1. Discriminative Sub-categorization Minh Hoai Nguyen, Andrew Zisserman University of Oxford 1

2. Sub-category 1Sub-category 2Sub-category 3Sub-category 4Sub-category 5 Head-images Sub-categorization Why sub-categorization? - Better head detector - Extra information (looking direction)

3. Sub-categorization with Clustering K-means clustering Max-margin clustering (e.g., Xu et al. ‘04, Hoai & De la Torre ‘12) SVMs with latent variables (Latent SVM) (e.g., Andrews et al. ‘03, Felzenszwalb et al. ‘10) Data from a category Suitable for tasks requiring separation between positive & negative (e.g., detection)

4. Latent SVM 4 + + + + + + + + ++ + + + + + + - - - - - - - - - + + + + + + + + + Often leads to cluster degeneration: a few clusters claim most data points A latent variable for positive sample No latent variable for negative sample Objective: -Optimize SVM parameters -Determine latent variables -Given and, Iterative optimization, alternating: -Given, update latent variables update SVMs’ parameters

5. Cluster Degeneration 5 Suppose Cluster 1 has many more members than Cluster 2  It is much harder to separate Cluster 1 from negative data  Cluster 1 has a much smaller margin An explanation (not rigorous proof): the big gets bigger    Big cluster will claim even more samples 

6. Discriminative Sub-Categorization (DSC) 6 To this formulation (called DSC) Change from the Latent SVM formulation: Margin violation + + Coupled with latent variable Margin violation + Proportion of samples in Cluster DSC is equivalent to k: # of clusters n: # of positive samples : cluster assignment : SVM parameter

7. Cluster Assignment 7 To DSC formulation Change from Latent SVM formulation: Similarity between DSC and K-means:

8. Experiment: Sub-categorization Result 8 Input images from TVHI dataset Output HOG weight vectors Low-score images High-score images

9. Experiment: DSC versus LSVM DSC (ours) 6 sub-categories 3 sub-categories 6 sub-categories Latent SVM

10. 10 - Uses DSC for initialization Examples of Upper body Experiment: DSC for Object Detection - Each sub-category is a component Recall Precision - Train a DPM ( Felzenszwalb et al.) to detect upper bodies

11. 11 - Uses DSC for initialization Examples of Upper body Experiment: Comparison with k-means - Train a DPM ( Felzenszwalb et al.) to detect upper bodies - Each sub-category is a component Recall Precision

12. Experiment: Numerical Analysis Vary C, the trade-off parameter for large margin and less constraint violation Classification accuracyCluster Purity Cluster Imbalance Vary the amount of negative data

13. Experiment: Cluster Purity 13 Dataset #classe s#features#pointsk-meansLSVMDSC (ours) Gas Sensor61281391046.38 ± 0.6956.74 ± 1.8860.82 ± 1.64 Landsat636443578.72 ± 2.0869.37 ± 2.3276.73 ± 2.38 Segmentation719231071.96 ± 1.7565.89 ± 2.3674.41 ± 1.85 Steel Plates727194153.29 ± 1.5152.64 ± 2.0254.60 ± 1.98 Wine quality712489843.43 ± 1.5855.00 ± 2.3554.21 ± 1.65 Digits1064562076.38 ± 1.7277.83 ± 1.5780.15 ± 1.18 Semeion10256159364.64 ± 1.2064.32 ± 1.5866.74 ± 1.43 MNIST107846000065.38 ± 1.4363.99 ± 1.3666.18 ± 1.34 Letter26162000033.35 ± 0.4840.27 ± 0.8844.38 ± 0.74 Isolet26617623862.15 ± 1.2261.95 ± 1.2264.08 ± 1.18 Amazon Reviews5010000150024.93 ± 0.3224.89 ± 0.4125.08 ± 0.38 Results within one standard error of the maximum value are printed in bold

14. Summary sub-categorize What the algorithm does: Properties of the algorithm: Benefits of the algorithm: - Max-margin separation from negative data - Quadratic objective with linear constraints - Visually interpretable - Useful for object detection using DPM of - Does not suffer from cluster degeneration a few clusters claim most data points Precision Recall With sub-categorization Without sub-categorization Input: Output: Felzenszwalb et al.