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Chapter: Data Warehousing and Data Mining : Clustering and Applications and Trends in Data Mining

Type of Data in Clustering Analysis

Data structure Data matrix (two modes) object by variable Structure


TYPE OF DATA IN CLUSTERING ANALYSIS

Data structure Data matrix (two modes) object by variable Structure


Dissimilarity matrix (one mode) object –by-object structure

 


We describe how object dissimilarity can be computed for object by Interval-scaled variables,

 

Binary variables, Nominal, ordinal, and ratio variables, Variables of mixed types

 

Interval-Scaled variables (continuous measurement of a roughly linear scale) Standardize data


Using mean absolute deviation is more robust than using standard deviation

 

Similarity and Dissimilarity Between Objects

 

Distances are normally used to measure the similarity or dissimilarity between two data objects

 

Some popular ones include: Minkowski distance:



Also, one can use weighted distance, parametric Pearson product moment correlation, or other dissimilarity measures

 

Binary Variables

 

A contingency table for binary data


Distance measure for symmetric binary variables:


 

Distance measure for asymmetric binary variables:


Jaccard coefficient (similarity measure for asymmetric binary variables):


 

Categorical variables

 

A generalization of the binary variable in that it can take more than 2 states, e.g., red, yellow, blue, green

 

Method 1: Simple matching

m: # of matches, p: total # of variables


Method 2: use a large number of binary variables

 

creating a new binary variable for each of the M nominal states

Ordinal Variables

An ordinal variable can be discrete or continuous

 

Order is important, e.g., rank

 

Can be treated like interval-scaled

 

replace xif  by their rank

 

map the range of each variable onto [0, 1] by replacing i-th object in the f-th variable


compute the dissimilarity using methods for interval-scaled variables

Ratio-scaled variable:

 

a positive measurement on a nonlinear scale, approximately at exponential scale, such as AeBt or

Ae-Bt

Methods:

 

treat them like interval-scaled variables—not a good choice! (why?—the scale can be distorted)

 

apply logarithmic transformation yif = log(xif)

 

treat them as continuous ordinal data treat their rank as interval-scaled

 

Variables of Mixed Types

 

A database may contain all the six types of variables symmetric binary, asymmetric binary,

 

nominal, ordinal, interval and ratio

 

One may use a weighted formula to combine their effects


Vector Objects

 

Vector objects: keywords in documents, gene features in micro-arrays, etc.

 

Broad applications: information retrieval, biologic taxonomy, etc.

 

Cosine measure




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