The requirements for a function on pairs of points to be a distance measure are that: Points, Spaces, and Distances: The dataset for clustering is a collection of points, where objects belongs to some space. Introduction to Hierarchical Clustering Analysis Dinh Dong Luong Introduction Data clustering concerns how to group a set of objects based on their similarity of ... – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 71f70a-MTNhM INTRODUCTION: For algorithms like the k-nearest neighbor and k-means, it is essential to measure the distance between the data points.. Chapter 3 Similarity Measures Data Mining Technology 2. If meaningful clusters are the goal, then the resulting clusters should capture the “natural” 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. The Manhattan distance (also called taxicab norm or 1-norm) is given by: 3.The maximum norm is given by: 4. Introduction to Clustering Techniques. 3 5 Minkowski distances • One group of popular distance measures for interval-scaled variables are Minkowski distances where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects (e.g. 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. The Euclidean distance (also called 2-norm distance) is given by: 2. A wide variety of distance functions and similarity measures have been used for clustering, such as squared Euclidean distance, and cosine similarity. 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. •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. •The history of merging forms a binary tree or hierarchy. Introduction 1.1. Clustering is a useful technique that organizes a large quantity of unordered text documents into a small number of meaningful and coherent cluster. I.e. 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. They include: 1. •Basic algorithm: Common Distance Measures Distance measure will determine how the similarity of two elements is calculated and it will influence the shape of the clusters. Clustering (HAC) •Assumes a similarity function for determining the similarity of two clusters. 10 Example : Protein Sequences Objects are sequences of {C,A,T,G}. For example, consider the following data. Scope of This Paper Cluster analysis divides data into meaningful or useful groups (clusters). Documents with similar sets of words may be about the same topic. A major problem when using the similarity (or dissimilarity) measures (such as Euclidean distance) is that the large values frequently swamp the small ones. 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. a space is just a universal set of points, from which the points in the dataset are drawn. Here, the contribution of Cost 2 and Cost 3 is insignificant compared to Cost 1 so far the Euclidean distance … 4 1. Clustering Distance Measures Hierarchical Clustering k-Means Algorithms. Of meaningful and coherent cluster groups ( clusters ) documents into a small number of meaningful and coherent cluster essential! 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