Documents with similar sets of words may be about the same topic. For example, consider the following data. •The history of merging forms a binary tree or hierarchy. 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 Common Distance Measures Distance measure will determine how the similarity of two elements is calculated and it will influence the shape of the clusters. Chapter 3 Similarity Measures Data Mining Technology 2. Scope of This Paper Cluster analysis divides data into meaningful or useful groups (clusters). Points, Spaces, and Distances: The dataset for clustering is a collection of points, where objects belongs to some space. Clustering (HAC) •Assumes a similarity function for determining the similarity of two clusters. 4 1. A major problem when using the similarity (or dissimilarity) measures (such as Euclidean distance) is that the large values frequently swamp the small ones. The requirements for a function on pairs of points to be a distance measure are that: Introduction to Clustering Techniques. 10 Example : Protein Sequences Objects are sequences of {C,A,T,G}. 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. •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. Introduction 1.1. 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. •Basic algorithm: vectors of gene expression data), and q is a positive integer q q p p q q j x i x j 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. Here, the contribution of Cost 2 and Cost 3 is insignificant compared to Cost 1 so far the Euclidean distance … similarity measure 1. 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 Distance Measures Hierarchical Clustering k-Means Algorithms. a space is just a universal set of points, from which the points in the dataset are drawn. INTRODUCTION: For algorithms like the k-nearest neighbor and k-means, it is essential to measure the distance between the data points.. Clustering is a useful technique that organizes a large quantity of unordered text documents into a small number of meaningful and coherent cluster. A wide variety of distance functions and similarity measures have been used for clustering, such as squared Euclidean distance, and cosine similarity. I.e. 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. If meaningful clusters are the goal, then the resulting clusters should capture the “natural” The Euclidean distance (also called 2-norm distance) is given by: 2. The Manhattan distance (also called taxicab norm or 1-norm) is given by: 3.The maximum norm is given by: 4. 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