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K-means clustering

K-means clustering. What are clustering algorithms?. What is clustering ? Clustering of data is a method by which large sets of data is grouped into clusters of smaller sets of similar data. Example: The balls of same color are clustered into a group as shown below :

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K-means clustering

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  1. K-means clustering Yan Wang and Lihua Lin

  2. What are clustering algorithms? What is clustering ? Clustering of data is a method by which large sets of data is grouped into clusters of smaller sets of similar data. Example: The balls of same color are clustered into a group as shown below : Thus, we see clustering means grouping of data or dividing a large data set into smaller data sets of some similarity. Yan Wang and Lihua Lin

  3. What is a clustering algorithm ? • A clustering algorithm attempts to find natural groups of components (or data) based on some similarity. • The clustering algorithm also finds the centroid of a group of data sets. • The centroid of a cluster is a point whose parameter values are the mean of the parameter values of all the points in the clusters. Yan Wang and Lihua Lin

  4. What is the common metric for clustering techniques ? • Generally, the distance between two points is taken as a common metric to assess the similarity among the components of a population. The most commonly used distance measure is the Euclidean metric which defines the distance between two points p= ( p1, p2, ....) and q = ( q1, q2, ....) as : Yan Wang and Lihua Lin

  5. Uses of clustering algorithms • Engineering sciences: pattern recognition, artificial intelligence, cybernetics etc. Typical examples to which clustering has been applied include handwritten characters, samples of speech, fingerprints, and pictures. • Life sciences (biology, botany, zoology, entomology, cytology, microbiology): the objects of analysis are life forms such as plants, animals, and insects. • Information, policy and decision sciences: the various applications of clustering analysis to documents include votes on political issues, survey of markets, survey of products, survey of sales programs, and R & D. Yan Wang and Lihua Lin

  6. Types of clustering algorithms • The various clustering concepts available can be grouped into two broad categories : • Hierarchial methods – Minimal Spanning Tree Method (Fig) • Nonhierarchial methods – K-means Algorithm Yan Wang and Lihua Lin

  7. K-Means Clustering Algorithm Definition: This nonheirarchial method initially takes the number of components of the population equal to the final required number of clusters. In this step itself the final required number of clusters is chosen such that the points are mutually farthest apart. Next, it examines each component in the population and assigns it to one of the clusters depending on the minimum distance. The centroid's position is recalculated everytime a component is added to the cluster and this continues until all the components are grouped into the final required number of clusters. Yan Wang and Lihua Lin

  8. K-Means Clustering Algorithm Yan Wang and Lihua Lin

  9. The Parameters and options for the k-means algorithm • Initialization: Different init Methods • Distance Measure:There are different distance measures that can be used. (Manhattan distance & Euclidean distance). • Termination: k-means should terminate when no more pixels are changing classes. • Quality: the quality of the results provided by k-means classification • Parallelism: There are several ways to parallelize the k-means algorithm • What to do with dead classes:A class is "dead" if no pixels belong to it. • Variants: one pass on-the-fly calculation of means • Number of classes: Number of classes is usually given as an input variable. Yan Wang and Lihua Lin

  10. Comments on the K-means Methods • Strength of the K-means: • Relatively efficient: O(tkn), where n is the number of objects, k is the number of clusters, and t is number of iterations. Normally, k,t << n. • Often terminates at a local optimum. • Weakness of the k-means: • Applicable only when mean is defined, then what about categorical data? • Need to specify k, the number of clusters, in advance. • Unable tom handle noisy data and outlines. • Not suitable to discover clusters with non-convex shapes. Yan Wang and Lihua Lin

  11. Direct k-means clustering algorithm Yan Wang and Lihua Lin

  12. Demo (I) 2 Initial Clusters Yan Wang and Lihua Lin

  13. Demo (I) 2-means Clustering Yan Wang and Lihua Lin

  14. Demo (II) – Init Method: Random Yan Wang and Lihua Lin

  15. Demo (II) – Init Method: Linear Yan Wang and Lihua Lin

  16. Demo (II) – Init Method: Cube Yan Wang and Lihua Lin

  17. Demo (II) – Init Method: Statistics Yan Wang and Lihua Lin

  18. Demo (II) – Init Method: Possibility Yan Wang and Lihua Lin

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