Generative learning methods for bags of features

Transcription

1 Generative learning methos for bags of features Moel the robability of a bag of features given a class Many slies aate from Fei-Fei Li, Rob Fergus, an Antonio Torralba

2 Generative methos We ill cover to moels, both insire by text ocument analysis: Naïve Bayes Probabilistic Latent Semantic Analysis

3 The Naïve Bayes moel Assume that each feature is conitionally ineenent given the class N f, K, f c = f c 1 N i i= 1 f i : ith feature in the image N: number of features in the image Csurka et al. 2004

4 The Naïve Bayes moel Assume that each feature is conitionally ineenent given the class N M n 1 c i= 1 = 1 f, K, f = = N c fi c f i : ith feature in the image N: number of features in the image : th visual or in the vocabulary M: sie of visual vocabulary n : number of features of tye in the image Csurka et al. 2004

5 The Naïve Bayes moel Assume that each feature is conitionally ineenent given the class N M n 1 c i= 1 = 1 f, K, f = = N c fi c No. of features of tye in training images of class c c = Total no. of features in training images of class c Csurka et al. 2004

6 The Naïve Bayes moel Assume that each feature is conitionally ineenent given the class N M n 1 c i= 1 = 1 f, K, f = = N c fi c No. of features of tye in training images of class c + 1 c = Total no. of features in training images of class c + M Lalace l smoothing to avoi ero counts Csurka et al. 2004

7 The Naïve Bayes moel Maximum A Posteriori ecision: c* = arg max c c M = 1 c n = arg max c log c + M = 1 n log c you shoul comute the log of the likelihoo instea of the likelihoo itself in orer to avoi unerflo Csurka et al. 2004

8 The Naïve Bayes moel Grahical moel : c N Csurka et al. 2004

9 Probabilistic Latent Semantic Analysis = Image ebra grass tree visual toics T. Hofmann, Probabilistic Latent Semantic Analysis, UAI 1999

10 Probabilistic Latent Semantic Analysis Unsuervise technique To-level generative moel: a ocument is a mixture of toics, an each toic has its on characteristic or istribution ocument toic or P P T. Hofmann, Probabilistic Latent Semantic Analysis, UAI 1999

11 Probabilistic Latent Semantic Analysis Unsuervise technique To-level generative moel: a ocument is a mixture of toics, an each toic has its on characteristic or istribution i K = k = 1 i k k T. Hofmann, Probabilistic Latent Semantic Analysis, UAI 1999

12 The LSA moel i K = k = 1 i k k Probability of or i Probability of Probability of in ocument knon or i given toic k unknon toic k given ocument unknon

13 The LSA moel i K = k = 1 i k k ocuments toics ocuments ors ors toics k i = i k Observe coeor Coeor istributions Class istributions istributions er toic class er image M N M K K N

14 Learning LSA arameters Maximie likelihoo of ata: Observe counts of or i in ocument M number of coeors N number of images Slie creit: Josef Sivic

15 Inference Fining the most likely toic class for an image: = arg max

16 Inference Inference Fining the most likely toic class for an image: max arg = Fining the most likely toic class for a visual Fining the most likely toic class for a visual or in a given image: = = arg max, arg max

17 Toic iscovery in images J. Sivic, B. Russell, A. Efros, A. Zisserman, B. Freeman, Discovering Obects an their Location in Images, ICCV 2005

18 Alication of LSA: Action recognition Sace-time interest oints Juan Carlos Niebles, Hongcheng Wang an Li Fei-Fei, Unsuervise Learning of Human Action Categories Using Satial-Temoral Wors, IJCV 2008.

19 Alication of LSA: Action recognition Juan Carlos Niebles, Hongcheng Wang an Li Fei-Fei, Unsuervise Learning of Human Action Categories Using Satial-Temoral Wors, IJCV 2008.

20 LSA moel i K = k = 1 i k k Probability bilit of or i Probability of Probability of in vieo knon or i given toic k unknon toic k given vieo unknon i = satial-temoral or = vieo n i, = co-occurrence table # of occurrences of or i in vieo = toic, corresoning to an action

21 Action recognition examle

22 Multile Actions

23 Multile Actions

24 Summary: Generative moels Naïve Bayes Unigram moels in ocument analysis Assumes conitional ineenence of ors given class Parameter estimation: frequency counting Probabilistic Latent Semantic Analysis Unsuervise technique Each ocument is a mixture of toics image is a mixture of classes Can be thought of as matrix ecomosition Parameter estimation: Exectation-Maximiation