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src
shogun
lib
slep
flsa
flsa.h
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/* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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* Copyright (C) 2009 - 2012 Jun Liu and Jieping Ye
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*/
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#ifndef FLSA_SLEP
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#define FLSA_SLEP
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#include <
shogun/lib/config.h
>
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/*
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In this file, we solve the Fused Lasso Signal Approximator (FLSA) problem:
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min_x 1/2 \|x-v\|^2 + lambda1 * \|x\|_1 + lambda2 * \|A x\|_1, (1)
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It can be shown that, if x* is the solution to
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min_x 1/2 \|x-v\|^2 + lambda2 \|A x\|_1, (2)
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then
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x**= sgn(x*) max(|x*|-lambda_1, 0) (3)
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is the solution to (1).
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By some derivation (see the description in sfa.h), (2) can be solved by
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x*= v - A^T z*,
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where z* is the optimal solution to
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min_z 1/2 z^T A AT z - < z, A v>,
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subject to \|z\|_{infty} \leq lambda2 (4)
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*/
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/*
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In flsa, we solve (1) corresponding to a given (lambda1, lambda2)
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void flsa(double *x, double *z, double *gap,
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double * v, double *z0,
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double lambda1, double lambda2, int n,
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int maxStep, double tol, int flag)
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Output parameters:
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x: the solution to problem (1)
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z: the solution to problem (4)
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infor: the information about running the subgradient finding algorithm
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infor[0] = gap: the computed gap (either the duality gap
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or the summation of the absolute change of the adjacent solutions)
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infor[1] = steps: the number of iterations
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infor[2] = lambad2_max: the maximal value of lambda2_max
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infor[3] = numS: the number of elements in the support set
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Input parameters:
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v: the input vector to be projected
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z0: a guess of the solution of z
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lambad1: the regularization parameter
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labmda2: the regularization parameter
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n: the length of v and x
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maxStep: the maximal allowed iteration steps
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tol: the tolerance parameter
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tau: the program sfa is checked every tau iterations for termination
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flag: the flag for initialization and deciding calling sfa
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switch ( flag )
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1-4, 11-14: sfa
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switch ( flag )
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case 1, 2, 3, or 4:
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z0 is a "good" starting point
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(such as the warm-start of the previous solution,
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or the user want to test the performance of this starting point;
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the starting point shall be further projected to the L_{infty} ball,
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to make sure that it is feasible)
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case 11, 12, 13, or 14: z0 is a "random" guess, and thus not used
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(we shall initialize z as follows:
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if lambda2 >= 0.5 * lambda_2^max, we initialize the solution of the linear system;
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if lambda2 < 0.5 * lambda_2^max, we initialize with zero
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this solution is projected to the L_{infty} ball)
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switch( flag )
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5, 15: sfa_special
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switch( flag )
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5: z0 is a good starting point
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15: z0 is a bad starting point, use the solution of the linear system
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switch( flag )
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6, 16: sfa_one
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switch( flag )
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6: z0 is a good starting point
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16: z0 is a bad starting point, use the solution of the linear system
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Revision made on October 31, 2009.
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The input variable z0 is not modified after calling sfa. For this sake, we allocate a new variable zz to replace z0.
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*/
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void
flsa
(
double
*x,
double
*z,
double
*infor,
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double
* v,
double
*z0,
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double
lambda1,
double
lambda2,
int
n,
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int
maxStep,
double
tol,
int
tau,
int
flag);
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#endif
/* ----- #ifndef FLSA_SLEP ----- */
config.h
flsa
void flsa(double *x, double *z, double *infor, double *v, double *z0, double lambda1, double lambda2, int n, int maxStep, double tol, int tau, int flag)
Definition:
flsa.cpp:24
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