Find closest/similar value(vector) inside a matrix

Question

let\'s say I have the following numpy matrix (simplified):

matrix = np.array([[1, 1],
               [2, 2],
               [5, 5],
               [6, 6]]
           


        

Answer 1

Approach #1

We can use Cython-powered kd-tree for quick nearest-neighbor lookup, which is very efficient both memory-wise and with performance -

In [276]: from scipy.spatial import cKDTree

In [277]: matrix[cKDTree(matrix).query(search_vec, k=1)[1]]
Out[277]: array([2, 2])

Approach #2

With SciPy's cdist -

In [286]: from scipy.spatial.distance import cdist

In [287]: matrix[cdist(matrix, np.atleast_2d(search_vec)).argmin()]
Out[287]: array([2, 2])

Approach #3

With Scikit-learn's Nearest Neighbors -

from sklearn.neighbors import NearestNeighbors

nbrs = NearestNeighbors(n_neighbors=1).fit(matrix)
closest_vec = matrix[nbrs.kneighbors(np.atleast_2d(search_vec))[1][0,0]]

Approach #4

With Scikit-learn's kdtree -

from sklearn.neighbors import KDTree
kdt = KDTree(matrix, metric='euclidean')
cv = matrix[kdt.query(np.atleast_2d(search_vec), k=1, return_distance=False)[0,0]]

Approach #5

From eucl_dist package (disclaimer: I am its author) and following the wiki contents, we could leverage matrix-multiplication -

M = matrix.dot(search_vec)
d = np.einsum('ij,ij->i',matrix,matrix) + np.inner(search_vec,search_vec) -2*M
closest_vec = matrix[d.argmin()]