Dissimilarities Class 
Namespace: Imsl.Stat
The Dissimilarities type exposes the following members.
Name  Description  

Compute 
Computes a matrix of dissimilarities (or similarities) between the
columns (or rows) of a matrix.
 
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
GetHashCode  Serves as a hash function for a particular type. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
ToString  Returns a string that represents the current object. (Inherited from Object.) 
Name  Description  

DistanceMatrix 
The distance matrix.
 
DistanceMethod 
The method in computing the dissimilarities or similarities.
 
Index 
The indices of the rows.
 
NumberOfProcessors 
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
 
Row 
Identifies whether distances are computed between rows or columns of x.
 
ScalingOption 
The scaling option used if the L2Norm, L1Norm, or
InfinityNorm distance methods are specified. See
DistanceMethod.

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 kth element in the ith column, denotes the corresponding element in the jth 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.