Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Socializing the Semantic Gap: A Comparative Survey on Image Tag Assignment, Refinement and Retrieval

Where previous reviews on content-based image retrieval emphasize on what can be seen in an image to bridge the semantic gap, this survey considers what people tag about an image. A comprehensive treatise of three closely linked problems, i.e., image tag assignment, refinement, and tag-based image retrieval is presented. While existing works vary in terms of their targeted tasks and methodology, they rely on the key functionality of tag relevance, i.e. estimating the relevance of a specific tag with respect to the visual content of a given image and its social context. By analyzing what information a specific method exploits to construct its tag relevance function and how such information is exploited, this paper introduces a taxonomy to structure the growing literature, understand the ingredients of the main works, clarify their connections and difference, and recognize their merits and limitations. For a head-to-head comparison between the state-of-the-art, a new experimental protocol is presented, with training sets containing 10k, 100k and 1m images and an evaluation on three test sets, contributed by various research groups. Eleven representative works are implemented and evaluated. Putting all this together, the survey aims to provide an overview of the past and foster progress for the near future.Comment: to appear in ACM Computing Survey

LEARNet Dynamic Imaging Network for Micro Expression Recognition

Unlike prevalent facial expressions, micro expressions have subtle, involuntary muscle movements which are short-lived in nature. These minute muscle movements reflect true emotions of a person. Due to the short duration and low intensity, these micro-expressions are very difficult to perceive and interpret correctly. In this paper, we propose the dynamic representation of micro-expressions to preserve facial movement information of a video in a single frame. We also propose a Lateral Accretive Hybrid Network (LEARNet) to capture micro-level features of an expression in the facial region. The LEARNet refines the salient expression features in accretive manner by incorporating accretion layers (AL) in the network. The response of the AL holds the hybrid feature maps generated by prior laterally connected convolution layers. Moreover, LEARNet architecture incorporates the cross decoupled relationship between convolution layers which helps in preserving the tiny but influential facial muscle change information. The visual responses of the proposed LEARNet depict the effectiveness of the system by preserving both high- and micro-level edge features of facial expression. The effectiveness of the proposed LEARNet is evaluated on four benchmark datasets: CASME-I, CASME-II, CAS(ME)^2 and SMIC. The experimental results after investigation show a significant improvement of 4.03%, 1.90%, 1.79% and 2.82% as compared with ResNet on CASME-I, CASME-II, CAS(ME)^2 and SMIC datasets respectively.Comment: Dynamic imaging, accretion, lateral, micro expression recognitio

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage