├── calculate_L.m
├── Proof of Eq.(7).png
├── Go.m
├── IPU.m
├── README.md
└── SDFS.m


/calculate_L.m:
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https://raw.githubusercontent.com/StevenWangNPU/L20_FS_IJCAI2020/HEAD/calculate_L.m


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/Proof of Eq.(7).png:
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https://raw.githubusercontent.com/StevenWangNPU/L20_FS_IJCAI2020/HEAD/Proof of Eq.(7).png


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/Go.m:
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 1 | % max tr(W'AW), subject to W'W=I, ||W||_2,0 <= k
 2 | % W is d-by-m, A is d-by-d
 3 | % Require: m<=k<=d, rank(A)<=m
 4 | 
 5 | function W = Go(A, m, k)
 6 | 
 7 | [d, ~] = size(A);
 8 | Aopt=A;
 9 | 
10 | if rank(A) > m
11 |     [vec, val] = eigs(A, m);
12 |     A = vec * val * vec';
13 | end
14 | 
15 | [~, ind] = sort(diag(A), 'descend');
16 | opt_index = sort(ind(1:k));
17 | 
18 | W = zeros(d, m);
19 | Aopt = Aopt(opt_index, opt_index);
20 | [V, ~] = eigs(Aopt, m);
21 | 
22 | W(opt_index, :) = V;
23 | 
24 | end


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/IPU.m:
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 1 | % max tr(W'AW), subject to W'W=I, ||W||_2,0 <= k
 2 | % W is d-by-m, A is d-by-d
 3 | % Require: m<=k<=d
 4 | function W = IPU(A, m, k,d,W0)
 5 | 
 6 | NITER = 20;
 7 | 
 8 | if nargin < 4
 9 |     W0 = Go(A, m, k);
10 | end
11 | W = W0;
12 | 
13 | if rank(A) <= m
14 |     W = W0;
15 |     return;
16 | end
17 | 
18 | for iter = 1:NITER
19 |    P = A*W*pinv(W'*A*W)*W'*A;
20 |    [~, ind] = sort(diag(P), 'descend');
21 |    opt_index = sort(ind(1:k));
22 |    Aopt = A(opt_index, opt_index);
23 |    [V, ~] = eigs(Aopt, m);
24 |    W(opt_index, :) = V;
25 |    W(setdiff(1:d,opt_index),:) = 0;
26 | end
27 | 
28 | end


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/README.md:
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 1 | # L20-FS
 2 | 
 3 | The matlab function named SDFS is the main funciton of the following paper. If you hava any question and problem, please contact me via 
 4 | email:  zhengwangml@gmail.com
 5 | 
 6 | Discriminative Feature Selection via A Structured Sparse Subspace Learning Module  IJCAI 2020
 7 | 
 8 | please cite our paper by 
 9 | 
10 | @inproceedings{wang2020discriminative,
11 |   title={Discriminative Feature Selection via A Structured Sparse Subspace Learning Module.},
12 |   author={Wang, Zheng and Nie, Feiping and Tian, Lai and Wang, Rong and Li, Xuelong},
13 |   booktitle={IJCAI},
14 |   pages={3009--3015},
15 |   year={2020}
16 | }
17 | 


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/SDFS.m:
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 1 | function [W, obj] = SDFS(X, Y, m, k)
 2 | % X: d by n
 3 | % Y: n by 1
 4 | % Written by Steven Wang, email: zhengwangml@gmail.com
 5 | d = size(X,1);
 6 | W0 = orth(rand(d,m));
 7 | [Sb, Sw, ~, ~] = calculate_L(X',Y);
 8 | lambda = trace(W0'*Sb*W0)/trace(W0'*Sw*W0);
 9 | obj = [];
10 | for iter = 1:50
11 | obj = [obj;lambda];
12 | % The abs of smallest value ensures step 18
13 | eigvalue = eigs(Sb - lambda*Sw,1,'SA');
14 | if eigvalue>=0
15 |     A = Sb - lambda*Sw;
16 | else
17 |     eta = - eigvalue;
18 |     A = Sb - lambda*Sw + eta*eye(d);
19 | end
20 | W = IPU(A,m,k,d,W0);
21 | lambda = trace(W'*Sb*W)/trace(W'*Sw*W);
22 | W0 = W;
23 | end


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