## 5 Experimental Results and Discussions  
### Individual Method  
To begin with, Tables 1 and 2 show the WER (%) values for the various features including the baseline ones and those processed by any of MN, MVN, RASTA, and RPCA-SPC, with respect to GMM-HMM and DNN-HMM scenarios. From these two tables, we have the following findings:  
1. Both MFCC and FBANK (with GMM-HMM and DNN-HMM as the acoustic models, respectively) give very low WERs for the clean noise-free set, i.e., Set 1. However, FBANK with DNN-HMM outperforms MFCC with GMM-HMM by giving even lower WERs, which is in general attributed to the deep learning scheme in DNN.
2. As for the second sub-group, Sets 2-7, the WERs of both MFCC and FBANK are much higher in comparison with those obtained in Set 1. Thus, we observe that noise deteriorates the performance of speech recognition, and MFCC and FBANK are quite vulnerable to noise. In addition, comparing the WERs obtained from Sets 8-14 with those from Sets 1-7, we see that an extra channel distortion results in further degradation of recognition accuracy. Furthermore, unlike the clean noise-free case, FBANK with DNN-HMM behaves almost equally to MFCC with GMM-HMM, implying that the deep learning structure in acoustic modeling does not necessarily benefit the recognition accuracy under adverse environments.
3. For the clean noise-free case, only MN behaves better than the baseline in promoting both MFCC (with GMM-HMM) and FBANK (with DNN-HMM), while the other methods including MVN, RASTA, and RPCA-SPC worsen the recognition accuracy of the baseline features in particular for the case of GMM-HMM. The probable explanation is as follows: Compared with the other methods, MN simply applies a subtraction operation and does the least change to the original features. By contrast, RASTA and RPCA-SPC always remove some components from speech features in Set 1, which does not have any noise distortion. Accordingly RASTA and PRCA-SPC corrupt clean noise-free speech features by diminishing speech-relevant information or introducing extra distortions.
4. For the mismatched Test Sets (sets 2-7 and 8-14), RPCA-SPC is shown to substantially improve the recognition accuracy relative to the baseline, which undoubtedly shows the effectiveness of the newly proposed RPCA-SPC in enhancing noise robustness of speech features. These results also support our claim that extracting the sparse component in noisy speech features can highlight the clean-speech portion and/or reduce the pure noise portion.
5. For the sets containing noise only (sets 2-7) and the sets containing both channel and noise interferences (sets 8-14), all the methods discussed here provide baseline features with significantly better recognition accuracy. For example, in Sets 2-7, RASTA shows around 23% and 21% in averaged accuracy improvement for the cases of DNN-HMM and GMM-HMM, respectively, and RPCA-SPC gives rise to an averaged accuracy improvement of around 25% and 20% for the cases of DNN-HMM and GMM-HMM, respectively. It is also shown that RPCA-SPC behaves better than MN, MVN, and RASTA in reducing the effect of noise and channel distortions on speech recognition for the case of DNN-HMM.
6. For mismatched noise/channel cases, the recognition accuracy achieved by DNN-HMM is consistently superior to that by GMM-HMM, which coincides with the general idea that deep learning techniques benefit speech recognition. The proposed RPCA-SPC is shown to profit speech features under the DNN-HMM scenario in particular, giving lower word error rates than the other methods, and is thus revealed to further capture the speech-related information beyond what the DNN structure does.