Class Dissimilarities computes an upper triangular matrix (excluding the diagonal) of dissimilarities (or similarities) between the columns (or rows) of a matrix. Nine different distance measures can be computed. For the first three measures, three different scaling options can be employed. The distance matrix computed is generally used as input to clustering or multidimensional scaling functions.

The following discussion assumes that the distance measure is being computed between the columns of the matrix. If distances between the rows of the matrix are desired, use Row = true.

The distance method and scaling option used by Dissimilarities can be set via properties DistanceMethod and ScalingOption, respectively. For distance methods L2Norm, L1Norm, or InfinityNorm, each row of x is first scaled according to the value of ScalingOption. The scaling parameters are obtained from the values in the row scaled as either the standard deviation of the row or the row range; the standard deviation is computed from the unbiased estimate of the variance. If no scaling is performed, the parameters in the following discussion are all 1.0 (see ScalingOption). Once the scaling value (if any) has been computed, the distance between column i and column j is computed via the difference vector , where denotes the k-th element in the i-th column, denotes the corresponding element in the j-th column, and ndstm is the number of rows if differencing columns and the number of columns if differencing rows. For given , the distance methods that allow scaling are defined as:

DistanceMethod	Metric
L2Norm	Euclidean distance ( norm)
L1Norm	Sum of the absolute differences ( norm)
InfinityNorm	Maximum difference ( norm)

The following distance measures do not allow for scaling.

DistanceMethod	Metric
Mahalanobis	Mahalanobis distance
AbsCosine	Absolute value of the cosine of the angle between the vectors
AngleInRadians	Angle in radians (0, ) between the lines through the origin defined by the vectors
CorrelationCoefficient	Correlation coefficient
AbsCorrelationCoefficient	Absolute value of the correlation coefficient
ExactMatches	Number of exact matches, where .

For the Mahalanobis distance, any variable used in computing the distance measure that is (numerically) linearly dependent upon the previous variables in the Index property is omitted from the distance measure.