Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach
Abstract
:1. Introduction
2. Previous Work
3. Problem Formulation
4. Iterative Projections Solution
Optimality Conditions
- 1.
- 2.
Algorithm 1 Arimoto Blahut pseudocode for rate distortion with second order statistics constraints |
Require: Ensure: Fix
|
5. Compressed Representation CCA for Empirical Data
5.1. Previous Results
5.2. Our Suggested Method
5.2.1. Lattice Quantization
5.2.2. CRCCA by Quantization
Algorithm 2 A single step of CRCCA by quantization |
Require: , a fixed uniform quantizer
|
5.2.3. Convergence Analysis
5.3. Regularization
6. Experiments
6.1. Synthetic Experiments
6.2. Real-World Experiment
7. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. A Proof for Lemma 1
Appendix B. A Proof for Lemma 2
Appendix C. Synthetic Experiment Description
Appendix D. Visualizations of the Real World Experiment
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Painsky, A.; Feder, M.; Tishby, N. Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach. Entropy 2020, 22, 208. https://doi.org/10.3390/e22020208
Painsky A, Feder M, Tishby N. Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach. Entropy. 2020; 22(2):208. https://doi.org/10.3390/e22020208
Chicago/Turabian StylePainsky, Amichai, Meir Feder, and Naftali Tishby. 2020. "Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach" Entropy 22, no. 2: 208. https://doi.org/10.3390/e22020208