diff scripts/nmftools.py @ 9:c4841876a8ff branch-tests

adding notebooks and trying to explain classifier coefficients

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/nmftools.py	Mon Sep 11 19:06:40 2017 +0100
@@ -0,0 +1,158 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Oct 26 12:46:13 2016
+
+@author: https://github.com/keik/nmftools/blob/master/nmftools/core.py
+"""
+
+import numpy as np
+
+
+def nmf(Y, R=3, n_iter=50, init_H=[], init_U=[], verbose=False):
+    """
+    decompose non-negative matrix to components and activation with NMF
+    Y ≈ HU
+    Y ∈ R (m, n)
+    H ∈ R (m, k)
+    HU ∈ R (k, n)
+    parameters
+    ----
+    Y: target matrix to decompose
+    R: number of bases to decompose
+    n_iter: number for executing objective function to optimize
+    init_H: initial value of H matrix. default value is random matrix
+    init_U: initial value of U matrix. default value is random matrix
+    return
+    ----
+    Array of:
+    0: matrix of H
+    1: matrix of U
+    2: array of cost transition
+    """
+
+    eps = np.spacing(1)
+
+    # size of input spectrogram
+    M = Y.shape[0]
+    N = Y.shape[1]
+
+    # initialization
+    if len(init_U):
+        U = init_U
+        R = init_U.shape[0]
+    else:
+        U = np.random.rand(R,N);
+
+    if len(init_H):
+        H = init_H;
+        R = init_H.shape[1]
+    else:
+        H = np.random.rand(M,R)
+
+    # array to save the value of the euclid divergence
+    cost = np.zeros(n_iter)
+
+    # computation of Lambda (estimate of Y)
+    Lambda = np.dot(H, U)
+
+    # iterative computation
+    for i in range(n_iter):
+
+        # compute euclid divergence
+        cost[i] = euclid_divergence(Y, Lambda)
+
+        # update H
+        H *= np.dot(Y, U.T) / (np.dot(np.dot(H, U), U.T) + eps)
+
+        # update U
+        U *= np.dot(H.T, Y) / (np.dot(np.dot(H.T, H), U) + eps)
+
+        # recomputation of Lambda
+        Lambda = np.dot(H, U)
+
+    return [H, U, cost]
+
+
+def ssnmf(Y, R=3, n_iter=50, F=[], init_G=[], init_H=[], init_U=[], verbose=False):
+    """
+    decompose non-negative matrix to components and activation with semi-supervised NMF
+    Y ≈ FG + HU
+    Y ∈ R (m, n)
+    F ∈ R (m, x)
+    G ∈ R (x, n)
+    H ∈ R (m, k)
+    U ∈ R (k, n)
+    parameters
+    ----
+    Y: target matrix to decompose
+    R: number of bases to decompose
+    n_iter: number for executing objective function to optimize
+    F: matrix as supervised base components
+    init_W: initial value of W matrix. default value is random matrix
+    init_H: initial value of W matrix. default value is random matrix
+    return
+    ----
+    Array of:
+    0: matrix of F
+    1: matrix of G
+    2: matrix of H
+    3: matrix of U
+    4: array of cost transition
+    """
+
+    eps = np.spacing(1)
+
+    # size of input spectrogram
+    M = Y.shape[0];
+    N = Y.shape[1];
+    X = F.shape[1]
+
+    # initialization
+    if len(init_G):
+        G = init_G
+        X = init_G.shape[1]
+    else:
+        G = np.random.rand(X, N)
+
+    if len(init_U):
+        U = init_U
+        R = init_U.shape[0]
+    else:
+        U = np.random.rand(R, N)
+
+    if len(init_H):
+        H = init_H
+        R = init_H.shape[1]
+    else:
+        H = np.random.rand(M, R)
+
+    # array to save the value of the euclid divergence
+    cost = np.zeros(n_iter)
+
+    # computation of Lambda (estimate of Y)
+    Lambda = np.dot(F, G) + np.dot(H, U)
+
+    # iterative computation
+    for it in range(n_iter):
+
+        # compute euclid divergence
+        cost[it] = euclid_divergence(Y, Lambda + eps)
+
+        # update of H
+        H *= (np.dot(Y, U.T) + eps) / (np.dot(np.dot(H, U) + np.dot(F, G), U.T) + eps)
+
+        # update of U
+        U *= (np.dot(H.T, Y) + eps) / (np.dot(H.T, np.dot(H, U) + np.dot(F, G)) + eps)
+
+        # update of G
+        G *= (np.dot(F.T, Y) + eps)[np.arange(G.shape[0])] / (np.dot(F.T, np.dot(H, U) + np.dot(F, G)) + eps)
+
+        # recomputation of Lambda (estimate of V)
+        Lambda = np.dot(H, U) + np.dot(F, G)
+
+    return [F, G, H, U, cost]
+
+
+def euclid_divergence(V, Vh):
+    d = 1 / 2 * (V ** 2 + Vh ** 2 - 2 * V * Vh).sum()
+    return d
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