Similarity Measures for Binary Data Similarity measures between objects that contain only binary attributes are called similarity coefficients, and typically have values between 0 and 1. Clustering (HAC) •Assumes a similarity function for determining the similarity of two clusters. Chapter 3 Similarity Measures Written by Kevin E. Heinrich Presented by Zhao Xinyou [email_address] 2007.6.7 Some materials (Examples) are taken from Website. •Starts with all instances in a separate cluster and then repeatedly joins the two clusters that are most similar until there is only one cluster. Common Distance Measures Distance measure will determine how the similarity of two elements is calculated and it will influence the shape of the clusters. •The history of merging forms a binary tree or hierarchy. A value of 1 indicates that the two objects are completely similar, while a value of 0 indicates that the objects are not at all similar. Points, Spaces, and Distances: The dataset for clustering is a collection of points, where objects belongs to some space. In KNN we calculate the distance between points to find the nearest neighbor, and in K-Means we find the distance between points to group data points into clusters based on similarity. They include: 1. INTRODUCTION: For algorithms like the k-nearest neighbor and k-means, it is essential to measure the distance between the data points.. Documents with similar sets of words may be about the same topic. Chapter 3 Similarity Measures Data Mining Technology 2. The requirements for a function on pairs of points to be a distance measure are that: If meaningful clusters are the goal, then the resulting clusters should capture the “natural” Clustering Distance Measures Hierarchical Clustering k-Means Algorithms. Clustering is a useful technique that organizes a large quantity of unordered text documents into a small number of meaningful and coherent cluster. vectors of gene expression data), and q is a positive integer q q p p q q j x i x j similarity measure 1. Introduction 1.1. The Manhattan distance (also called taxicab norm or 1-norm) is given by: 3.The maximum norm is given by: 4. •Basic algorithm: For example, consider the following data. 10 Example : Protein Sequences Objects are sequences of {C,A,T,G}. A major problem when using the similarity (or dissimilarity) measures (such as Euclidean distance) is that the large values frequently swamp the small ones. 4 1. Here, the contribution of Cost 2 and Cost 3 is insignificant compared to Cost 1 so far the Euclidean distance … A wide variety of distance functions and similarity measures have been used for clustering, such as squared Euclidean distance, and cosine similarity. 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