pytudes._2021.miscellany.machine_learning.linear_algebra

Module Contents

Functions

cosine_similarity(A, B)	For samples x features matrixes or 1 x features column vectors
euclidean_length(arr)	Args:

pytudes._2021.miscellany.machine_learning.linear_algebra.cosine_similarity(A, B)

For samples x features matrixes or 1 x features column vectors

[

[cosine_similarity(A[0], B[0]), … ,cosine_similarity(A[0], B[len(B)-1])], …, [cosine_similarity(A[len(A)-1], B[len(B]-1), … ,cosine_similarity(A[len(A)-1], B[len(B)-1])],

]

[

[A_1 . B_1, … ,A_1 . B_m], … [A_n . B_1, … ,A_n . B_m],

] Args:

A: B:

Examples:

>>> x = np.array([3, 45, 7, 2] )
>>> y = np.array([2,54,13,15] )
>>> cosine_similarity(x, y)[0]
0.9722842517123499
>>> assert cosine_similarity(x, y) == cosine_similarity(y, x)
>>> cosine_similarity(x, x)[0]
1.0
>>> cosine_similarity(x, -x)[0]
-1.0
>>> cosine_similarity(x, np.zeros(x.shape))[0]
0.0
>>> np.testing.assert_almost_equal(cosine_similarity(x, y), 1 - scipy.spatial.distance.cosine(x, y))
>>> a, b = np.array([x,y]), np.array([y,x])
>>> cosine_similarity(a, a)
array([[1.        , 0.97228425],
       [0.97228425, 1.        ]])
>>> cosine_similarity(a, b)
array([[0.97228425, 1.        ],
       [1.        , 0.97228425]])
>>> np.testing.assert_almost_equal(cosine_similarity(a, b), 1 - scipy.spatial.distance.cdist(a, b, "cosine"))

Parameters:

• A (numpy.ndarray) –

• B (numpy.ndarray) –

Return type:

numpy.ndarray

pytudes._2021.miscellany.machine_learning.linear_algebra.euclidean_length(arr)

Args:

arr:

Examples:

>>> x = np.array([3, 45, 7, 2] )
>>> y = np.array([2,54,13,15] )
>>> euclidean_length(x)[0]
45.68369512200168
>>> euclidean_length(y)[0]
57.56735185849702
>>> euclidean_length(np.array([x,y]))
array([[45.68369512],
       [57.56735186]])

Parameters:

arr (numpy.ndarray) –

Return type:

numpy.ndarray