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Algorithm Experiments Conclusions RS-2DLDA Random Subspace Two-dimensional LDA for Face Recognition Garrett Bingham B.S. Computer Science & Mathematics, Yale University 19 July 25, 2017 RS-2DLDA Garrett Bingham 1 Algorithm

  1. Algorithm Experiments Conclusions RS-2DLDA Random Subspace Two-dimensional LDA for Face Recognition Garrett Bingham B.S. Computer Science & Mathematics, Yale University ’19 July 25, 2017 RS-2DLDA Garrett Bingham 1

  2. Algorithm Experiments Conclusions Table of Contents 1. Algorithm Background Information RS-2DLDA 2. Experiments Datasets Experiment Design Results 3. Conclusions Insights Future Work References RS-2DLDA Garrett Bingham 2

  3. Algorithm Background Information Experiments RS-2DLDA Conclusions Algorithm RS-2DLDA Garrett Bingham 3

  4. Algorithm Background Information Experiments RS-2DLDA Conclusions Linear Discriminant Analysis Principal Component Analysis • Keeps images of the same • Spreads the data out as much person close together, while as possible spreading those of different • Useful in dimensionality people farther apart reduction • Generally more effective in face • Doesn’t consider which images recognition than PCA belong to which people https://sebastianraschka.com/images/blog/2014/linear-discriminant-analysis/lda_1.png RS-2DLDA Garrett Bingham 4

  5. Algorithm Background Information Experiments RS-2DLDA Conclusions 2D Version Normally, image matrices are first converted to 1D vectors. In 2DLDA and 2DPCA how- ever, they are left in matrix form. Advantages include: • Avoids using high-dimensional vectors, making it computationally efficient • Structure of face is preserved RS-2DLDA Garrett Bingham 5

  6. Algorithm Background Information Experiments RS-2DLDA Conclusions Right, Left, and Bilateral Projection Schemes Y j = U T A j Y j = A j V Image reconstruction by R2DPCA and L2DPCA of an example ORL image. RS-2DLDA Garrett Bingham 6

  7. Algorithm Background Information Experiments RS-2DLDA Conclusions 2DLDA In 2DLDA we keep the top d eigenvectors. Each image matrix is multiplied by these eigenvectors and projected to a new space. If we choose d too small, accuracy will be poor. On the other hand, if d is too large the algorithm will overfit to the training data and won’t be able to generalize to new information. RS-2DLDA Garrett Bingham 7

  8. Algorithm Background Information Experiments RS-2DLDA Conclusions Applying the Random Subspace Method In RS-2DLDA, we select d eigenvectors at random to make one classifier. we can repeat this many times, creating several different classifiers. This allows us to utilize the information from all eigenvectors without risk of overfitting. If each classifier makes different mistakes, then we can combine their outputs into one final decision to increase accuracy. This is known as a diverse set of classifiers. We can quantify diversity with entropy measure. RS-2DLDA Garrett Bingham 8

  9. Algorithm Background Information Experiments RS-2DLDA Conclusions Entropy Experiments Figure: Choosing 10 random eigenvectors results in high entropy If we choose too few eigenvectors, each classifier is too weak and makes a large number of errors, resulting in low entropy. On the other hand, if we choose too many eigenvectors, then the classifiers will make near identical predictions, again resulting in low entropy. RS-2DLDA Garrett Bingham 9

  10. Algorithm Background Information Experiments RS-2DLDA Conclusions Entropy Experiments Figure: Entropy levels off Not training enough classi- fiers results in low entropy, be- cause we haven’t sampled the eigenvectors thoroughly. Changing these parameters affects the entropy, but the accuracy remains more or less stable. This implies that although we aren’t affecting the the unweighted accuracy, we may be able to increase overall accuracy with a weighted voting scheme. RS-2DLDA Garrett Bingham 10

  11. Algorithm Background Information Experiments RS-2DLDA Conclusions Estimating Classifier Performance The adjusted Rand index (ARI) is a clustering similarity measure. We use it to measure how well each classifier keeps images of the same person close together. We suspect that classifiers with a higher ARI will be more accurate on the testing data. We want to give classifiers that have a higher ARI more weight in the final decision. If we raise each ARI to a common exponent b , we can control how much extra in- fluence the strong classifiers have over the weak ones. RS-2DLDA Garrett Bingham 11

  12. Algorithm Background Information Experiments RS-2DLDA Conclusions Weighting Scheme Figure: The weighting scheme is tested on MORPH-II using two different random seeds Choosing a moderate value for b gives an extra 2-5% in overall accuracy. The optimal value for b may be different with datasets of different size and difficulty. RS-2DLDA Garrett Bingham 12

  13. Algorithm Datasets Experiments Experiment Design Conclusions Results Experiments RS-2DLDA Garrett Bingham 13

  14. Algorithm Datasets Experiments Experiment Design Conclusions Results ORL The ORL dataset contains images of 40 people collected from 1992 to 1994. Each image was collected in a lab, is grayscale, and has dimension 112 × 92. There are 10 images per person, each with minor variations in pose and facial expression. Available at http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html RS-2DLDA Garrett Bingham 14

  15. Algorithm Datasets Experiments Experiment Design Conclusions Results MORPH-II The MORPH-II dataset [5] is a longitudinal dataset collected over five years. It contains 55,134 images from 13,617 individuals. Subjects’ ages range from 16-77 years of age. MORPH-II suffers from high variability in pose, facial expression, and illumination. To account for this, the images were rotated so that the eyes were horizontal, and then cropped to 70 × 60 to reduce noise from the background or the subject’s hair. Example pre-processed MORPH-II images RS-2DLDA Garrett Bingham 15

  16. Algorithm Datasets Experiments Experiment Design Conclusions Results Experiment Design: ORL All 40 people from ORL were used in the experiments. 5 images per person were selected at random for training and 5 for testing. The eigenvectors from 2D-LDA and 2D-PCA were computed, and those that explained less than 1% of the variability (or discriminability in the case of 2D-LDA) were discarded because they are likely just random noise. Of the remaining eigenvectors, I choose 5 at random to build a classifier. I build 50 such classifiers and then use a weighted voting scheme to combine their results into a final decision. Each classifier uses KNN ( k = 1) to make its individual decision. Different distance metrics are considered. RS-2DLDA Garrett Bingham 16

  17. Algorithm Datasets Experiments Experiment Design Conclusions Results Experiment Design: MORPH-II 50 arbitrary people were chosen from MORPH-II. 5 images per person were selected at random for training and 5 for testing. The eigenvectors from 2D-LDA and 2D-PCA were computed, and those that explained less than 1% of the variability (or discriminability in the case of 2D-LDA) were discarded because they are likely just random noise. Of the remaining eigenvectors, I choose 10 at random to build a classifier. I build 50 such classifiers and then use a weighted voting scheme to combine their results into a final decision. Each classifier uses KNN ( k = 5) to make its individual decision. Different distance metrics are considered. RS-2DLDA Garrett Bingham 17

  18. Algorithm Datasets Experiments Experiment Design Conclusions Results Results: ORL Each experiment was conducted thirty times and results averaged to obtain the following accuracies: Face Recognition on ORL Euclidean Cosine Algorithm Weighted Unweighted Original Weighted Unweighted Original B2DLDA .931 (.017) .924 (.017) .935 .939 (.015) .936 (.016) .940 L2DLDA .914 (.013) .909 (.014) .940 .937 (.016) .935 (.017) .940 R2DLDA .929 (.013) .923 (.016) .935 .948 (.015) .943 (.013) .945 B2DPCA .914 (.013) .911 (.014) .870 .908 (.015) .908 (.013) .865 L2DPCA .895 (.011) .893 (.010) .865 .884 (.012) .884 (.013) .860 R2DPCA .905 (.010) .903* (.011) .895 .916 (.016) .914 (.016) .895 Figure: Experiments conducted on ORL. Standard error is shown in parentheses, and top accuracy in bold. The framework introduced by Nguyen et al. in [2] is denoted (*). RS-2DLDA Garrett Bingham 18

  19. Algorithm Datasets Experiments Experiment Design Conclusions Results Results: MORPH-II Each experiment was conducted thirty times and results averaged to obtain the following accuracies: Face Recognition on MORPH-II Euclidean Cosine Algorithm Weighted Unweighted Original Weighted Unweighted Original B2DLDA .727 (.019) .678 (.026) .764 .781 (.018) .786 (.015) .768 L2DLDA .743 (.008) .735 (.009) .756 .788 (.010) .780 (.012) .776 R2DLDA .704 (.016) .662 (.018) .704 .723 (.018) .733 (.016) .704 B2DPCA .706 (.013) .701 (.013) .564 .702 (.018) .692 (.013) .556 L2DPCA .678 (.009) .667 (.011) .552 .670 (.018) .660 (.016) .544 R2DPCA .611 (.010) .609* (.007) .580 .609 (.009) .612 (.009) .584 Figure: Experiments conducted on MORPH-II. Standard error is shown in parentheses, and top accuracy in bold. The framework introduced by Nguyen et al. in [2] is denoted (*). RS-2DLDA Garrett Bingham 19

  20. Algorithm Insights Experiments Future Work Conclusions References Conclusions RS-2DLDA Garrett Bingham 20

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