Sparse PCA: a Geometric Approach
Authors: Dimitris Bertsimas, Driss Lahlou Kitane
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test the proposed method on publicly available real world data sets and compare its performance vs. existing methods and show that the geometrical approach produces solutions of higher quality than alternative state-of-the-art methods. We report results in Table 1. |
| Researcher Affiliation | Academia | Dimitris Bertsimas EMAIL Driss Lahlou Kitane EMAIL Operations Research Center Massachusetts Institute of Technology 77, Massachusetts Ave. Cambridge, MA 02138, USA |
| Pseudocode | Yes | Algorithm 1: Constraints generation algorithm for PCs with a common support Algorithm 2: Approximate solution for problem (2) Algorithm 3: Constraints generation algorithm for group of PCs with disjoint supports |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that the authors' implementation code for the described methodology is publicly available. |
| Open Datasets | Yes | We selected publicly available data sets that are widely used in the literature including Mturk (n; p) = (180; 500) (Cheng et al., 2016) ... Colon (n; p) = (62; 2, 000) (Alon et al., 1999) ... Arcene (n, p) = (700; 10, 000) ... (Guyon et al., 2007) and CGD (n; p) = (286; 22, 283) (Wang et al., 2005) ... We chose to use face recognition for its ease of interpretation to test the method and use the data set (Martinez and Kak, 2001). |
| Dataset Splits | Yes | For each person, 26 pictures are provided with the different face expressions and lightning configurations. In 12 of the 26 pictures, parts of the face is hidden either by black glasses or scarves (a sample of pictures is provided in Figure7). ... for each person represented in the data set, we use the 14 pictures in which the whole face is visible for training and test on the 12 pictures in which part of the face is hidden. |
| Hardware Specification | Yes | All tests are conducted computations on an Intel Core i7-8750H CPU at 2.20GHz with 16Gb of RAM on Windows 10 Pro. |
| Software Dependencies | Yes | The solver we used is Gurobi Optimizer 9.1 running with Python 3.6.5. |
| Experiment Setup | Yes | We first tune a by finding a suitable number of PCs for the classic PCA following a standard procedure. ... The parameter η is found using Algorithm 2. We start by choosing η0 that is large (for example ||X||2 F ) and then Algotrithm 2 tightens the values of η by updating ηt. ... For Geo SSPCA, we choose k = 5 and increase a to have a number of PCs varying from 10 to 70. ... the resolution of the images is reduced from 165 × 120 to 38 × 27 |