Sandeep Kumar

Aditya Hemant Shahane, Prathosh A. P, Sandeep Kumar

Graphs are growing rapidly, along with the number of distinct label categories associated with them. Applications like e-commerce, healthcare, recommendation systems, and various social media platforms are rapidly moving towards graph representation of data due to their ability to capture both structural and attribute information. One crucial task in graph analysis is node classification, where unlabeled nodes are categorized into predefined classes. In practice, novel classes appear incrementally sometimes with just a few labels (seen classes) or even without any labels (unseen classes), either because they are new or haven't been explored much. Traditional methods assume abundant labeled data for training, which isn't always feasible. We investigate a broader objective: \emph{Graph Class Incremental Learning under Weak Supervision (GCL)}, addressing this challenge by meta-training on base classes with limited labeled instances. During the incremental streams, novel classes can have few-shot or zero-shot representation. Our proposed framework GOTHAM efficiently accommodates these unlabeled nodes by finding the closest prototype representation, serving as class representatives in the attribute space. For Text-Attributed Graphs (TAGs), our framework additionally incorporates semantic information to enhance the representation. By employing teacher-student knowledge distillation to mitigate forgetting, GOTHAM achieves promising results across various tasks. Experiments on datasets such as Cora-ML, Amazon, and OBGN-Arxiv showcase the effectiveness of our approach in handling evolving graph data under limited supervision. The repository is available here: \href{https://github.com/adityashahane10/GOTHAM--Graph-based-Class-Incremental-Learning-Framework-under-Weak-Supervision}{\small \textcolor{blue}{Code}}

Sandeep Kumar, Jiaxi Ying, José Vinícius de M. Cardoso et al.

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. Useful structured graphs include the multi-component graph, bipartite graph, connected graph, sparse graph, and regular graph. In general, structured graph learning is an NP-hard combinatorial problem, therefore, designing a general tractable optimization method is extremely challenging. In this paper, we introduce a unified graph learning framework lying at the integration of Gaussian graphical models and spectral graph theory. To impose a particular structure on a graph, we first show how to formulate the combinatorial constraints as an analytical property of the graph matrix. Then we develop an optimization framework that leverages graph learning with specific structures via spectral constraints on graph matrices. The proposed algorithms are provably convergent, computationally efficient, and practically amenable for numerous graph-based tasks. Extensive numerical experiments with both synthetic and real data sets illustrate the effectiveness of the proposed algorithms. The code for all the simulations is made available as an open source repository.

Samarth Bhatia, Yukti Makhija, Manoj Kumar et al.

Graph clustering is an important unsupervised learning technique for partitioning graphs with attributes and detecting communities. However, current methods struggle to accurately capture true community structures and intra-cluster relations, be computationally efficient, and identify smaller communities. We address these challenges by integrating coarsening and modularity maximization, effectively leveraging both adjacency and node features to enhance clustering accuracy. We propose a loss function incorporating log-determinant, smoothness, and modularity components using a block majorization-minimization technique, resulting in superior clustering outcomes. The method is theoretically consistent under the Degree-Corrected Stochastic Block Model (DC-SBM), ensuring asymptotic error-free performance and complete label recovery. Our provably convergent and time-efficient algorithm seamlessly integrates with graph neural networks (GNNs) and variational graph autoencoders (VGAEs) to learn enhanced node features and deliver exceptional clustering performance. Extensive experiments on benchmark datasets demonstrate its superiority over existing state-of-the-art methods for both attributed and non-attributed graphs.

Mohit Kataria, Nikita Malik, Sandeep Kumar et al.

Graph structure learning is a core problem in graph-based machine learning, essential for uncovering latent relationships and ensuring model interpretability. However, most existing approaches are ill-suited for large-scale and dynamically evolving graphs, as they often require complete re-learning of the structure upon the arrival of new nodes and incur substantial computational and memory costs. In this work, we propose GraphFLEx: a unified and scalable framework for Graph Structure Learning in Large and Expanding Graphs. GraphFLEx mitigates the scalability bottlenecks by restricting edge formation to structurally relevant subsets of nodes identified through a combination of clustering and coarsening techniques. This dramatically reduces the search space and enables efficient, incremental graph updates. The framework supports 48 flexible configurations by integrating diverse choices of learning paradigms, coarsening strategies, and clustering methods, making it adaptable to a wide range of graph settings and learning objectives. Extensive experiments across 26 diverse datasets and Graph Neural Network architectures demonstrate that GraphFLEx achieves state-of-the-art performance with significantly improved scalability.

Badri N. Patro, Vinod K. Kurmi, Sandeep Kumar et al.

Generating natural questions from an image is a semantic task that requires using vision and language modalities to learn multimodal representations. Images can have multiple visual and language cues such as places, captions, and tags. In this paper, we propose a principled deep Bayesian learning framework that combines these cues to produce natural questions. We observe that with the addition of more cues and by minimizing uncertainty in the among cues, the Bayesian network becomes more confident. We propose a Minimizing Uncertainty of Mixture of Cues (MUMC), that minimizes uncertainty present in a mixture of cues experts for generating probabilistic questions. This is a Bayesian framework and the results show a remarkable similarity to natural questions as validated by a human study. We observe that with the addition of more cues and by minimizing uncertainty among the cues, the Bayesian framework becomes more confident. Ablation studies of our model indicate that a subset of cues is inferior at this task and hence the principled fusion of cues is preferred. Further, we observe that the proposed approach substantially improves over state-of-the-art benchmarks on the quantitative metrics (BLEU-n, METEOR, ROUGE, and CIDEr). Here we provide project link for Deep Bayesian VQG \url{https://delta-lab-iitk.github.io/BVQG/}

Sandeep Kumar, Jiaxi Ying, Jos'e Vin'icius de M. Cardoso et al.

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible to convert the structural constraints of structure into eigenvalue constraints of the graph Laplacian matrix. Then we introduce a unified graph learning framework, lying at the integration of the spectral properties of the Laplacian matrix with Gaussian graphical modeling that is capable of learning structures of a large class of graph families. The proposed algorithms are provably convergent and practically amenable for large-scale semi-supervised and unsupervised graph-based learning tasks. Extensive numerical experiments with both synthetic and real data sets demonstrate the effectiveness of the proposed methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.

Sandeep Kumar, Ketan Rajawat, Daniel P. Palomar

In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex) regularization function. The proposed algorithm incorporates ideas from several existing approaches such as alternate direction method of multipliers (ADMM), successive convex approximation (SCA), distributed and asynchronous algorithms, and inexact gradient methods. Different from a number of existing approaches, however, the proposed framework is flexible enough to incorporate a class of non-convex objective functions, allow distributed operation with and without a fusion center, and include variance reduced methods as special cases. Remarkably, the proposed algorithms are robust to uncertainties arising from random, deterministic, and adversarial sources. The part I of the paper develops two variants of the algorithm under very mild assumptions and establishes first-order convergence rate guarantees. The proof developed here allows for generic errors and delays, paving the way for different variance-reduced, asynchronous, and stochastic implementations, outlined and evaluated in part II.

Badri N. Patro, Vinod K. Kurmi, Sandeep Kumar et al.

In this paper, we propose a method for obtaining sentence-level embeddings. While the problem of securing word-level embeddings is very well studied, we propose a novel method for obtaining sentence-level embeddings. This is obtained by a simple method in the context of solving the paraphrase generation task. If we use a sequential encoder-decoder model for generating paraphrase, we would like the generated paraphrase to be semantically close to the original sentence. One way to ensure this is by adding constraints for true paraphrase embeddings to be close and unrelated paraphrase candidate sentence embeddings to be far. This is ensured by using a sequential pair-wise discriminator that shares weights with the encoder that is trained with a suitable loss function. Our loss function penalizes paraphrase sentence embedding distances from being too large. This loss is used in combination with a sequential encoder-decoder network. We also validated our method by evaluating the obtained embeddings for a sentiment analysis task. The proposed method results in semantic embeddings and outperforms the state-of-the-art on the paraphrase generation and sentiment analysis task on standard datasets. These results are also shown to be statistically significant.

Ketan Rajawat, Sandeep Kumar

Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates the use of batch optimization algorithms that are not scalable to large-sized problems. This paper considers an alternative stochastic stress minimization framework that is amenable to incremental and distributed solutions. A novel linear-complexity stochastic optimization algorithm is proposed that is provably convergent and simple to implement. The applicability of the proposed algorithm to localization and visualization tasks is also expounded. Extensive tests on synthetic and real datasets demonstrate the efficacy of the proposed algorithm.