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

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Discriminative Sub-categorization. Minh Hoai Nguyen, Andrew Zisserman University of Oxford. S ub-categorization. Head-images. Sub-category 1. Sub-category 2. Sub-category 3. Sub-category 4. Sub-category 5. Why sub-categorization?. - Better head detector. - PowerPoint PPT Presentation

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Mining videos for behavior assessment

Discriminative Sub-categorizationMinh Hoai Nguyen, Andrew ZissermanUniversity of Oxford1et al: italicTitles: should be capitalsInconsitent use of periods. In prensentation, no periods.Tile slide: put CMU1

Sub-category 1Sub-category 2Sub-category 3Sub-category 4Sub-category 5

Head-imagesSub-categorizationWhy sub-categorization?- Better head detector- Extra information (looking direction)

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 categorySuitable for tasks requiringseparation between positive & negative (e.g., detection)Latent SVM4++++++++++++++++---------+++++++++

Often leads to cluster degeneration: a few clusters claim most data points

A latent variable for positive sampleNo latent variable for negative sampleObjective: Optimize SVM parameters

Determine latent variables

Given and ,Iterative optimization, alternating: Given , update latent variablesupdate SVMs parameters

Cluster Degeneration5Suppose 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 marginAn explanation (not rigorous proof): the big gets bigger

Big cluster will claim even more samples Discriminative Sub-Categorization (DSC)6To this formulation (called DSC)Change from the Latent SVM formulation:Margin violation+Margin violation+Coupled with latent variable

Margin violation+Proportion of samples in Cluster

DSC is equivalent tok: # of clustersn: # of positive samples : cluster assignment : SVM parameter

Cluster Assignment7To DSC formulationChange from Latent SVM formulation:

Similarity between DSC and K-means:

Experiment: Sub-categorization Result8

Input images from TVHI datasetOutput HOG weight vectorsLow-score imagesHigh-score imagesExperiment: DSC versus LSVM

DSC (ours)6 sub-categories3 sub-categories3 sub-categories6 sub-categoriesLatent SVM10- Uses DSC for initialization

Examples of Upper bodyExperiment: DSC for Object Detection- Each sub-category is a component

RecallPrecision- Train a DPM (Felzenszwalb et al.) to detect upper bodies11- Uses DSC for initialization

Examples of Upper bodyExperiment: Comparison with k-means- Train a DPM (Felzenszwalb et al.) to detect upper bodies- Each sub-category is a component

RecallPrecisionExperiment: Numerical AnalysisVary C, the trade-off parameter for large margin and less constraint violation

Classification accuracy

Cluster Purity

Cluster Imbalance

Vary the amount of negative dataExperiment: Cluster Purity13Dataset#classes#features#pointsk-meansLSVMDSC (ours)Gas Sensor 61281391046.38 0.6956.74 1.8860.82 1.64Landsat 636443578.72 2.0869.37 2.3276.73 2.38Segmentation 719231071.96 1.7565.89 2.3674.41 1.85Steel Plates 727194153.29 1.5152.64 2.0254.60 1.98Wine quality 712489843.43 1.5855.00 2.3554.21 1.65Digits 1064562076.38 1.7277.83 1.5780.15 1.18Semeion 10256159364.64 1.2064.32 1.5866.74 1.43MNIST 107846000065.38 1.4363.99 1.3666.18 1.34Letter 26162000033.35 0.4840.27 0.8844.38 0.74Isolet 26617623862.15 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 boldSummary

sub-categorizeWhat 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 degenerationa few clusters claim most data points

PrecisionRecallWith sub-categorizationWithout sub-categorizationInput:Output:Felzenszwalb et al.14