Recognizing actions from still images is popularly studied recently. In this paper, we model an action class as a flexible number of spatial configurations of body parts by proposing a new spatial SPN (Sum-Product Networks). First, we discover a set of parts in image collections via unsupervised learning. Then, our new spatial SPN is applied to model the spatial relationship and also the high-order correlations of parts. To learn robust networks, we further develop a hierarchical spatial SPN method, which models pairwise spatial relationship between parts inside sub-images and models the correlation of sub-images via extra layers of SPN. Our method is shown to be effective on two benchmark datasets.
SPN (Sum-Product Networks) @cite_23 is a newly proposed deep structure that can capture the high-order correlations between its leaf nodes. A number of papers later investigate this structure theoretically @cite_37 @cite_44 . In addition, SPN is proved to be successful in several tasks of computer vision, including image classification @cite_11 , facial attribute analysis @cite_7 , and action recognition in videos @cite_29 . In this paper, we characterize an action class by several configurations of body parts, and represent it using SPN. Amer and Todorovic @cite_29 propose to learn a Bag-of-Words representation for a video and model the deep correlations of parts using SPN with a stochastic structure. However, the spatial relationships of the parts are not taken into consideration. For the first time, in this work, we propose spatial SPN to explicitly model the spatial relationship of parts for robust action recognition.
@cite_37 @cite_7 @cite_29 @cite_44 @cite_23 @cite_11
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We investigate the representational power of sum-product networks (computation networks analogous to neural networks, but whose individual units compute either products or weighted sums), through a theoretical analysis that compares deep (multiple hidden layers) vs. shallow (one hidden layer) architectures. We prove there exist families of functions that can be represented much more efficiently with a deep network than with a shallow one, i.e. with substantially fewer hidden units. Such results were not available until now, and contribute to motivate recent research involving learning of deep sum-product networks, and more generally motivate research in Deep Learning. Recent works have shown that facial attributes are useful in a number of applications such as face recognition and retrieval. However, estimating attributes in images with large variations remains a big challenge. This challenge is addressed in this paper. Unlike existing methods that assume the independence of attributes during their estimation, our approach captures the interdependencies of local regions for each attribute, as well as the high-order correlations between different attributes, which makes it more robust to occlusions and misdetection of face regions. First, we have modeled region interdependencies with a discriminative decision tree, where each node consists of a detector and a classifier trained on a local region. The detector allows us to locate the region, while the classifier determines the presence or absence of an attribute. Second, correlations of attributes and attribute predictors are modeled by organizing all of the decision trees into a large sum-product network (SPN), which is learned by the EM algorithm and yields the most probable explanation (MPE) of the facial attributes in terms of the region's localization and classification. Experimental results on a large data set with 22,400 images show the effectiveness of the proposed approach. This paper addresses recognition of human activities with stochastic structure, characterized by variable spacetime arrangements of primitive actions, and conducted by a variable number of actors. We demonstrate that modeling aggregate counts of visual words is surprisingly expressive enough for such a challenging recognition task. An activity is represented by a sum-product network (SPN). SPN is a mixture of bags-of-words (BoWs) with exponentially many mixture components, where subcomponents are reused by larger ones. SPN consists of terminal nodes representing BoWs, and product and sum nodes organized in a number of layers. The products are aimed at encoding particular configurations of primitive actions, and the sums serve to capture their alternative configurations. The connectivity of SPN and parameters of BoW distributions are learned under weak supervision using the EM algorithm. SPN inference amounts to parsing the SPN graph, which yields the most probable explanation (MPE) of the video in terms of activity detection and localization. SPN inference has linear complexity in the number of nodes, under fairly general conditions, enabling fast and scalable recognition. A new Volleyball dataset is compiled and annotated for evaluation. Our classification accuracy and localization precision and recall are superior to those of the state-of-the-art on the benchmark and our Volleyball datasets. Sum-product networks (SPNs) are a deep probabilistic representation that allows for efficient, exact inference. SPNs generalize many other tractable models, including thin junction trees, latent tree models, and many types of mixtures. Previous work on learning SPN structure has mainly focused on using top-down or bottom-up clustering to find mixtures, which capture variable interactions indirectly through implicit latent variables. In contrast, most work on learning graphical models, thin junction trees, and arithmetic circuits has focused on finding direct interactions among variables. In this paper, we present ID-SPN, a new algorithm for learning SPN structure that unifies the two approaches. In experiments on 20 benchmark datasets, we find that the combination of direct and indirect interactions leads to significantly better accuracy than several state-of-the-art algorithms for learning SPNs and other tractable models. The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sum-product networks (SPNs). SPNs are directed acyclic graphs with variables as leaves, sums and products as internal nodes, and weighted edges. We show that if an SPN is complete and consistent it represents the partition function and all marginals of some graphical model, and give semantics to its nodes. Essentially all tractable graphical models can be cast as SPNs, but SPNs are also strictly more general. We then propose learning algorithms for SPNs, based on backpropagation and EM. Experiments show that inference and learning with SPNs can be both faster and more accurate than with standard deep networks. For example, SPNs perform image completion better than state-of-the-art deep networks for this task. SPNs also have intriguing potential connections to the architecture of the cortex. Sum-product networks are a new deep architecture that can perform fast, exact inference on high-treewidth models. Only generative methods for training SPNs have been proposed to date. In this paper, we present the first discriminative training algorithms for SPNs, combining the high accuracy of the former with the representational power and tractability of the latter. We show that the class of tractable discriminative SPNs is broader than the class of tractable generative ones, and propose an efficient backpropagation-style algorithm for computing the gradient of the conditional log likelihood. Standard gradient descent suffers from the diffusion problem, but networks with many layers can be learned reliably using "hard" gradient descent, where marginal inference is replaced by MPE inference (i.e., inferring the most probable state of the non-evidence variables). The resulting updates have a simple and intuitive form. We test discriminative SPNs on standard image classification tasks. We obtain the best results to date on the CIFAR-10 dataset, using fewer features than prior methods with an SPN architecture that learns local image structure discriminatively. We also report the highest published test accuracy on STL-10 even though we only use the labeled portion of the dataset.