# Euclidean Distance¶

The Euclidean distance for real valued features is the square root of the sum of squared disparity between the corresponding feature dimensions of two data points.

$d({\bf x},{\bf x'})= \sqrt{\sum_{i=0}^{d}|{\bf x_i}-{\bf x'_i}|^2}$

where $$\bf x$$ and $$\bf x'$$ are $$d$$ dimensional feature vectors.

## 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 = Shogun::RealFeatures.new f_feats_a
features_b = Shogun::RealFeatures.new f_feats_b

features_a <- RealFeatures(f_feats_a)
features_b <- RealFeatures(f_feats_b)

features_a = shogun.RealFeatures(f_feats_a)
features_b = shogun.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 CEuclideanDistance by passing it CDenseFeatures.

distance = EuclideanDistance(features_a, features_a)

distance = EuclideanDistance(features_a, features_a);

EuclideanDistance distance = new EuclideanDistance(features_a, features_a);

distance = Shogun::EuclideanDistance.new features_a, features_a

distance <- EuclideanDistance(features_a, features_a)

distance = shogun.EuclideanDistance(features_a, features_a)

EuclideanDistance distance = new EuclideanDistance(features_a, features_a);

auto distance = some<CEuclideanDistance>(features_a, features_a);


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$get_distance_matrix()  distance_matrix_aa = distance:get_distance_matrix()  double[,] distance_matrix_aa = distance.get_distance_matrix();  auto distance_matrix_aa = distance->get_distance_matrix();  We can use the same instance with new CDenseFeatures to compute distance. distance.init(features_a, features_b)  distance.init(features_a, features_b);  distance.init(features_a, features_b);  distance.init features_a, features_b  distance$init(features_a, features_b)

distance:init(features_a, features_b)

distance.init(features_a, features_b);

distance->init(features_a, features_b);


If desired, squared distance can be extracted like:

distance.set_disable_sqrt(True)
distance_matrix_ab = distance.get_distance_matrix()

distance.set_disable_sqrt(true);
distance_matrix_ab = distance.get_distance_matrix();

distance.set_disable_sqrt(true);
DoubleMatrix distance_matrix_ab = distance.get_distance_matrix();

distance.set_disable_sqrt true
distance_matrix_ab = distance.get_distance_matrix

distance$set_disable_sqrt(TRUE) distance_matrix_ab <- distance$get_distance_matrix()

distance:set_disable_sqrt(True)
distance_matrix_ab = distance:get_distance_matrix()

distance.set_disable_sqrt(true);
double[,] distance_matrix_ab = distance.get_distance_matrix();

distance->set_disable_sqrt(true);
auto distance_matrix_ab = distance->get_distance_matrix();