A Taxonomy of Emerging Multilinear Discriminant Analysis Solutions in .NET

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A Taxonomy of Emerging Multilinear Discriminant Analysis Solutions
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1.LDA 2.ULDA 3.DATER 4.GTDA 5.TR1DA 6.UMLDA 10 Number of Features (c) PIET30R20 CCR D2
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1.LDA 2.ULDA 3.DATER 4.GTDA 5.TR1DA 6.UMLDA 10 Number of Features (d)
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Figure 2.8. (Continued)
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Table 2.2. Face Recognition Results on PIE Database L 5 10 20 30 Fisherface (LDA) 0.574 0.708 0.785 0.891 ULDA 0.626 0.684 0.774 0.880 DATER 0.651 0.776 0.866 0.906 GTDA 0.537 0.684 0.801 0.856 TR1DA 0.370 0.525 0.672 0.749 UMLDA 0.639 0.763 0.856 0.894
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2.4 Empirical Comparison of MLDA Variants on Face Recognition
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Face Recognition Results on YaleB Database
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The Extended Yale face database B (YaleB) consists of 2414 frontal face images of 38 individuals, which were captured under various laboratory-controlled lighting conditions. There are about 64 samples per subject and 60 sample face images for a subject are shown in Figure 2.7b. Figure 2.9 shows the detailed face recognition results on the YaleB database; and the best results for each algorithm on the YaleB database are reported in Table 2.3, in a similar way as Section 2.4.2 for various values of L.
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1.LDA 2.ULDA 3.DATER 4.GTDA 5.TR1DA 6.UMLDA 10
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Figure 2.9. Detailed face recognition results on the YaleB database with (a) L = 5, (b) L = 10, (c)
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L = 20, and (d) L = 30.
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A Taxonomy of Emerging Multilinear Discriminant Analysis Solutions
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1.LDA 2.ULDA 3.DATER 4.GTDA 5.TR1DA 6.UMLDA 10 Number of Features (c) YaleBT30R20 CCR D2
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1.LDA 2.ULDA 3.DATER 4.GTDA 5.TR1DA 6.UMLDA 10 Number of Features
Figure 2.9. (Continued)
From the detailed results in Figure 2.9, it can be seen that the rst a few features extracted by the UMLDA algorithm again consistently outperforms all the other algorithms. The heuristic TR1DA algorithm performs the worst for L = 5, 10. From Table 2.3, the DATER algorithm outperforms the GTDA slightly on the YaleB
Table 2.3. Face Recognition Results on YaleB Database L 5 10 20 30 Fisherface (LDA) 0.653 0.783 0.858 0.812 ULDA 0.632 0.695 0.628 0.792 DATER 0.685 0.797 0.870 0.900 GTDA 0.657 0.777 0.856 0.894 TR1DA 0.480 0.640 0.758 0.819 UMLDA 0.720 0.831 0.892 0.921
2.4 Empirical Comparison of MLDA Variants on Face Recognition
database but the performance gap is quite small. Overall, the MLDA variants based on scatter ratio again obtained better results than the MLDA variants based on scatter difference. As in Section 2.4.2, we focus on the scatter-ratio-based variants, UMLDA and DATER, for the comparison between MLDA-TTP and MLDA-TVP. From Figure 2.9 and Table 2.3, UMLDA consistently outperforms DATER signi cantly on this database, especially for a smaller L, although the performance of UMLDA deteriorates when the number of features exceeds a certain number. Thus, on this database the UMLDA, an MLDA-TVP approach extracting uncorrelated features, shows its advantage against the MLDA-TTP approach, where the features can be viewed to be extracted through interdependent EMPs. Regarding the comparison between LDA and MLDA, there is an interesting observation from this experiment. For the Fisherface (LDA) approach, when L increases from 20 to 30, the recognition rate ironically decreases, as seen in Table 2.3. For the ULDA, when L increases from 10 to 20, the recognition rate surprisingly decreases too, as in Table 2.3. This is in contrary with our belief that more training samples should result in better recognition performance. On the other hand, all the four MLDA variants do not have this problem on this database, with recognition rate increasing as L increases, showing that MLDA approaches are more stable and consistent. Furthermore, the UMLDA algorithm outperforms the LDA and ULDA signi cantly, especially for a larger L, demonstrating again the bene ts of extracting features directly from the natural 2-D representation of face images rather than from their vectorized representation.
Discussions
In summary, through the comparison in Figures 2.8 and 2.9 and in Tables 2.2 and 2.3, it can be seen that by treating face images in their natural 2-D representation, the MLDA solution UMLDA achieves very good recognition results consistently on two very challenging face databases, for various number of training samples per subjects (L = 5, 10, 20, and 30). It is also observed that the MLDA variants based on scatter ratio generally outperform the MLDA variants based on scatter difference; and with scatter ratio as the separation criterion, the overall performance of MLDA-TVP is better than that of MLDA-TTP. In addition, MLDA variants are shown to be more stable and consistent than LDA approaches. Considering the short period of research and development in multilinear learning solutions for biometric signal recognition, the empirical evaluation results presented here are very encouraging and we believe that there is still great potential in further development of multilinear learning algorithms that operate directly on natural tensorial representations. The materials provided in this chapter represent a good starting point for newcomers to this eld; and the taxonomy of various multilinear projections and MLDA variants, together with discussions on their connections, is also bene cial for researchers already working in this eld.