ICCV2009: Max-Margin Ađitive Classifiers for Detection
- 1. Max-Margin Additive Classifiers for DetectionSubhransuMaji & Alexander BergUniversity of California at Berkeley Columbia UniversityICCV 2009, Kyoto, Japan
- 2. Accuracy vs. Evaluation Timefor SVM ClassifiersNon-linear KernelEvaluation timeLinear KernelAccuracy
- 3. Accuracy vs. Evaluation Timefor SVM ClassifiersNon-linear KernelEvaluation timeOur CVPR 08Linear KernelAccuracy
- 4. Non-linear Kernel Additive KernelEvaluation timeOur CVPR 08Linear KernelAccuracyAccuracy vs. Evaluation Timefor SVM Classifiers
- 5. Additive KernelNon-linear Kernel Additive KernelEvaluation timeOur CVPR 08Linear KernelAccuracyAccuracy vs. Evaluation Timefor SVM Classifiers
- 6. Accuracy vs. Evaluation Timefor SVM ClassifiersAdditive KernelNon-linear KernelEvaluation timeOur CVPR 08Linear Kernel Additive KernelAccuracyMade it possible to use SVMs with additive kernels for detection.
- 7. Additive ClassifiersMuch work already uses them! SVMs with additive kernels are additive classifiersHistogram based kernelsHistogram intersection, chi-squared kernelPyramid Match Kernel (Grauman & Darell, ICCV’05)Spatial Pyramid Match Kernel (Lazebniket.al., CVPR’06)….
- 8. Accuracy vs. Training Timefor SVM ClassifiersNon-linearTraining timeLinear KernelAccuracy
- 9. Accuracy vs. Training Timefor SVM ClassifiersNon-linearTraining time<=1990sLinearAccuracy
- 10. Accuracy vs. Training Timefor SVM ClassifiersNon-linearTraining timeTodayLinearAccuracyEg. Cutting Plane, Stoc. Gradient Descend, Dual Coordinate Descend
- 11. Accuracy vs. Training Timefor SVM ClassifiersNon-linearAdditiveTraining timeOur CVPR 08LinearAccuracy
- 12. Accuracy vs. Training Timefor SVM ClassifiersNon-linearAdditiveTraining timeOur CVPR 08✗LinearAccuracy
- 13. Accuracy vs. Training Timefor SVM ClassifiersNon-linearAdditiveTraining timeThis PaperLinearAccuracy
- 14. Accuracy vs. Training Timefor SVM ClassifiersNon-linearTraining timeThis PaperLinearAdditiveAccuracyMakes it possible to train additive classifiers very fast.
- 15. SummaryAdditive classifiers are widely used and can provide better accuracy than linearOur CVPR 08: SVMs with additive kernels are additive classifiers and can be evaluated in O(#dim) -- same as linear.This work: additive classifiers can be trained directly as efficiently (up to a small constant) as the best approaches for training linear classifiers.An example
- 16. Support Vector MachinesEmbedded SpaceInput SpaceKernel Function Inner Product in the embedded space
- 17. Can learn non-linear boundaries in input space Classification FunctionKernel Trick
- 18. Embeddings…These embeddings can be high dimensional (even infinite)Our approach is based on embeddings thatapproximate kernels.We’d like this to be as accurate as possibleWe are going to use fast linear classifier training algorithms on the so sparseness is important.
- 19. Key Idea: Embedding an Additive KernelAdditive Kernels are easy to embed, just embed each dimension independentlyLinear Embedding for min Kernel for integersFor non integers can approximate by quantizing
- 20. Issues: Embedding ErrorQuantization leads to large errorsBetter encodingxy
- 21. Issues: SparsityRepresent with sparse values
- 22. Linear SVM objective (solve with LIBLINEAR):Encoded SVM objective (not practical): Linear vs. Encoded SVMs
- 23. Linear vs. Encoded SVMs Linear SVM objective (solve with LIBLINEAR):Encoded SVM modified (custom solver): Encourages smooth functionsClosely approximates min kernel SVMCustom solver : PWLSGD (see paper)
- 24. Linear SVM objective (solve with LIBLINEAR):Encoded SVM objective (solve with LIBLINEAR) : Linear vs. Encoded SVMs
- 26. Additive Classifier ChoicesAccuracy Increases RegularizationEncodingEvaluation times are similar
- 27. Additive Classifier ChoicesAccuracy Increases RegularizationEncodingAccuracy Increases Evaluation times are similar
- 28. Additive Classifier ChoicesAccuracy Increases RegularizationEncodingAccuracy Increases Standard solverEg. LIBSVMFew lines of code + standard solverEg. LIBLINEAR
- 29. Additive Classifier ChoicesAccuracy Increases RegularizationEncodingAccuracy Increases Custom solver
- 30. Additive Classifier ChoicesAccuracy Increases RegularizationEncodingAccuracy Increases Classifier Notations
- 31. Experiments“Small” Scale: Caltech 101 (Fei-Fei, et.al.)“Medium” Scale: DC Pedestrians (Munder & Gavrila)“Large” Scale : INRIA Pedestrians (Dalal & Triggs)
- 32. Experiment : DC Pedestrians(3.18s, 89.25%)(1.86s, 88.80%)(363s, 89.05%)(2.98s, 85.71%)100x fastertraining time ~ linear SVMaccuracy ~ kernel SVM (1.89s, 72.98%)20,000 features, 656 dimensional100 bins for encoding6-fold cross validation
- 33. Experiment : Caltech 101(291s, 55.35%)(2687s, 56.49%)(102s, 54.8%)(90s, 51.64%)10x fasterSmall loss in accuracy(41s, 46.15%)30 training examples per category100 bins for encodingPyramid HOG + Spatial Pyramid Match Kernel
- 34. Experiment : INRIA Pedestrians(140 mins, 0.95)(76s, 0.94)(27s, 0.88)300x fastertraining time ~ linear SVMaccuracy ~ kernel SVMtrains the detector in < 2 mins (122s, 0.85)(20s, 0.82)SPHOG: 39,000 features, 2268 dimensional 100 bins for encodingCross Validation Plots
- 35. Experiment : INRIA Pedestrians300x fastertraining time ~ linear SVMaccuracy ~ kernel SVMtrains the detector in < 2 mins SPHOG: 39,000 features, 2268 dimensional 100 bins for encodingCross Validation Plots
- 36. Take Home MessagesAdditive models are practical for large scale dataCan be trained discriminatively: Poor man’s version : encode + Linear SVM SolverMiddle man’s version : encode + Custom SolverRich man’s version : Min Kernel SVMEmbedding only Approximates kernels, leads to small loss in accuracy but up to 100x speedup in training timeEveryone should use: see code on our websitesFast IKSVM from CVPR’08, Encoded SVMs, etc
- 37. Thank You
Editor's Notes
- #2: Thankyou. Good afternoon everybody. I am going to present ways to train additive classifiers efficiently . This work is a part of an ongoing collaboration with alex berg.
- #3: For any classification task the two main things we care about are accuracy and evaluation time. Especially for object detection where one evalutaes a classifier on thousands of windowsPer image – the evalutation time becomes very important. In the past linear SVMs though relatively less accurate were preferred over kernel SVMs for real-time applications.
- #4: In our CVPR 08 paper…
- #5: We identified a subset of non-linear kernels, called additive kernels that are used in many of the current object recognition tasks. These kernels have the special form that they decompose as a sum of Kernels over individual dimensions.
- #6: We identified a subset of non-linear kernels, called additive kernels that are used in many of the current object recognition tasks. These kernels have the special form that they decompose as a sum of Kernels over individual dimensions.
- #7: And showed that they can be evaulated efficiently. This makes it possible for one to use more accurate classifiers with relatively no loss in speed. In fact more than half of thisYear’s submissions to the PACCAL VOC object detection challenge use variants of additive kernels.
- #8: In this talk we are going to talk about additive models in general – where the classifier decomposes into dimensions. This may seem restrictive but it’s a useful class of classifiers which iis strictly more general than linear classifiers.In fact if the underlying kernel for the SVM is additive then the classifier is also additive
- #9: Pic looks similar to that for evaluation time… it is important to note that this was not the case even somewhat recently…
- #11: Maybe put some refs on this…
- #12: Maybe put some refs on this…As mentioned before, our previous work identified a subset of non-linear classifiers with an additive structure and showed they could be evaluated efficiently, but unfortunately did not address improving efficiency for training…
- #13: Maybe put some refs on this…
- #14: This paper addresses efficient training for additive classifiers, developing training methods that are about as efficient as the best methods fortraining linear classifiers. We also demonstrate the accuracy avantages on some popular datasets.?....
- #15: Should we change the wording? Drop SVM?
- #16: (finish this by 5 mins)
- #17: The idea of support vector machines is to find a separating hyperplane on the data into a high dimension space using a Kernel.The final classifier is ofcouse a line in a very high dimensional space but can be expressed using only the Kernel function using the so called kernel trick. If the embedded space is low dimensional then one can take advantage of the very fast linear SVM training algorithms which scale linearly with trainingData as opposed to the quadratic growth for the kernel SVM.
- #18: Unfortunately these embeddings are often high dimensionalOur approach can be seen as finding embeddings that are both sparse and accurate so that we can use the very best of the linear SVM training algorithms for trainingThe classifier. In fact we would ideally like the number of non zero entries in the embedded features to be a small multiple of the nonn zero entries in the input features.
- #19: A key idea of the paper is to realize that additive kernels are easy to embed as the final embedding is just a concatenation of the individual dimension embeddingsAS as example the min kernel or the histogram intersection kernel defined as A well known embedding for min kernel for integers is the unaryencoding where each number is represented in the unaryExample …For non-integers one may just approximate this by quantization