Fuzzy Clustering.

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Presentation transcript:

Fuzzy Clustering

What is Clustering? Be considered the most important unsupervised learning problem. Finding a structure in a collection of unlabeled data. The process of organizing objects into groups whose members are similar in some way

Goals of Clustering Determine the intrinsic grouping in a set of unlabeled data. What constitutes a good clustering? We could be interested in: finding representatives for homogeneous groups (data reduction). finding “natural clusters” and describe their unknown properties (“natural” data types). finding useful and suitable groupings (“useful” data classes). finding unusual data objects (outlier detection).

Possible Applications Marketing: finding groups of customers with similar behavior given a large database of customer data containing their properties and past buying records; Biology: classification of plants and animals given their features; Libraries: book ordering; Insurance: identifying groups of motor insurance policy holders with a high average claim cost; identifying frauds; City-planning: identifying groups of houses according to their house type, value and geographical location; Earthquake studies: clustering observed earthquake epicenters to identify dangerous zones; WWW: document classification; clustering weblog data to discover groups of similar access patterns.

Classification Exclusive Clustering Overlapping Clustering Hierarchical Clustering Probabilistic Clustering

Distance Measure Minkowski metric

Fuzzy C-Means Clustering Minimization of the following objective function Iterative optimization of the objective function with the update of membership uij and the cluster centers cj by: This iteration will stop

FCM Algorithm