forked from FeeLab/seqNMF
-
Notifications
You must be signed in to change notification settings - Fork 0
/
seqNMF.m
260 lines (235 loc) · 10.6 KB
/
seqNMF.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
function [W, H, cost,loadings,power] = seqNMF(X, varargin)
%
% USAGE:
%
% [W, H, cost, loadings, power] = seqNMF(X, ... % X is the data matrix
% 'K', 10, 'L', 20, 'lambda', .1, ... % Other inputs optional
% 'W_init', W_init, 'H_init', H_init, ...
% 'showPlot', 1, 'maxiter', 20, 'tolerance', -Inf, 'shift', 1, ...
% 'competeW', 0, 'competeH', 0, 'lambdaL1W', 0, 'lambdaL1H', 0, ...
% 'lambdaOrthoH', 0, 'lambdaOrthoW', 0)
%
% ------------------------------------------------------------------------
% DESCRIPTION:
%
% Factorizes the NxT data matrix X into K factors
% Factor exemplars are returned in the NxKxL tensor W
% Factor timecourses are returned in the KxT matrix H
%
% ----------
% L / /|
% / / |
% ---------------- /---------/ | ----------------
% | | | | | | |
% N | X | = N | W | / (*) K | H |
% | | | | / | |
% ---------------- /----------/ ----------------
% T K T
% See paper:
% XXXXXXXXXXXXXXXXX
%
% ------------------------------------------------------------------------
%
% INPUTS:
%
% Name Default Description
% X Data matrix (NxT) to factorize
% 'K' 10 Number of factors
% 'L' 100 Length (timebins) of each factor exemplar
% 'lambda' .001 Regularization parameter
% 'W_init' max(X(:))*rand(N,K,L) Initial W
% 'H_init' max(X(:))*rand(K,T)./(sqrt(T/3)) Initial H (rows have norm ~1 if max(data) is 1)
% 'showPlot' 1 Plot every iteration? no=0
% 'maxiter' 100 Maximum # iterations to run
% 'tolerance' -Inf Stop if improved less than this; Set to -Inf to always run maxiter
% 'shift' 1 Shift factors to center; Helps avoid local minima
% 'lambdaL1W' 0 L1 sparsity parameter; Increase to make W's more sparse
% 'lambdaL1H' 0 L1 sparsity parameter; Increase to make H's more sparse
% 'W_fixed' 0 Fix W during the fitting proceedure
% 'SortFactors' 1 Sort factors by loadings
% 'lambdaOrthoH' 0 ||HSH^T||_1,i~=j; Encourages events-based factorizations
% 'lambdaOrthoW' 0 ||Wflat^TWflat||_1,i~=j; ; Encourages parts-based factorizations
% 'useWupdate' 1 Wupdate for cross orthogonality often doesn't change results much, and can be slow, so option to remove
% ------------------------------------------------------------------------
% OUTPUTS:
%
% W NxKxL tensor containing factor exemplars
% H KxT matrix containing factor timecourses
% cost 1x(#Iterations+1) vector containing
% reconstruction error at each iteration.
% cost(1) is error before 1st iteration.
% loadings 1xK vector containing loading of each factor
% (Fraction power in data explained by each factor)
% power Fraction power in data explained
% by whole reconstruction
%
% ------------------------------------------------------------------------
% CREDITS:
% Emily Mackevicius and Andrew Bahle, 2/1/2018
%
% Original CNMF algorithm: Paris Smaragdis 2004
% (https://link.springer.com/chapter/10.1007/978-3-540-30110-3_63)
% Adapted from NMF toolbox by Colin Vaz 2015 (http://sail.usc.edu)
%
% Please cite our paper:
% https://www.biorxiv.org/content/early/2018/03/02/273128
%% parse function inputs
% Check that we have non-negative data
if min(X(:)) < 0
error('Negative values in data!');
end
% Globally rescale data to avoid potential overflow/underflow
% X = X / max(X(:));
% Parse inputs
[X,N,T,K,L,params] = parse_seqNMF_params(X, varargin);
%% initialize
W = params.W_init;
H = params.H_init;
Xhat = helper.reconstruct(W, H);
smoothkernel = ones(1,(2*L)-1); % for factor competition
smallnum = max(X(:))*1e-6;
lasttime = 0;
% Calculate initial cost
cost = zeros(params.maxiter+1, 1);
cost(1) = sqrt(mean((X(:)-Xhat(:)).^2));
for iter = 1 : params.maxiter
% Stopping criteria... Stop if reach maxiter or if change in cost function is less than the tolerance
if (iter == params.maxiter) || ((iter>5) && (cost(iter+1)+params.tolerance)>mean(cost((iter-5):iter)))
cost = cost(1 : iter+1); % trim vector
lasttime = 1;
if iter>1
params.lambda = 0; % Do one final CNMF iteration (no regularization, just prioritize reconstruction)
end
end
% Compute terms for standard CNMF H update
WTX = zeros(K, T);
WTXhat = zeros(K, T);
for l = 1 : L
%X_shifted = circshift(X,-l+1,2);
X_shifted = circshift(X,[0,-l+1]);
%Xhat_shifted = circshift(Xhat,-l+1,2);
Xhat_shifted = circshift(Xhat,[0,-l+1]);
WTX = WTX + W(:, :, l)' * X_shifted;
WTXhat = WTXhat + W(:, :, l)' * Xhat_shifted;
end
% Compute regularization terms for H update
if params.lambda>0
dRdH = params.lambda.*(~eye(K))*conv2(WTX, smoothkernel, 'same');
else
dRdH = 0;
end
if params.lambdaOrthoH>0
dHHdH = params.lambdaOrthoH*(~eye(K))*conv2(H, smoothkernel, 'same');
else
dHHdH = 0;
end
dRdH = dRdH + params.lambdaL1H + dHHdH; % include L1 sparsity, if specified
% Update H
H = H .* WTX ./ (WTXhat + dRdH +eps);
% Shift to center factors
if params.shift
[W, H] = helper.shiftFactors(W, H);
W = W+smallnum; % add small number to shifted W's, since multiplicative update cannot effect 0's
end
% Renormalize so rows of H have constant energy
norms = sqrt(sum(H.^2, 2))';
H = diag(1 ./ (norms+eps)) * H;
for l = 1 : L
W(:, :, l) = W(:, :, l) * diag(norms);
end
if ~params.W_fixed
% Update each Wl separately
Xhat = helper.reconstruct(W, H);
if params.lambdaOrthoW>0
Wflat = sum(W,3);
end
if params.lambda>0 && params.useWupdate
XS = conv2(X, smoothkernel, 'same');
end
for l = 1 : L % could parallelize to speed up for long L
% Compute terms for standard CNMF W update
%H_shifted = circshift(H,l-1,2);
H_shifted = circshift(H,[0,l-1]);
XHT = X * H_shifted';
XhatHT = Xhat * H_shifted';
% Compute regularization terms for W update
if params.lambda>0 && params.useWupdate; % Often get similar results with just H update, so optionto skip W update
dRdW = params.lambda.*XS*(H_shifted')*(~eye(K));
else
dRdW = 0;
end
if params.lambdaOrthoW>0
dWWdW = params.lambdaOrthoW*Wflat*(~eye(K));
else
dWWdW = 0;
end
dRdW = dRdW + params.lambdaL1W + dWWdW; % include L1 and Worthogonality sparsity, if specified
% Update W
W(:, :, l) = W(:, :, l) .* XHT ./ (XhatHT + dRdW + eps);
end
end
% Calculate cost for this iteration
Xhat = helper.reconstruct(W, H);
cost(iter+1) = sqrt(mean((X(:)-Xhat(:)).^2));
% Plot to show progress
if params.showPlot
SimpleWHPlot(W, H, Xhat,0);
title(sprintf('iteration #%i',iter));
drawnow
end
if lasttime
break
end
end
% Undo zeropadding by truncating X, Xhat and H
X = X(:,L+1:end-L);
Xhat = Xhat(:,L+1:end-L);
H = H(:,L+1:end-L);
% Compute explained power of whole reconstruction and each factor
power = (sum(X(:).^2)-sum((X(:)-Xhat(:)).^2))/sum(X(:).^2); % fraction power explained by whole reconstruction
[loadings,ind] = sort(helper.computeLoadingPercentPower(X,W,H),'descend'); % fraction power explained by each factor
% sort factors by loading power
if params.SortFactors
W = W(:,ind,:);
H = H(ind,:);
end
function [X,N,T,K,L,params] = parse_seqNMF_params(X, inputs);
% parse inputs, set unspecified parameters to the defaults
% Get data dimensions
[N, T] = size(X);
p = inputParser; %
%USAGE: addOptional(p,'parametername',defaultvalue);
addOptional(p,'K',10);
addOptional(p,'L',100);
addOptional(p,'lambda',.001);
addOptional(p,'showPlot',1);
addOptional(p,'maxiter',100);
addOptional(p,'tolerance',-Inf);
addOptional(p,'shift',1);
addOptional(p,'lambdaL1W',0);
addOptional(p,'lambdaL1H',0);
addOptional(p,'W_fixed',0);
addOptional(p,'W_init', nan); % depends on K--initialize post parse
addOptional(p,'H_init', nan); % depends on K--initialize post parse
addOptional(p,'SortFactors', 1); % sort factors by loading?
addOptional(p,'lambdaOrthoW',0); % for this regularization: ||Wflat^TWflat||_1,i~=j
addOptional(p,'lambdaOrthoH',0); % for this regularization: ||HSH^T||_1,i~=j
addOptional(p,'useWupdate',1); % W update for cross orthogonality often doesn't change results much, and can be slow, so option to skip it
parse(p,inputs{:});
L = p.Results.L;
K = p.Results.K;
params = p.Results;
% zeropad data by L
X = [zeros(N,L),X,zeros(N,L)];
[N, T] = size(X);
% initialize W_init and H_init, if not provided
if isnan(params.W_init)
params.W_init = max(X(:))*rand(N, K, L);
end
if isnan(params.H_init)
params.H_init = max(X(:))*rand(K,T)./(sqrt(T/3)); % normalize so frobenius norm of each row ~ 1
else
params.H_init = [zeros(K,L),params.H_init,zeros(K,L)];
end
end
end