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Register a new userDeep Generalized Canonical Correlation Analysis
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Adrian Benton
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We present Deep Generalized Canonical Correlation Analysis (DGCCA) -- a method for learning nonlinear transformations of arbitrarily many views of data, such that the resulting transformations are maximally informative of each other. While methods for nonlinear two-view representation learning (Deep CCA, (Andrew et al., 2013)) and linear many-view representation learning (Generalized CCA (Horst, 1961)) exist, DGCCA is the first CCA-style multiview representation learning technique that combines the flexibility of nonlinear (deep) representation learning with the statistical power of incorporating information from many independent sources, or views. We present the DGCCA formulation as well as an efficient stochastic optimization algorithm for solving it. We learn DGCCA representations on two distinct datasets for three downstream tasks: phonetic transcription from acoustic and articulatory measurements, and recommending hashtags and friends on a dataset of Twitter users. We find that DGCCA representations soundly beat existing methods at phonetic transcription and hashtag recommendation, and in general perform no worse than standard linear many-view techniques.
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Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word embedding, and clustering. Recent work has given CCA probabilistic footing in a deep learning context and uses a variational lower bound for the data log likelihood to estimate model parameters. Alternatively, adversarial techniques have arisen in recent years as a powerful alternative to variational Bayesian methods in autoencoders. In this work, we explore straightforward adversarial alternatives to recent work in Deep Variational CCA (VCCA and VCCA-Private) we call ACCA and ACCA-Private and show how these approaches offer a stronger and more flexible way to match the approximate posteriors coming from encoders to much larger classes of priors than the VCCA and VCCA-Private models. This allows new priors for what constitutes a good representation, such as disentangling underlying factors of variation, to be more directly pursued. We offer further analysis on the multi-level disentangling properties of VCCA-Private and ACCA-Private through the use of a newly designed dataset we call Tangled MNIST. We also design a validation criteria for these models that is theoretically grounded, task-agnostic, and works well in practice. Lastly, we fill a minor research gap by deriving an additional variational lower bound for VCCA that allows the representation to use view-specific information from both input views.
We present an efficient stochastic algorithm (RSG+) for canonical correlation analysis (CCA) using a reparametrization of the projection matrices. We show how this reparametrization (into structured matrices), simple in hindsight, directly presents an opportunity to repurpose/adjust mature techniques for numerical optimization on Riemannian manifolds. Our developments nicely complement existing methods for this problem which either require $O(d^3)$ time complexity per iteration with $O(frac{1}{sqrt{t}})$ convergence rate (where $d$ is the dimensionality) or only extract the top $1$ component with $O(frac{1}{t})$ convergence rate. In contrast, our algorithm offers a strict improvement for this classical problem: it achieves $O(d^2k)$ runtime complexity per iteration for extracting the top $k$ canonical components with $O(frac{1}{t})$ convergence rate. While the paper primarily focuses on the formulation and technical analysis of its properties, our experiments show that the empirical behavior on common datasets is quite promising. We also explore a potential application in training fair models where the label of protected attribute is missing or otherwise unavailable.
Multimodal signals are more powerful than unimodal data for emotion recognition since they can represent emotions more comprehensively. In this paper, we introduce deep canonical correlation analysis (DCCA) to multimodal emotion recognition. The basic idea behind DCCA is to transform each modality separately and coordinate different modalities into a hyperspace by using specified canonical correlation analysis constraints. We evaluate the performance of DCCA on five multimodal datasets: the SEED, SEED-IV, SEED-V, DEAP, and DREAMER datasets. Our experimental results demonstrate that DCCA achieves state-of-the-art recognition accuracy rates on all five datasets: 94.58% on the SEED dataset, 87.45% on the SEED-IV dataset, 84.33% and 85.62% for two binary classification tasks and 88.51% for a four-category classification task on the DEAP dataset, 83.08% on the SEED-V dataset, and 88.99%, 90.57%, and 90.67% for three binary classification tasks on the DREAMER dataset. We also compare the noise robustness of DCCA with that of existing methods when adding various amounts of noise to the SEED-V dataset. The experimental results indicate that DCCA has greater robustness. By visualizing feature distributions with t-SNE and calculating the mutual information between different modalities before and after using DCCA, we find that the features transformed by DCCA from different modalities are more homogeneous and discriminative across emotions.
For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected datasets, compared to standard Canonical Correlation Analysis (CCA) using only two data sets. We illustrate our theoretical results with simulations and a real data experiment.
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve $epsilon$-suboptimality in the population objective in $operatorname{poly}(frac{1}{epsilon})$ iterations. We also consider practical variants of the proposed algorithms and compare them with other methods for CCA both theoretically and empirically.
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