Source code for evomap.mapping._cmds

Classic (SVD-based) Multidimensional Scaling, as proposed in:

Torgerson, W.S. Multidimensional scaling: I. Theory and method. Psychometrika 17, 401–419 (1952).

Thanks to Francis Song, from whom this implementation has borrowed. Source:

from __future__ import division 
import numpy as np

[docs] class CMDS(): def __init__(self, n_dims = 2): self.n_dims = 2
[docs] @staticmethod def _cmdscale(D, n_dims): """ Classical multidimensional scaling (MDS) Parameters ---------- D : (n, n) array Symmetric distance matrix. Returns ------- Y : (n, p) array Configuration matrix. Each column represents a dimension. Only the p dimensions corresponding to positive eigenvalues of B are returned. Note that each dimension is only determined up to an overall sign, corresponding to a reflection. e : (n,) array Eigenvalues of B. """ # Number of points n = len(D) # Centering matrix H = np.eye(n) - np.ones((n, n))/n # YY^T B =**2).dot(H)/2 # Diagonalize evals, evecs = np.linalg.eigh(B) # Sort by eigenvalue in descending order idx = np.argsort(evals)[::-1] evals = evals[idx] evecs = evecs[:,idx] # Compute the coordinates using positive-eigenvalued components only w, = np.where(evals > 0) L = np.diag(np.sqrt(evals[w])) V = evecs[:,w] Y = return Y[:, :n_dims], evals[evals > 0]
[docs] def fit(self, X): self.Y_, _ = self._cmdscale(X, self.n_dims) return self
[docs] def fit_transform(self, X): return self.Y_