# Lec7b - DATA MINING Susan Holmes Stats202 Lecture 7(b) Fall...

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. . . . . . DATA MINING Susan Holmes © Stats202 Lecture 7(b) Fall 2010 ABabcdfghiejkl

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. . . . . . Multidimensional Scaling From a non-technical point of view, the purpose of multidimensional scaling (MDS) is to provide a visual representation of the pattern of proximities (i.e., similarities or distances) among a set of objects. For example, given a matrix of perceived similarities/ indices of confusion between various types of chocolate, MDS plots the types on a map such that those those that are perceived to be very similar to each other are placed near each other on the map, and those brands that are perceived to be very different from each other are placed far away from each other on the map.
. . . . . . MDS for Text Analysis We can take different texts and compute distances between based on word occurrences. We can then map the proximities between texts. We will see more examples when we do association analysis. Critias, Laws, Republic, Timœus, Philebus, Sophist, Politæ Tim Laws Rep Soph Phil Pol Crit Axis #1: 69% Axis #2: 16% -0.2 0.0 0.2 0.4 0.0 -0.2 -0.3 -0.1 0.1

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. . . . . . Given the matrix of distances among cities shown below, MDS produces a new map. In this example, the relationship between input proximities and distances among points on the map is positive: the smaller the input proximity, the closer (smaller) the distance between points, and vice versa. Had the input data been similarities, the relationship would have been negative: the smaller the input similarity between items, the farther apart in the picture they would be. From a slightly more technical point of view, what MDS does is ±nd a set of vectors in p-dimensional space such that the matrix of euclidean distances among them corresponds as closely as possible to some function of the input matrix according to a criterion function called stress.
. . . . . . A simplifed view oF the algorithm is as Follows:

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## This note was uploaded on 07/29/2011 for the course STAT 202 at Stanford.

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Lec7b - DATA MINING Susan Holmes Stats202 Lecture 7(b) Fall...

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