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small pieces and updates learned patterns gradually using accumulated statistics. With this approach, only a limited segment of the input signal is processed at a time. The online estimated dictionary is sufficient enough in basis subspace to avoid speech distortion. The

The computing demand for both offline learning and online learning consists of updating the coefficient matrix C and the pattern matrix D. The learning task is defined as an optimization problem, which aims to minimize an objective cost function f(D) with respect to the pattern matrix D. It is observed that the reconstruction error for both the online and offline methods converges to a similar value after several iterations and not monotonically decreasing at the beginning. Both batch and online learning converge to a stationary point of the expected cost function f(D) with unlimited data and unlimited computing resources. This situation is only valid in theory. For small-scale tasks where data are limited, but computing resources are unlimited, batch learning converges to a stationary point of the cost function ft(D), while online learning fails to converge, resulting in suboptimal patterns. For large-scale tasks, the more common situation is where training data are abundant but computing resources are limited. In this situation, due to its early learning property, online learning tends to obtain lower empirical cost than batch learning [49]. For sparse coding where the pattern matrix is overcomplete, for example, (K > M), then online learning is slower than batch learning. The online learning is significantly faster than the batch alternating learning by a factor of the large number of

In short, dictionary learning plays an important role in machine learning, where data vectors are modeled as sparse linear combinations of basis factors (i.e., dictionary). However, how to conduct dictionary learning in noisy environment has not been well studied. In this chapter, we have reviewed speech enhancement techniques based on dictionary learning. The dictionary learning-based algorithms have gained a lot of attention due to their success in finding high-"quality" dictionary atoms (basis vectors) that best describe latent features of the underprocessed data. As a multivariate data analysis and dimensionality reduction technique, two relatively novel paradigms for dimensionality reduction and sparse representation, NMF and SR, have been in the ascendant since its inception. They enhance learning and data representation due to their parts-based and sparse representation from the nonnegativity or purely additive constraint. NMF and SR produce high-quality enhancement results when the dictionaries for different sources are sufficiently distinct. This survey chapter mainly focuses on the theoretical research into dictionary learning-based speech enhancement where the principles, basic models, properties, algorithms, and employing on SR and NMF are summa-

This research is partially supported by the Ministry of Science and Technology under Grant Number 108-2634-F-008 -004 through Pervasive Artificial Intelligence Research (PAIR) Labs,

online approaches tend to give better performance than batch learning [53].

spectrograms reconstructed at each iteration [60].

rized systematically.

82 Active Learning - Beyond the Future

Taiwan.

Acknowledgements

Viet-Hang Duong<sup>1</sup> , Manh-Quan Bui<sup>2</sup> and Jia-Ching Wang2,3\*

\*Address all correspondence to: jiacwang@gmail.com

1 Faculty of Information Technology, BacLieu University, Vietnam

2 Department of Computer Science Information Engineering, National Central University, Taiwan

3 Pervasive Artificial Intelligence Research (PAIR) Labs, Taiwan
