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
Generative methos We ill cover to moels, both insire by text ocument analysis: Naïve Bayes Probabilistic Latent Semantic Analysis
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
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
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
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
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
The Naïve Bayes moel Grahical moel : c N Csurka et al. 2004
Probabilistic Latent Semantic Analysis = 1 + 2 + 3 Image ebra grass tree visual toics T. Hofmann, Probabilistic Latent Semantic Analysis, UAI 1999
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
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
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
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
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
Inference Fining the most likely toic class for an image: = arg max
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
Toic iscovery in images J. Sivic, B. Russell, A. Efros, A. Zisserman, B. Freeman, Discovering Obects an their Location in Images, ICCV 2005
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.
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.
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
Action recognition examle
Multile Actions
Multile Actions
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