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general_altra.h
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1 /* This program is free software: you can redistribute it and/or modify
2  * it under the terms of the GNU General Public License as published by
3  * the Free Software Foundation, either version 3 of the License, or
4  * (at your option) any later version.
5  *
6  * This program is distributed in the hope that it will be useful,
7  * but WITHOUT ANY WARRANTY; without even the implied warranty of
8  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
9  * GNU General Public License for more details.
10  *
11  * You should have received a copy of the GNU General Public License
12  * along with this program. If not, see <http://www.gnu.org/licenses/>.
13  *
14  * Copyright (C) 2009 - 2012 Jun Liu and Jieping Ye
15  */
16 
17 
18 #ifndef GENERAL_ALTRA_SLEP
19 #define GENERAL_ALTRA_SLEP
20 
21 #include <shogun/lib/config.h>
22 #ifdef USE_GPL_SHOGUN
23 
24 
25 /*
26  * Important Notice: September 20, 2010
27  *
28  * In this head file, we deal with the case that the features might not be well ordered.
29  *
30  * If the features in the tree strucutre are well ordered, i.e., the indices of the left nodes is always less
31  * than the right nodes, please refer to "altra.h".
32  *
33  * The advantage of "altra.h" is that, we donot need to use an explicit
34  * variable for recording the indices.
35  *
36  *
37  */
38 
39 /*
40  * -------------------------------------------------------------------
41  * Functions and parameter
42  * -------------------------------------------------------------------
43  *
44  * general_altra solves the following problem
45  *
46  * 1/2 \|x-v\|^2 + \sum \lambda_i \|x_{G_i}\|,
47  *
48  * where x and v are of dimension n,
49  * \lambda_i >=0, and G_i's follow the tree structure
50  *
51  * It is implemented in Matlab as follows:
52  *
53  * x=general_altra(v, n, G, ind, nodes);
54  *
55  * G contains the indices of the groups.
56  * It is a row vector. Its length equals to \sum_i \|G_i\|.
57  * If all the entries are penalized with L1 norm,
58  * its length is \sum_i \|G_i\| - n.
59  *
60  * ind is a 3 x nodes matrix.
61  * Each column corresponds to a node.
62  *
63  * The first element of each column is the starting index,
64  * the second element of each column is the ending index
65  * the third element of each column corrreponds to \lambbda_i.
66  *
67  *
68  *
69  * The following example shows how G and ind works:
70  *
71  * G={ {1, 2}, {4, 5}, {3, 6}, {7, 8},
72  * {1, 2, 3, 6}, {4, 5, 7, 8},
73  * {1, 2, 3, 4, 5, 6, 7, 8} }.
74  *
75  * ind={ [1, 2, 100]', [3, 4, 100]', [5, 6, 100]', [7, 8, 100]',
76  * [9, 12, 100]', [13, 16, 100]', [17, 24, 100]' }
77  *
78  * where "100" denotes the weight for the nodes.
79  *
80  *
81  *
82  * -------------------------------------------------------------------
83  * Notices:
84  * -------------------------------------------------------------------
85  *
86  * 1. The features in the tree might not be well ordered. Otherwise, you are
87  * suggested to use "altra.h".
88  *
89  * 2. When each elements of x are penalized via the same L1
90  * (equivalent to the L2 norm) parameter, one can simplify the input
91  * by specifying
92  * the "first" column of ind as (-1, -1, lambda)
93  *
94  * In this case, we treat it as a single "super" node. Thus in the value
95  * nodes, we only count it once.
96  *
97  * 3. The values in "ind" are in [1,length(G)].
98  *
99  * 4. The third element of each column should be positive. The program does
100  * not check the validity of the parameter.
101  *
102  * 5. The values in G should be within [1, n].
103  *
104  * It is still valid to use the zero regularization parameter.
105  * In this case, the program does not change the values of
106  * correponding indices.
107  *
108  *
109  * -------------------------------------------------------------------
110 * History:
111 * -------------------------------------------------------------------
112 *
113 * Composed by Jun Liu on April 20, 2010
114 *
115 * For any question or suggestion, please email j.liu@asu.edu.
116 *
117 */
118 void general_altra(double *x, double *v, int n, double *G, double *ind, int nodes, double mult=1.0);
119 
120 /*
121  * altra_mt is a generalization of altra to the
122  *
123  * multi-task learning scenario (or equivalently the multi-class case)
124  *
125  * altra_mt(X, V, n, k, G, ind, nodes);
126  *
127  * It applies altra for each row (1xk) of X and V
128  *
129  */
130 void general_altra_mt(double *X, double *V, int n, int k, double *G, double *ind, int nodes, double mult=1.0);
131 
132 /*
133  * compute
134  * lambda2_max=general_computeLambda2Max(x,n,G, ind,nodes);
135  *
136  * compute the 2 norm of each group, which is divided by the ind(3,:),
137  * then the maximum value is returned
138  */
139 /*
140  *This function does not consider the case ind={[-1, -1, 100]',...}
141  *
142  *This functions is not used currently.
143  */
144 void general_computeLambda2Max(double *lambda2_max, double *x, int n, double *G, double *ind, int nodes);
145 
146 /*
147  * -------------------------------------------------------------------
148  * Function and parameter
149  * -------------------------------------------------------------------
150  *
151  * treeNorm compute
152  *
153  * \sum \lambda_i \|x_{G_i}\|,
154  *
155  * where x is of dimension n,
156  * \lambda_i >=0, and G_i's follow the tree structure
157  *
158  * The file is implemented in the following in Matlab:
159  *
160  * tree_norm=general_treeNorm(x, n, G, ind,nodes);
161  */
162 double general_treeNorm(double *x, int ldx, int n, double *G, double *ind, int nodes);
163 
164 /*
165  * -------------------------------------------------------------------
166  * Function and parameter
167  * -------------------------------------------------------------------
168  *
169  * findLambdaMax compute
170  *
171  * the lambda_{max} that achieves a zero solution for
172  *
173  * min 1/2 \|x-v\|^2 + \lambda_{\max} * \sum w_i \|x_{G_i}\|,
174  *
175  * where x is of dimension n,
176  * w_i >=0, and G_i's follow the tree structure
177  *
178  * The file is implemented in the following in Matlab:
179  *
180  * lambdaMax=general_findLambdaMax(v, n, G, ind,nodes);
181  */
182 double general_findLambdaMax(double *v, int n, double *G, double *ind, int nodes);
183 
184 /*
185  * findLambdaMax_mt is a generalization of findLambdaMax to the
186  *
187  * multi-task learning scenario (or equivalently the multi-class case)
188  *
189  * lambdaMax=general_findLambdaMax_mt(X, V, n, k, G, ind, nodes);
190  *
191  * It applies findLambdaMax for each row (1xk) of X and V
192  *
193  */
194 double general_findLambdaMax_mt(double *V, int n, int k, double *G, double *ind, int nodes);
195 #endif //USE_GPL_SHOGUN
196 #endif /* ----- #ifndef GENERAL_ALTRA_SLEP ----- */
197 

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