Fuzzy Clustering Algorithms

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Presentation transcript:

Fuzzy Clustering Algorithms

What is Clustering?

Crisp & Fuzzy Clustering Each point belongs to exactly one cluster. C-Means Clustering FUZZY Cluster membership is a matter of degree. Fuzzy C-Means Clustering (FCM)

C-Means Clustering Fixed number of clusters. One centroid per cluster. Each data point belongs to the cluster corresponding to the closest centroid.

distance between data point and cluster center C-Means Clustering distance between data point and cluster center # of clusters cost function cost of the ith cluster data points belonging to the ith group

C-Means Clustering pick c centroids at random assign each data point to the cluster corresponding to the nearest centroid. move each centroid to the mean value of its cluster’s data points.

Fuzzy C-Means Clustering Fuzzy C-Means Clustering (FCM) Fuzzy C-Means Clustering Fixed number of clusters. One centroid per cluster. Clusters are fuzzy sets. Membership degree of a point can be any number between 0 and 1. Sum of all degrees for a point must add up to 1.

Fuzzy C-Means Clustering Fuzzy C-Means Clustering (FCM) C-Means Fuzzy (FCM) summing over all data points fuzziness exponent membership degree

Fuzzy C-Means Clustering pick c centroids at random assign membership degrees according to: move each centroid to the following position: Note: formulas are result of the method of Lagrange multipliers as applied to aforementioned cost function

Crisp & Fuzzy Clustering Each point belongs to exactly one cluster. C-Means Clustering FUZZY Cluster membership is a matter of degree. Fuzzy C-Means Clustering (FCM)