Research map / Learning theory and algorithms / Matrix and tensor methods
Upper bounds for Model-Free Row-Sparse Principal Component Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace exact sparse PCA feasible region with SOCP convex relaxation (SOCP-Relax) and piecewise-linear SOS-II upper bounding (SOCIP-impl) for dual bounds | Sparse PCA upper bound (SOCIP-impl) · Artificial blocked spiked covariance (d=500), r=2,3 | primal-dual gap | Helped |
| Use SOCIP-impl dual bound instead of Baseline-1 (sum of top-k diagonal entries) | Real instances Eisen-1, Eisen-2 · Eisen-1 (d=79), Eisen-2 (d=118) | primal-dual gap | Helped |
| Use SOCIP-impl instead of Baseline-1 as dual bound as k increases | Colon cancer, Lymphoma, Reddit real data · d=500 and d=1000/2000 real data | primal-dual gap | Mixed |
| Use SDP lifted relaxation (Baseline-2) as dual bound | Sparse PCA dual bound · Artificial and real instances with d=500 to 2000 | feasibility of obtaining bounds | Hurt |
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