Explaining Indian Stock Market through Geometry of Scale free Networks

This paper presents an analysis of the Indian stock market using a method based on embedding the network in a hyperbolic space using Machine learning techniques. We claim novelty on four counts. First, it is demonstrated that the hyperbolic clusters resemble the topological network communities more closely than the Euclidean clusters. Second, we are able to clearly distinguish between periods of market stability and volatility through a statistical analysis of hyperbolic distance and hyperbolic shortest path distance corresponding to the embedded network. Third, we demonstrate that using the modularity of the embedded network significant market changes can be spotted early. Lastly, the coalescent embedding is able to segregate the certain market sectors thereby underscoring its natural clustering ability.

Synergizing Contrastive Learning and Optimal Transport for 3D Point Cloud Domain Adaptation

Recently, the fundamental problem of unsupervised domain adaptation (UDA) on 3D point clouds has been motivated by a wide variety of applications in robotics, virtual reality, and scene understanding, to name a few. The point cloud data acquisition procedures manifest themselves as significant domain discrepancies and geometric variations among both similar and dissimilar classes. The standard domain adaptation methods developed for images do not directly translate to point cloud data because of their complex geometric nature. To address this challenge, we leverage the idea of multimodality and alignment between distributions. We propose a new UDA architecture for point cloud classification that benefits from multimodal contrastive learning to get better class separation in both domains individually. Further, the use of optimal transport (OT) aims at learning source and target data distributions jointly to reduce the cross-domain shift and provide a better alignment. We conduct a comprehensive empirical study on PointDA-10 and GraspNetPC-10 and show that our method achieves state-of-the-art performance on GraspNetPC-10 (with approx 4-12% margin) and best average performance on PointDA-10. Our ablation studies and decision boundary analysis also validate the significance of our contrastive learning module and OT alignment.

GrapeQA: GRaph Augmentation and Pruning to Enhance Question-Answering

Commonsense question-answering (QA) methods combine the power of pre-trained Language Models (LM) with the reasoning provided by Knowledge Graphs (KG). A typical approach collects nodes relevant to the QA pair from a KG to form a Working Graph (WG) followed by reasoning using Graph Neural Networks(GNNs). This faces two major challenges: (i) it is difficult to capture all the information from the QA in the WG, and (ii) the WG contains some irrelevant nodes from the KG. To address these, we propose GrapeQA with two simple improvements on the WG: (i) Prominent Entities for Graph Augmentation identifies relevant text chunks from the QA pair and augments the WG with corresponding latent representations from the LM, and (ii) Context-Aware Node Pruning removes nodes that are less relevant to the QA pair. We evaluate our results on OpenBookQA, CommonsenseQA and MedQA-USMLE and see that GrapeQA shows consistent improvements over its LM + KG predecessor (QA-GNN in particular) and large improvements on OpenBookQA.

Person Re-Identification with a Locally Aware Transformer

Person Re-Identification is an important problem in computer vision-based surveillance applications, in which the same person is attempted to be identified from surveillance photographs in a variety of nearby zones. At present, the majority of Person re-ID techniques are based on Convolutional Neural Networks (CNNs), but Vision Transformers are beginning to displace pure CNNs for a variety of object recognition tasks. The primary output of a vision transformer is a global classification token, but vision transformers also yield local tokens which contain additional information about local regions of the image. Techniques to make use of these local tokens to improve classification accuracy are an active area of research. We propose a novel Locally Aware Transformer (LA-Transformer) that employs a Parts-based Convolution Baseline (PCB)-inspired strategy for aggregating globally enhanced local classification tokens into an ensemble of $\sqrt{N}$ classifiers, where $N$ is the number of patches. An additional novelty is that we incorporate blockwise fine-tuning which further improves re-ID accuracy. LA-Transformer with blockwise fine-tuning achieves rank-1 accuracy of $98.27 \%$ with standard deviation of $0.13$ on the Market-1501 and $98.7\%$ with standard deviation of $0.2$ on the CUHK03 dataset respectively, outperforming all other state-of-the-art published methods at the time of writing.

Self-Supervised Few-Shot Learning on Point Clouds

The increased availability of massive point clouds coupled with their utility in a wide variety of applications such as robotics, shape synthesis, and self-driving cars has attracted increased attention from both industry and academia. Recently, deep neural networks operating on labeled point clouds have shown promising results on supervised learning tasks like classification and segmentation. However, supervised learning leads to the cumbersome task of annotating the point clouds. To combat this problem, we propose two novel self-supervised pre-training tasks that encode a hierarchical partitioning of the point clouds using a cover-tree, where point cloud subsets lie within balls of varying radii at each level of the cover-tree. Furthermore, our self-supervised learning network is restricted to pre-train on the support set (comprising of scarce training examples) used to train the downstream network in a few-shot learning (FSL) setting. Finally, the fully-trained self-supervised network's point embeddings are input to the downstream task's network. We present a comprehensive empirical evaluation of our method on both downstream classification and segmentation tasks and show that supervised methods pre-trained with our self-supervised learning method significantly improve the accuracy of state-of-the-art methods. Additionally, our method also outperforms previous unsupervised methods in downstream classification tasks.

Simplicial Complex based Point Correspondence between Images warped onto Manifolds

Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved higher-order matching algorithms on warped images due to projection. Although currently, several existing methods "flatten" such 3D images to use planar graph / hypergraph matching methods, they still suffer from severe distortions and other undesired artifacts, which result in inaccurate matching. Alternatively, current planar methods cannot be trivially extended to effectively match points on images warped onto manifolds. Hence, matching on these warped images persists as a formidable challenge. In this paper, we pose the assignment problem as finding a bijective map between two graph induced simplicial complexes, which are higher-order analogues of graphs. We propose a constrained quadratic assignment problem (QAP) that matches each p-skeleton of the simplicial complexes, iterating from the highest to the lowest dimension. The accuracy and robustness of our approach are illustrated on both synthetic and real-world spherical / warped (projected) images with known ground-truth correspondences. We significantly outperform existing state-of-the-art spherical matching methods on a diverse set of datasets.

Learning Representations using Spectral-Biased Random Walks on Graphs

Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility. In this work, we are interested in studying how much a probabilistic bias in this stochastic process affects the quality of the nodes picked by the process. In particular, our biased walk, with a certain probability, favors movement towards nodes whose neighborhoods bear a structural resemblance to the current node's neighborhood. We succinctly capture this neighborhood as a probability measure based on the spectrum of the node's neighborhood subgraph represented as a normalized laplacian matrix. We propose the use of a paragraph vector model with a novel Wasserstein regularization term. We empirically evaluate our approach against several state-of-the-art node embedding techniques on a wide variety of real-world datasets and demonstrate that our proposed method significantly improves upon existing methods on both link prediction and node classification tasks.

Solving Partial Assignment Problems using Random Clique Complexes

We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure. The proposed method creates random clique adjacency matrices for each k-skeleton of the random clique complexes and matches them, taking into account each point as the affine combination of its geometric neighbourhood. We justify our solution theoretically, by analyzing the runtime and storage complexity of our algorithm along with the asymptotic behaviour of the quadratic assignment problem (QAP) that is associated with the underlying random clique adjacency matrices. Experiments on both synthetic and real-world datasets, containing severe occlusions and distortions, provide insight into the accuracy, efficiency, and robustness of our approach. We outperform diverse matching algorithms by a significant margin.