Form Similarity Matrix

Data Values

This specifies the variates and the type of each variate. The similarity type of a variate determines how differences in variate values for each unit contribute to the overall similarity between units. Variates can be added to this list by double-clicking on a variate name within the Available data list. Alternatively, multiple selections can be transferred from the Available data list by clicking the

button. When a variate name is transferred from the Available data list the type for the variate is set using the measure within the Default type of test list. The type for a variate can be changed within the Data Values list by double-clicking on the variate in this list and selecting a new similarity measure from the resulting dialog.

Similarity Measures

Jaccard is appropriate for dichotomous variables, simple matching for qualitative variables and the other settings give different ways for handling quantitative variables. The form of contribution to the similarity is as follows:

Type Contribution Weight

Jaccard if x_i = x_j = 1, then 1
1

if x_i = x_j = 0, then 0
0

if x_i /= x_j, then 0
1

Simple Matching if x_i = x_j, then 1
1

if x_i /= x_j, then 0
1

Dice if x_i = x_j = 1, then 1
1

if x_i = x_j = 0, then 0
0

if x_i /= x_j, then 0
0.5

Sneath and Sokal if x_i = x_j, then 1
1

if x_i /= x_j, then 0
0.5

Russell and Rao if x_i = x_j, then 1
1

if x_i = 0 or x_j = 0, then 0
1

Antidice if x_i = x_j = 1, then 1
1

if x_i = x_j = 0, then 0
0

if x_i /= x_j, then 0
2

Rogers and Tanimoto if x_i = x_j, then 1
1

if x_i /= x_j, then 0
2

Cityblock 1 - |x_i - x_j| / range 1

Manhattan synonymous with cityblock

Ecological 1 - |x_i - x_j| / range 1

unless x_i = x_j = 0 0

Euclidean 1 - {(x_i - x_j) / range}² 1

Pythagorean synonymous with Euclidean

Divergence 1 - {(x_i - x_j) / (x_i + x_j)}² 1

Canberra 1 - |x_i - x_j| / (|x_i| + |x_j|) 1/p

Bray and Curtis 1 - |x_i - x_j| x_i + x_j

Soergel 1 - |x_i - x_j| max(x_i, x_j)

The measure of similarity is formed by multiplying each contribution by the corresponding weight, summing all these values, and then dividing by the sum of the weights.

Available Data

This lists data structures appropriate to the current input field. The contents will change as you move from one field to the next. Double-click on a name to copy it to the current input field; alternatively, you can type the name directly into the input field.

Default type of test

This specifies the default similarity used when items are added to the Data Values list. For example, when you double-click on a variate name within the Available Data list to transfer it to the Data Values list.

Name of new matrix

Specifies the name of the identifier of a symmetric matrix to save the similarity matrix.

Unit Labels

Allows you to specify a text or variate which is to be used to label the rows of the similarity matrix.

Type	Contribution	Weight
Jaccard	if x_i = x_j = 1, then 1	1
	if x_i = x_j = 0, then 0	0
	if x_i /= x_j, then 0	1
Simple Matching	if x_i = x_j, then 1	1
	if x_i /= x_j, then 0	1
Dice	if x_i = x_j = 1, then 1	1
	if x_i = x_j = 0, then 0	0
	if x_i /= x_j, then 0	0.5
Sneath and Sokal	if x_i = x_j, then 1	1
	if x_i /= x_j, then 0	0.5
Russell and Rao	if x_i = x_j, then 1	1
	if x_i = 0 or x_j = 0, then 0	1
Antidice	if x_i = x_j = 1, then 1	1
	if x_i = x_j = 0, then 0	0
	if x_i /= x_j, then 0	2
Rogers and Tanimoto	if x_i = x_j, then 1	1
	if x_i /= x_j, then 0	2
Cityblock	1 - \|x_i - x_j\| / range	1
Manhattan	synonymous with cityblock
Ecological	1 - \|x_i - x_j\| / range	1
	unless x_i = x_j = 0	0
Euclidean	1 - {(x_i - x_j) / range}²	1
Pythagorean	synonymous with Euclidean
Divergence	1 - {(x_i - x_j) / (x_i + x_j)}²	1
Canberra	1 - \|x_i - x_j\| / (\|x_i\| + \|x_j\|)	1/p
Bray and Curtis	1 - \|x_i - x_j\|	x_i + x_j
Soergel	1 - \|x_i - x_j\|	max(x_i, x_j)

Data Values

Available Data

Default type of test

Name of new matrix

Unit Labels

See Also