cvt.utils package

Submodules

cvt.utils.base module

Mathematical utilities

cvt.utils.base.canonical_angle(X, Y)

Calculate cannonical angles beween subspaces

Parameters

  • X (basis matrix, array-like, shape: (n_subdim_X, n_dim)) –

  • Y (basis matrix, array-like, shape: (n_subdim_Y, n_dim)) –

Returns

c

Return type

float, similarity of X, Y

cvt.utils.base.canonical_angle_matrix(X, Y)

Calculate canonical angles between subspaces example similarity = MathUtils.calc_basis_vector(X, Y)

Parameters

  • X (set of basis matrix, array-like, shape: (n_set_X, n_subdim, n_dim)) – n_subdim can be variable on each subspaces

  • Y (set of basis matrix, array-like, shape: (n_set_Y, n_subdim, n_dim)) – n_set can be variable from n_set of X n_subdim can be variable on each subspaces

  • Returns – C: similarity matrix, array-like, shape: (n_set_X, n_set_Y)

cvt.utils.base.canonical_angle_matrix_f(X, Y)

Calculate canonical angles between subspaces example similarity = MathUtils.calc_basis_vector(X, Y)

Parameters

  • X (set of basis matrix, array-like, shape: (n_set_X, n_subdim, n_dim)) – n_subdim can be variable on each subspaces

  • Y (set of basis matrix, array-like, shape: (n_set_Y, n_subdim, n_dim)) – n_set can be variable from n_set of X n_subdim can be variable on each subspaces

  • Returns – C: similarity matrix, array-like, shape: (n_set_X, n_set_Y)

cvt.utils.base.cross_similarities(refs, inputs)

Calc similarities between each reference spaces and each input subspaces

refs: list of array-like (n_dims, n_subdims_i) inputs: list of array-like (n_dims, n_subdims_j)

similarities: array-like, shape (n_refs, n_inputs)

cvt.utils.base.dual_vectors(K, n_subdims=None, higher=True, eps=1e-06)

Calc dual representation of vectors in kernel space

Karray-like, shape: (n_samples, n_samples)

Grammian Matrix of X: K(X, X)

n_subdims: int, default=None

Number of vectors of dual vectors to return

higher: boolean, default=None
If True, this function returns eigenbasis corresponding to

higher n_subdims eigenvalues in descending order.

If False, this function returns eigenbasis corresponding to

lower n_subdims eigenvalues in descending order.

eps: float, default=1e-20

lower limit of eigenvalues

Aarray-like, shape: (n_samples, n_samples)

Dual replesentation vectors. it satisfies lambda[i] * A[i] @ A[i] == 1, where lambda[i] is i-th biggest eigenvalue

e: array-like, shape: (n_samples, )

Eigen values descending sorted

cvt.utils.base.max_square_singular_values(X)

calculate mean square of singular values of X

X : array-like, shape: (n, m)

c: mean square of singular values

cvt.utils.base.mean_square_singular_values(X)

calculate mean square of singular values of X

X : array-like, shape: (n, m)

c: mean square of singular values

cvt.utils.base.subspace_bases(X, n_subdims=None, higher=True, return_eigvals=False)

Return subspace basis using PCA

Parameters

  • X (array-like, shape (n_dimensions, n_vectors)) – data matrix

  • n_subdims (integer) – number of subspace dimension

  • higher (bool) – if True, this function returns eigenvectors collesponding top-n_subdims eigenvalues. default is True.

  • return_eigvals (bool) – if True, this function also returns eigenvalues.

Returns

  • V (array-like, shape (n_dimensions, n_subdims)) – bases matrix

  • w (array-like shape (n_subdims)) – eigenvalues

cvt.utils.evaluation module

cvt.utils.evaluation.calc_eer(X, labels=None, data_type='S')

calculate Error Rate (ER)

Parameters

  • X (ndarray, shape (n_samples, n_elements)) – data matrix

  • labels(optional) (ndarray, shape (n_elements)) – labels that represents what class each element(row) belongs to if it’s not given, each rows are treated as independent class

  • data_type(optional) (string) – ‘S’: Similarity (default) ‘D’: Distance

Returns

  • eer (float) – equal error rate

  • thresh (float) – threashold

cvt.utils.evaluation.calc_er(X, y, labels=None, data_type='S')

calculate Error Rate (ER)

Parameters

  • X (ndarray, shape (n_samples, n_elements)) – data matrix

  • y (ndarray, shape (n_samples)) – true label (integer)

  • labels(optional) (ndarray, shape (n_elements)) – labels that represents what class each element(row) belongs to if it’s not given, each rows are treated as independent class

  • data_type(optional) (string) – ‘S’: Similarity (default) ‘D’: Distance

Returns

er – error rate

Return type

float

cvt.utils.kernel_functions module

Kernel functions

cvt.utils.kernel_functions.l2_kernel(X, Y)
cvt.utils.kernel_functions.linear_kernel(X, Y)

Linear kernel. this calculates simple inner product. K(x, y) = x @ y

Parameters

  • X (array of shape (n_dims, n_samples_X)) –

  • Y (array of shape (n_dims, n_samples_Y)) –

  • Returns –

  • -------- –

  • K (array-like, shape: (n_samples_X, n_samples_Y)) – Grammian matrix

cvt.utils.kernel_functions.rbf_kernel(X, Y, sigma=None)

RBF kernel. this is a wrapper of sklearn.metrics.pairwise.rbf_kernel. K(x, y) = exp(- (1/2) * (||x - y||/sigma)^2)

Parameters

  • X (array of shape (n_dims, n_samples_X)) –

  • Y (array of shape (n_dims, n_samples_Y)) –

  • sigma (float, default None) – If None, defaults to sqrt(n_dims / 2)

  • Returns –

  • -------- –

  • K (array-like, shape: (n_samples_X, n_samples_Y)) – Grammian matrix

Module contents