An Algorithm for Adjusted Kernel Linear Discriminant Analysis

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 An Algorithm for Adjusted Kernel Linear Discriminant Analysis Shiny App demo: : https:

An Algorithm for Adjusted Kernel Linear Discriminant Analysis Shiny App demo: : https: //lynnh 20. shinyapps. io/KLDA/. INTRODUCTION THE ALGORITHM Datasets with large amounts of features often contain noise and redundant information. Dimension reduction techniques may be implemented as a preprocessing step to such datasets in order to condense information while still retaining relevant information. Kernel Linear Discriminant Analysis (KLDA) is a kernel based method of dimension reduction that is able to separate non-linear data. In this work, we introduce an algorithm for ”adjusted” KLDA that extends beyond the capabilities of a previous implementation by allowing for approximations of non-invertible matrices defined in its objective function. • RESULTS KLDA projections of gender and race for SE and each set of extracted features. • Figure (b) LDA • EXPERIMENTAL DESIGN Morph-II [1] is a database containing 55, 134 mugshot images of 13, 617 unique individuals, as well as relevant metadata detailing age, gender, race, etc. The large scale of the Morph-II database makes it an ideal choice for modeling gender and race classifiers for facial recognition. Hispanic 4% Asian 0% Other 0% Female 16% White 20% Gender Classification Model Performance Logistic LDA Reg. KNN (K=7) Bagging Boosting SVM Male 84% Figure 2 Figure 1 Figures 1 and 2 depict the race and gender composition of the unique individuals in the Morph-II dataset. KLDA This uneven distribution of race and gender shown in the charts above can lead to overfitting in statistical modeling. To remediate this issue, we train our models with the images in an “even” subset of 1000 images, SE , that has as 3: 1 male to female ratio, and a 1: 1 black to white ratio. • SE + LBP SE + HOG Figure 3. Feature extraction methods for SE. ACKNOWLEDGEMENTS This project was funded by NSF grant 1659288. Special thanks to Dr. Yishi Wang and Dr. Cuixian Chen for their guidance and support throughout this research project. I would also like to thank Jackson Maris, Jaime Seith, and Ryan Wood. KNN (K=7) Bagging Boosting SVM . 906 . 901. 907 . 908 BIF . 962 . 96 . 959 . 951 . 954 . 963 LBP . 919 . 917. 919 . 92 . 91 LBP . 977 . 972. 974 . 972 . 979 HOG. 657 . 663. 654 . 652 . 696 . 726 HOG . 48 . 469. 471 . 468 Table 2 LBP features produce slightly more accurate models than BIF features do after undergoing KLDA, while HOG features seem to be unsuited for classifying race and gender. The difference between the BIF and LBP models may be because the separations within the LBP set are slightly better, rather than due to the features themselves. Within subsets, no statistical model significantly outperforms the others. CONCLUSIONS From the results, we see that the adjusted KDLA function can efficiently separate gender and race within the Morph-II dataset. This is reflected in the performance of the models using BIF and LBP features after reducing dimensions with KLDA. Because tuning parameters were manually selected, it is unclear if they are truly “optimal”. Future directions may include developing a more systematic method of tuning parameter selecting. Furthermore, given a more even and diverse dataset, adjusted KLDA may be used for multiple race classification models, rather than the binary ones featured in this project. SE + BIF SE Logistic LDA Reg. BIF Table 1 Black 76% Race Classification Model Performance Figure 4. Visualizing the race and gender make up of SE. KLDA is performed as a dimension reduction technique to 3 versions of a subset of the Morph-II dataset. Each version consists of the images in SE, and an attached set of optimally tuned [3] extracted features: BIF, LBP, or HOG [4]. We tune the adjusted KLDA function through visual analysis of projections. Once we have determined which tuning parameters to use, the transformed features are used to train and test several statistical models. REFERENCES [1] K. Ricanek and T. Tesafaye, “MORPH: a longitudinal image database of normal adult age-progression, ” 7 th International Conference on Automatic Face and Gesture Recognition (FGR 06), Southampton, 2006, pp. 341 -345. [2] S. Mika, G. Ratsch, J. Weston, B. Sch¨olkopf and K. R. Mullers, “Fisher discriminant analysis with kernels, ” Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No. 98 TH 8468), Madison, WI, 1999, pp. 41 -48. [3] K. Kempfert. Nonlinear dimension reduction using kernel representations. NSF-REU site at UNC Wilmington, 2017. [4] T. P. Kling. Morph-ii: Feature vector documentation. NSF-REU site at UNC Wilmington, 2017.