\\)<\/span>, and ranges between 0 and 1. A low value of Dunn\u2019s coefficient indicates a very fuzzy clustering, whereas a value close to 1 indicates a near-crisp clustering.<\/li>\n
    • clustering<\/strong>: the clustering vector containing the nearest crisp grouping of observations<\/li>\n<\/ul>\n
      For example, the R code below applies fuzzy clustering on the USArrests data set:<\/p>\n
      library(cluster)\r\ndf <- scale(USArrests)     # Standardize the data\r\nres.fanny <- fanny(df, 2)  # Compute fuzzy clustering with k = 2<\/code><\/pre>\n
      The different components can be extracted using the code below:<\/p>\n
      head(res.fanny$membership, 3) # Membership coefficients<\/code><\/pre>\n
      ##          [,1]  [,2]\r\n## Alabama 0.664 0.336\r\n## Alaska  0.610 0.390\r\n## Arizona 0.686 0.314<\/code><\/pre>\n
      res.fanny$coeff # Dunn's partition coefficient<\/code><\/pre>\n
      ## dunn_coeff normalized \r\n##      0.555      0.109<\/code><\/pre>\n
      head(res.fanny$clustering) # Observation groups<\/code><\/pre>\n
      ##    Alabama     Alaska    Arizona   Arkansas California   Colorado \r\n##          1          1          1          2          1          1<\/code><\/pre>\n
      To visualize observation groups, use the function fviz_cluster<\/em>() [factoextra<\/em> package]:<\/p>\n
      library(factoextra)\r\nfviz_cluster(res.fanny, ellipse.type = "norm", repel = TRUE,\r\n             palette = "jco", ggtheme = theme_minimal(),\r\n             legend = "right")<\/code><\/pre>\n
      <\/p>\n
      To evaluate the goodnesss of the clustering results, plot the silhouette coefficient as follow:<\/p>\n
      fviz_silhouette(res.fanny, palette = "jco",\r\n                ggtheme = theme_minimal())<\/code><\/pre>\n
      ##   cluster size ave.sil.width\r\n## 1       1   22          0.32\r\n## 2       2   28          0.44<\/code><\/pre>\n
      <\/p>\n<\/div>\n
      \n
      Summary<\/h2>\n
      Fuzzy clustering is an alternative to k-means clustering, where each data point has membership coefficient to each cluster. Here, we demonstrated how to compute and visualize fuzzy clustering using the combination of cluster<\/em> and factoextra<\/em> R packages.<\/p>\n<\/div>\n<\/div>\n
      <\/p>\n","protected":false},"excerpt":{"rendered":"
      Fuzzy clustering is also known as soft method. Standard clustering (K-means, PAM) approaches produce partitions, in which each observation belongs to only one cluster. This is known as hard clustering. In Fuzzy clustering, items can be a member of more than one cluster. Each item has a set of membership coefficients corresponding to the degree of being in a given cluster. In this article, we\u2019ll describe how to compute fuzzy clustering using the R software.<\/p>\n","protected":false},"author":1,"featured_media":7917,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-8079","dt_lessons","type-dt_lessons","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\nFuzzy Clustering Essentials - Datanovia<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.datanovia.com\/en\/lessons\/fuzzy-clustering-essentials\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fuzzy Clustering Essentials - Datanovia\" \/>\n<meta property=\"og:description\" content=\"Fuzzy clustering is also known as soft method. 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