Type of Data in Clustering Analysis

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 x_if  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 Ae^Bt or

_Ae-Bt

Methods:

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

apply logarithmic transformation y_if = log(x_if)

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