| Dissimilarities Class |
Inheritance HierarchyNamespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
SyntaxThe Dissimilarities type exposes the following members.
Methods| 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.) |
Properties| 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.
|
RemarksClass 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.
See Also