## 6 Conclusions  
In this paper, we propose exploiting robust principal component analysis (RPCA) to extract the sparse partition of the FBANK/MFCC features of noise-corrupted utterances, which corresponds to the speech-dominant elements. The resulting RPCA-wise features show significantly improved recognition performance relative to the original FBANK/MFCC features under the AUORA-4 median-vocabulary recognition task with the renowned deep neural network (DNN) as the acoustic models. Furthermore, the newly proposed features reveal good addition to the popular normalization methods, mean normalization (MN) and relative spectral (RASTA), as the respective integration provides further improvement in recognition accuracy compared with the individual component method. In particular, we do not claim that the proposed RPCA-SPC alone is competitive to state-of-the-art noise-robust algorithms, while it is likely to serve as a pre-processing/post-processing process of other noise-robust methods to achieve better performance. Notably, the acoustic models adopted in the evaluations for RPCA-SPC are either of DNN-HMM and GMM-HMM, while the recent findings reveal that novel deep neural network structures, such as a convolutional neural network (CNN), a recurrent neural network (RNN) and a bi-directional long-short term memory (BLSTM) network, can reduce noise effects significantly for an ASR when they serve as acoustic models. In our opinion, adopting these novel structures alone without any noise-robust feature techniques very likely works well for the ASR in which the training speech data are in a multi-condition manner, i.e., the training set consists of noisy data containing various sources of noise. While an ASR is operated in a clean-condition training scenario, it is less likely that these novel structures can learn the characteristics of noise existing in the application environment. In such a circumstance, a pre-processing stage consisting of noise-robust algorithms, like MN, MVN and the presented RPCA-SPC, for the input speech signals/features is still very beneficial to improve the recognition accuracy of an ASR. In addition, the effectiveness of the presented RPCA-SPC is just evidenced with the Aurora-4 database and task, in which noise-corrupted utterances are created by manually adding noise to clean utterances and thus they are artificial and not real noisy data. However, due to the fact that RPCA-SPC brings about a significant recognition improvement to the Aurora-4 task, it can be reasonably claimed RPCA-SPC is very likely helpful to deal with real noisy data, while this still needs to be further confirmed. As for the future avenue, we will further test RPCA-SPC in real noise-corrupted speech database such as the CHiME-4 dataset [37], investigate whether RPCA-SPC can be well applied to other ASR tasks with different deep learning architectures, and see if it is able to alleviate the reverberant interference in speech signals.  
As for the paper, Prof. [PERSON] gave the main idea, designed the algorithm and the respective experiments and did the most part of writing. Prof. [PERSON] served as a consultant and provided precious comments for revising this paper. Mr. [PERSON] implemented most of the experiments and did some parts of writing.  
Figure 8: The WER (%) for each of the 14 Test Sets of Aurora-4 for GFBANK features using DNN-HMM with respect to the baseline and RPCA-SPC.  
**Funding:** This research is partially sponsored by the Ministry of Science and Technology in Taiwan (Grant Number: MOST 106-2221-E-260-006).  
**Conflicts of Interest:** The authors declare no conflicts of interest.