Mahalanobis Distance

The Mahalanobis distance for real valued features computes the distance between a feature vector and a distribution of features characterized by its mean and covariance.

\[\sqrt{ ( x_{i} - \mu )^\top S^{-1} ( x_{i} - \mu )}\]

Example

Imagine we have files with data. We create CDenseFeatures (here 64 bit floats aka RealFeatures) as

features_a = RealFeatures(f_feats_a)
features_b = RealFeatures(f_feats_b)
features_a = RealFeatures(f_feats_a);
features_b = RealFeatures(f_feats_b);
RealFeatures features_a = new RealFeatures(f_feats_a);
RealFeatures features_b = new RealFeatures(f_feats_b);
features_a = Modshogun::RealFeatures.new f_feats_a
features_b = Modshogun::RealFeatures.new f_feats_b
features_a <- RealFeatures(f_feats_a)
features_b <- RealFeatures(f_feats_b)
features_a = modshogun.RealFeatures(f_feats_a)
features_b = modshogun.RealFeatures(f_feats_b)
RealFeatures features_a = new RealFeatures(f_feats_a);
RealFeatures features_b = new RealFeatures(f_feats_b);
auto features_a = some<CDenseFeatures<float64_t>>(f_feats_a);
auto features_b = some<CDenseFeatures<float64_t>>(f_feats_b);

We create an instance of CMahalanobisDistance by passing it CDenseFeatures.

distance = MahalanobisDistance(features_a, features_a)
distance = MahalanobisDistance(features_a, features_a);
MahalanobisDistance distance = new MahalanobisDistance(features_a, features_a);
distance = Modshogun::MahalanobisDistance.new features_a, features_a
distance <- MahalanobisDistance(features_a, features_a)
distance = modshogun.MahalanobisDistance(features_a, features_a)
MahalanobisDistance distance = new MahalanobisDistance(features_a, features_a);
auto distance = some<CMahalanobisDistance>(features_a, features_a);

The distance matrix can be extracted as follows:

distance_matrix_aa = distance.get_distance_matrix()
distance_matrix_aa = distance.get_distance_matrix();
DoubleMatrix distance_matrix_aa = distance.get_distance_matrix();
distance_matrix_aa = distance.get_distance_matrix 
distance_matrix_aa <- distance$get_distance_matrix()
distance_matrix_aa = distance:get_distance_matrix()
double[,] distance_matrix_aa = distance.get_distance_matrix();
auto distance_matrix_aa = distance->get_distance_matrix();

We can use the same instance with new CDenseFeatures to compute asymmetrical distance as follows:

distance.init(features_a, features_b)
distance_matrix_ab = distance.get_distance_matrix()
distance.init(features_a, features_b);
distance_matrix_ab = distance.get_distance_matrix();
distance.init(features_a, features_b);
DoubleMatrix distance_matrix_ab = distance.get_distance_matrix();
distance.init features_a, features_b
distance_matrix_ab = distance.get_distance_matrix 
distance$init(features_a, features_b)
distance_matrix_ab <- distance$get_distance_matrix()
distance:init(features_a, features_b)
distance_matrix_ab = distance:get_distance_matrix()
distance.init(features_a, features_b);
double[,] distance_matrix_ab = distance.get_distance_matrix();
distance->init(features_a, features_b);
auto distance_matrix_ab = distance->get_distance_matrix();