Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through the lens of non-Euclidean Riemannian (Riem) geometry often turns out to be better suited in capturing several desirable data properties. Inspired by the great success of dictionary learning and sparse coding (DLSC) for vector-valued data, our goal in this paper is to represent data in the form of SPD matrices as sparse conic combinations of SPD atoms from a learned dictionary via a Riem geometric approach. To that end, we formulate a novel Riem optimization objective for DLSC, in which the representation loss is characterized via the affine-invariant Riem metric. We also present a computationally simple algorithm for optimizing our model. Experiments on several computer vision data sets demonstrate superior classification and retrieval performance using our approach when compared with SC via alternative non-Riem formulations.

Human actions in video sequences are characterized by the complex interplay between spatial features and their temporal dynamics. In this paper, we propose novel tensor representations for compactly capturing such higher-order relationships between visual features for the task of action recognition. We propose two tensor-based feature representations, viz. (i) sequence compatibility kernel (SCK) and (ii) dynamics compatibility kernel (DCK). SCK builds on the spatio-temporal correlations between features, whereas DCK explicitly models the action dynamics of a sequence. We also explore generalization of SCK, coined SCK $\;\oplus$ , that operates on subsequences to capture the local-global interplay of correlations, which can incorporate multi-modal inputs e.g., skeleton 3D body-joints and per-frame classifier scores obtained from deep learning models trained on videos. We introduce linearization of these kernels that lead to compact and fast descriptors. We provide experiments on (i) 3D skeleton action sequences, (ii) fine-grained video sequences, and (iii) standard non-fine-grained videos. As our final representations are tensors that capture higher-order relationships of features, they relate to co-occurrences for robust fine-grained recognition (Lin, 2017), (Koniusz, 2018). We use higher-order tensors and so-called Eigenvalue Power Normalization (EPN) which have been long speculated to perform spectral detection of higher-order occurrences (Koniusz, 2013), (Koniusz, 2017), thus detecting fine-grained relationships of features rather than merely count features in action sequences. We prove that a tensor of order $r$ , built from $Z_*$ dimensional features, coupled with EPN indeed detects if at least one higher-order occurrence is ‘projected’ into one of its $\binom{Z_*}{r}$ subspaces of dim. $r$ represented by the tensor, thus forming a Tensor Power Normalization metric endowed with $\binom{Z_*}{r}$ such ‘detectors’.

We present a principled approach to uncover the structure of visual data by solving a deep learning task coined visual permutation learning. The goal of this task is to find the permutation that recovers the structure of data from shuffled versions of it. In the case of natural images, this task boils down to recovering the original image from patches shuffled by an unknown permutation matrix. Permutation matrices are discrete, thereby posing difficulties for gradient-based optimization methods. To this end, we resort to a continuous approximation using doubly-stochastic matrices and formulate a novel bi-level optimization problem on such matrices that learns to recover the permutation. Unfortunately, such a scheme leads to expensive gradient computations. We circumvent this issue by further proposing a computationally cheap scheme for generating doubly stochastic matrices based on Sinkhorn iterations. To implement our approach we propose DeepPermNet, an end-to-end CNN model for this task. The utility of DeepPermNet is demonstrated on three challenging computer vision problems, namely, relative attributes learning, supervised learning-to-rank, and self-supervised representation learning. Our results show state-of-the-art performance on relative attributes learning, supervised learning-to-rank, and competitive results in the classification and segmentation tasks of the PASCAL VOC dataset for self-supervised learning.

This paper introduces the Eighth Dialog System Technology Challenge. In line with recent challenges, the eighth edition focuses on applying end-to-end dialog technologies in a pragmatic way for multi-domain task-completion, noetic response selection, audio visual scene-aware dialog, and schema-guided dialog state tracking tasks. This paper describes the task definition, provided datasets, baselines and evaluation set-up for each track. We also summarize the results of the submitted systems to highlight the overall trends of the state-of-the-art technologies for the tasks.