Similarity Distance Based CCA

Through SDCCA latent space for multiview learning is determined by incorporating similarities and complementary information from multiple views with cross correlation analysis.

Package organization

Class SDCCA(scale = True, k = 2)

Parameters:

• scale : boolean, default = True, Whether to scale the data or not.

• k : int, default = 2, Number of neighbours to consider in K-Means Algorithm.

Attributes:

• x : first data set of dimension n x p with n samples and p features.
• y : second data set of dimension n x q with n samples and q features.
• n : number of samples in datasets
• p : number of features in x dataset
• q : number of features in y dataser
• wx , wy : final projection vectors of two views of p x p and q x q respectively

Methods

fit(self, x, y)

Fit the model from the data in x and the labels in y and finds the projection vectors

Parameters

• x : array-like, shape (n x p) Training vector, where n is the number of samples, and p is the number of features.
• y : array-like, shape (n x q) Training vector, where n is the number of samples, and q is the number of features.

Returns

• wx , wy : Projection vectors

---

fit_transform(self, x, y)

Applies the projection vectors on the dataset

Parameters

• x : array-like, shape (n x p) Training vector, where n is the number of samples, and p is the number of features.
• y : array-like, shape (n x q) Training vector, where n is the number of samples, and q is the number of features.

Returns

x_new , y_new : Projected views Input data transformed by the projected vectors

Usage

Example:1

from SDCCA import SDCCA
x = np.array([[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]])
y = np.array([[0.1, 0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]])
sdcca = SDCCA(scale = False)
wx,wy = sdcca.fit (x, y)
print(wx)
"""
array([[-28.4951993   0.2682586  -0.975527 ]
 [-42.1618415  -0.5543857   0.2679151]
 [-35.6725722   0.3283515   0.5998168]]) 
"""
print(wy)
"""
array([[257.9830053  -0.0865349]
 [262.5667474   0.0852448]])
"""

Example:2

from SDCCA import SDCCA
x = np.array([[1., 2.1, 1.], [1., 2.1, 0.5], [2.,2.,2.], [3.,5.,4.]])
y = np.array([[0.1, 4.2], [0.9, 2.1], [7.2, 5.9], [12.9, 1.3]])
sdcca = SDCCA(k=4)
x_new, y_new = sdcca.fit_transform(x,y)
print(x_new)
"""
[[ -5.8380473  -7.4261078  -6.2538804]
 [ -5.823948   -7.4249809  -6.2690812]
 [ -12.4623148 -13.7376682 -12.9121544]
 [ -18.0069253 -21.6219808 -18.9701994]]
"""
print(y_new)
"""
[[  3.896946    12.9154699]
 [ -1.4534688   8.8647358]
 [ -22.7799413  38.134078 ]
 [ -50.2993919  40.4397741]]
"""