Hamid Krim

Bo Jiang, Hamid Krim, Tianfu Wu et al.

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the $l^2$ Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.

Siddharth Roheda, Ashkan Panahi, Hamid Krim

In this paper, we address the problem of unsupervised Domain Adaptation. The need for such an adaptation arises when the distribution of the target data differs from that which is used to develop the model and the ground truth information of the target data is unknown. We propose an algorithm that uses optimal transport theory with a verifiably efficient and implementable solution to learn the best latent feature representation. This is achieved by minimizing the cost of transporting the samples from the target domain to the distribution of the source domain.

Sally Ghanem, Hamid Krim

In this work, we seek to exploit the deep structure of multi-modal data to robustly exploit the group subspace distribution of the information using the Convolutional Neural Network (CNN) formalism. Upon unfolding the set of subspaces constituting each data modality, and learning their corresponding encoders, an optimized integration of the generated inherent information is carried out to yield a characterization of various classes. Referred to as deep Multimodal Robust Group Subspace Clustering (DRoGSuRe), this approach is compared against the independently developed state-of-the-art approach named Deep Multimodal Subspace Clustering (DMSC). Experiments on different multimodal datasets show that our approach is competitive and more robust in the presence of noise.

Haoyu Yun, Hamid Krim, Yufang Bao

Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of conventional large-scale deep learning models. In this paper, a kernelized Volterra Neural Network (kVNN) is proposed. The key to the achieved efficiency lies in using a learnable multi-kernel representation, where different interaction orders are modeled by distinct polynomial-kernel components with compact, learnable centers, yielding an order-adaptive parameterization. Features are learned by the composition of layers, each of which consists of parallel branches of different polynomial orders, enabling kVNN filters to directly replace standard convolutional kernels within existing architectures. The theoretical results are substantiated by experiments on two representative tasks: video action recognition and image denoising. The results demonstrate favorable performance-efficiency trade-offs: kVNN consistently yields reduced model (parameters) and computational (GFLOPs) complexity with competitive and often improved performance. These results are maintained even when trained from scratch without large-scale pretraining. In summary, we substantiate that structured kernelized higher-order layers offer a practical path to balancing expressivity and computational cost in modern deep networks.

Vahid Jebraeeli, Bo Jiang, Derya Cansever et al.

In the era of big data, the sheer volume and complexity of datasets pose significant challenges in machine learning, particularly in image processing tasks. This paper introduces an innovative Autoencoder-based Dataset Condensation Model backed by Koopman operator theory that effectively packs large datasets into compact, information-rich representations. Inspired by the predictive coding mechanisms of the human brain, our model leverages a novel approach to encode and reconstruct data, maintaining essential features and label distributions. The condensation process utilizes an autoencoder neural network architecture, coupled with Optimal Transport theory and Wasserstein distance, to minimize the distributional discrepancies between the original and synthesized datasets. We present a two-stage implementation strategy: first, condensing the large dataset into a smaller synthesized subset; second, evaluating the synthesized data by training a classifier and comparing its performance with a classifier trained on an equivalent subset of the original data. Our experimental results demonstrate that the classifiers trained on condensed data exhibit comparable performance to those trained on the original datasets, thus affirming the efficacy of our condensation model. This work not only contributes to the reduction of computational resources but also paves the way for efficient data handling in constrained environments, marking a significant step forward in data-efficient machine learning.

Vahid Jebraeeli, Hamid Krim, Derya Cansever

Vision Transformer (ViT) based autoencoders often underutilize the global Class token and employ static attention mechanisms, limiting both generative control and optimization efficiency. This paper introduces ViTCAE, a framework that addresses these issues by re-purposing the Class token into a generative linchpin. In our architecture, the encoder maps the Class token to a global latent variable that dictates the prior distribution for local, patch-level latent variables, establishing a robust dependency where global semantics directly inform the synthesis of local details. Drawing inspiration from opinion dynamics, we treat each attention head as a dynamical system of interacting tokens seeking consensus. This perspective motivates a convergence-aware temperature scheduler that adaptively anneals each head's influence function based on its distributional stability. This process enables a principled head-freezing mechanism, guided by theoretically-grounded diagnostics like an attention evolution distance and a consensus/cluster functional. This technique prunes converged heads during training to significantly improve computational efficiency without sacrificing fidelity. By unifying a generative Class token with an adaptive attention mechanism rooted in multi-agent consensus theory, ViTCAE offers a more efficient and controllable approach to transformer-based generation.

Haoyu Yun, Hamid Krim

The Vision Transformer (ViT) architecture has become widely recognized in computer vision, leveraging its self-attention mechanism to achieve remarkable success across various tasks. Despite its strengths, ViT's optimization remains confined to modeling local relationships within individual images, limiting its ability to capture the global geometric relationships between data points. To address this limitation, this paper proposes a novel framework that integrates ViT with the proximal tools, enabling a unified geometric optimization approach to enhance feature representation and classification performance. In this framework, ViT constructs the tangent bundle of the manifold through its self-attention mechanism, where each attention head corresponds to a tangent space, offering geometric representations from diverse local perspectives. Proximal iterations are then introduced to define sections within the tangent bundle and project data from tangent spaces onto the base space, achieving global feature alignment and optimization. Experimental results confirm that the proposed method outperforms traditional ViT in terms of classification accuracy and data distribution.

Zhichao Hou, Weizhi Gao, Hamid Krim et al.

This work investigates a novel approach to boost adversarial robustness and generalization by incorporating structural prior into the design of deep learning models. Specifically, our study surprisingly reveals that existing dictionary learning-inspired convolutional neural networks (CNNs) provide a false sense of security against adversarial attacks. To address this, we propose Elastic Dictionary Learning Networks (EDLNets), a novel ResNet architecture that significantly enhances adversarial robustness and generalization. This novel and effective approach is supported by a theoretical robustness analysis using influence functions. Moreover, extensive and reliable experiments demonstrate consistent and significant performance improvement on open robustness leaderboards such as RobustBench, surpassing state-of-the-art baselines. To the best of our knowledge, this is the first work to discover and validate that structural prior can reliably enhance deep learning robustness under strong adaptive attacks, unveiling a promising direction for future research.

Vahid Jebraeeli, Bo Jiang, Hamid Krim et al.

Limited data availability in machine learning significantly impacts performance and generalization. Traditional augmentation methods enhance moderately sufficient datasets. GANs struggle with convergence when generating diverse samples. Diffusion models, while effective, have high computational costs. We introduce an Expansive Synthesis model generating large-scale, information-rich datasets from minimal samples. It uses expander graph mappings and feature interpolation to preserve data distribution and feature relationships. The model leverages neural networks' non-linear latent space, captured by a Koopman operator, to create a linear feature space for dataset expansion. An autoencoder with self-attention layers and optimal transport refines distributional consistency. We validate by comparing classifiers trained on generated data to those trained on original datasets. Results show comparable performance, demonstrating the model's potential to augment training data effectively. This work advances data generation, addressing scarcity in machine learning applications.

Bo Jiang, Hamid Krim, Tianfu Wu et al.

We introduce in this paper a new statistical perspective, exploiting the Jaccard similarity metric, as a measure-based metric to effectively invoke non-linear features in the loss of self-supervised contrastive learning. Specifically, our proposed metric may be interpreted as a dependence measure between two adapted projections learned from the so-called latent representations. This is in contrast to the cosine similarity measure in the conventional contrastive learning model, which accounts for correlation information. To the best of our knowledge, this effectively non-linearly fused information embedded in the Jaccard similarity, is novel to self-supervision learning with promising results. The proposed approach is compared to two state-of-the-art self-supervised contrastive learning methods on three image datasets. We not only demonstrate its amenable applicability in current ML problems, but also its improved performance and training efficiency.

Wen Tang, Emilie Chouzenoux, Jean-Christophe Pesquet et al.

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the recently improved Deep DL methods have also fallen short on a number of issues. We hence propose a novel Deep DL approach where each DL layer can be formulated and solved as a combination of one linear layer and a Recurrent Neural Network, where the RNN is flexibly regraded as a layer-associated learned metric. Our proposed work unveils new insights between the Neural Networks and Deep DL, and provides a novel, efficient and competitive approach to jointly learn the deep transforms and metrics. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing Deep DL, but also state-of-the-art generic Convolutional Neural Networks.

Sally Ghanem, Siddharth Roheda, Hamid Krim

We propose a deep structure encoder using the recently introduced Volterra Neural Networks (VNNs) to seek a latent representation of multi-modal data whose features are jointly captured by a union of subspaces. The so-called self-representation embedding of the latent codes leads to a simplified fusion which is driven by a similarly constructed decoding. The Volterra Filter architecture achieved reduction in parameter complexity is primarily due to controlled non-linearities being introduced by the higher-order convolutions in contrast to generalized activation functions. Experimental results on two different datasets have shown a significant improvement in the clustering performance for VNNs auto-encoder over conventional Convolutional Neural Networks (CNNs) auto-encoder. In addition, we also show that the proposed approach demonstrates a much-improved sample complexity over CNN-based auto-encoder with a superb robust classification performance.

Sally Ghanem, Ashkan Panahi, Hamid Krim et al.

Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. We build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors' data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.

Wen Tang, Emilie Chouzenoux, Jean-Christophe Pesquet et al.

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the improved recently proposed Deep DL (DDL) methods have also fallen short on a number of issues. We propose herein, a novel DDL approach where each DL layer can be formulated as a combination of one linear layer and a Recurrent Neural Network (RNN). The RNN is shown to flexibly account for the layer-associated and learned metric. Our proposed work unveils new insights into Neural Networks and DDL and provides a new, efficient and competitive approach to jointly learn a deep transform and a metric for inference applications. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing DDL but also state-of-the-art generic CNNs.

Siddharth Roheda, Hamid Krim

The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals in ML, and particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a Volterra filter-inspired Network architecture. This architecture introduces controlled non-linearities in the form of interactions between the delayed input samples of data. We propose a cascaded implementation of Volterra Filtering so as to significantly reduce the number of parameters required to carry out the same classification task as that of a conventional Neural Network. We demonstrate an efficient parallel implementation of this Volterra Neural Network (VNN), along with its remarkable performance while retaining a relatively simpler and potentially more tractable structure. Furthermore, we show a rather sophisticated adaptation of this network to nonlinearly fuse the RGB (spatial) information and the Optical Flow (temporal) information of a video sequence for action recognition. The proposed approach is evaluated on UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform state of the art CNN approaches.

Yuming Huang, Ashkan Panahi, Hamid Krim et al.

We investigate the widely encountered problem of detecting communities in multiplex networks, such as social networks, with an unknown arbitrary heterogeneous structure. To improve detectability, we propose a generative model that leverages the multiplicity of a single community in multiple layers, with no prior assumption on the relation of communities among different layers. Our model relies on a novel idea of incorporating a large set of generic localized community label constraints across the layers, in conjunction with the celebrated Stochastic Block Model (SBM) in each layer. Accordingly, we build a probabilistic graphical model over the entire multiplex network by treating the constraints as Bayesian priors. We mathematically prove that these constraints/priors promote existence of identical communities across layers without introducing further correlation between individual communities. The constraints are further tailored to render a sparse graphical model and the numerically efficient Belief Propagation algorithm is subsequently employed. We further demonstrate by numerical experiments that in the presence of consistent communities between different layers, consistent communities are matched, and the detectability is improved over a single layer. We compare our model with a "correlated model" which exploits the prior knowledge of community correlation between layers. Similar detectability improvement is obtained under such a correlation, even though our model relies on much milder assumptions than the correlated model. Our model even shows a better detection performance over a certain correlation and signal to noise ratio (SNR) range. In the absence of community correlation, the correlation model naturally fails, while ours maintains its performance.

Yuming Huang, Ashkan Panahi, Hamid Krim et al.

We present a novel adversarial framework for training deep belief networks (DBNs), which includes replacing the generator network in the methodology of generative adversarial networks (GANs) with a DBN and developing a highly parallelizable numerical algorithm for training the resulting architecture in a stochastic manner. Unlike the existing techniques, this framework can be applied to the most general form of DBNs with no requirement for back propagation. As such, it lays a new foundation for developing DBNs on a par with GANs with various regularization units, such as pooling and normalization. Foregoing back-propagation, our framework also exhibits superior scalability as compared to other DBN and GAN learning techniques. We present a number of numerical experiments in computer vision as well as neurosciences to illustrate the main advantages of our approach.

Shahin Mahdizadehaghdam, Ashkan Panahi, Hamid Krim

We propose a new approach to Generative Adversarial Networks (GANs) to achieve an improved performance with additional robustness to its so-called and well recognized mode collapse. We first proceed by mapping the desired data onto a frame-based space for a sparse representation to lift any limitation of small support features prior to learning the structure. To that end we start by dividing an image into multiple patches and modifying the role of the generative network from producing an entire image, at once, to creating a sparse representation vector for each image patch. We synthesize an entire image by multiplying generated sparse representations to a pre-trained dictionary and assembling the resulting patches. This approach restricts the output of the generator to a particular structure, obtained by imposing a Union of Subspaces (UoS) model to the original training data, leading to more realistic images, while maintaining a desired diversity. To further regularize GANs in generating high-quality images and to avoid the notorious mode-collapse problem, we introduce a third player in GANs, called reconstructor. This player utilizes an auto-encoding scheme to ensure that first, the input-output relation in the generator is injective and second each real image corresponds to some input noise. We present a number of experiments, where the proposed algorithm shows a remarkably higher inception score compared to the equivalent conventional GANs.

Wen Tang, Ashkan Panahi, Hamid Krim

Zero-shot learning (ZSL) which aims to recognize unseen object classes by only training on seen object classes, has increasingly been of great interest in Machine Learning, and has registered with some successes. Most existing ZSL methods typically learn a projection map between the visual feature space and the semantic space and mainly suffer which is prone to a projection domain shift primarily due to a large domain gap between seen and unseen classes. In this paper, we propose a novel inductive ZSL model based on projecting both visual and semantic features into a common distinct latent space with class-specific knowledge, and on reconstructing both visual and semantic features by such a distinct common space to narrow the domain shift gap. We show that all these constraints on the latent space, class-specific knowledge, reconstruction of features and their combinations enhance the robustness against the projection domain shift problem, and improve the generalization ability to unseen object classes. Comprehensive experiments on four benchmark datasets demonstrate that our proposed method is superior to state-of-the-art algorithms.

Siddharth Roheda, Hamid Krim, Benjamin S. Riggan

In recent years, multi-modal fusion has attracted a lot of research interest, both in academia, and in industry. Multimodal fusion entails the combination of information from a set of different types of sensors. Exploiting complementary information from different sensors, we show that target detection and classification problems can greatly benefit from this fusion approach and result in a performance increase. To achieve this gain, the information fusion from various sensors is shown to require some principled strategy to ensure that additional information is constructively used, and has a positive impact on performance. We subsequently demonstrate the viability of the proposed fusion approach by weakening the strong dependence on the functionality of all sensors, hence introducing additional flexibility in our solution and lifting the severe limitation in unconstrained surveillance settings with potential environmental impact. Our proposed data driven approach to multimodal fusion, exploits selected optimal features from an estimated latent space of data across all modalities. This hidden space is learned via a generative network conditioned on individual sensor modalities. The hidden space, as an intrinsic structure, is then exploited in detecting damaged sensors, and in subsequently safeguarding the performance of the fused sensor system. Experimental results show that such an approach can achieve automatic system robustness against noisy/damaged sensors.

Arman Rahbar, Ashkan Panahi, Morteza Haghir Chehreghani et al.

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

Wen Tang, Ashkan Panahi, Hamid Krim et al.

Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the learning stages. These various constraints, however, lead to additional computational complexity. We hence propose an efficient Discriminative Convolutional Analysis Dictionary Learning (DCADL) method, as a lower cost Discriminative DL framework, to both characterize the image structures and refine the interclass structure representations. The proposed DCADL jointly learns a convolutional analysis dictionary and a universal classifier, while greatly reducing the time complexity in both training and testing phases, and achieving a competitive accuracy, thus demonstrating great performance in many experiments with standard databases.

Wen Tang, Ashkan Panahi, Hamid Krim et al.

A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of discrimination. A simple classifier is also simultaneously included into the formulated functional to ensure a more complete consistent classification. The solution of the algorithm is efficiently obtained by the linearized alternating direction method of multipliers. Moreover, a distributed structured analysis dictionary learning is also presented to address large scale datasets. It can group-(class-) independently train the structured analysis dictionaries by different machines/cores/threads, and therefore avoid a high computational cost. A consensus structured analysis dictionary and a global classifier are jointly learned in the distributed approach to safeguard the discriminative power and the efficiency of classification. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, the training and testing computational complexity are also greatly reduced.

Wen Tang, Ashkan Panahi, Hamid Krim et al.

We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class characteristic structure of independent subspaces and impose it on the classification error constrained analysis dictionary learning. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, our method greatly reduces the training and testing computational complexity.

Ashkan Panahi, Hamid Krim, Liyi Dai

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we present an alternative semi-parametric framework which foregoes the ordinarily required feedback, by introducing the novel idea of geometric regularization. We show that certain deep learning techniques such as residual network (ResNet) architecture are closely related to our approach. Hence, our technique can be used to analyze these types of deep learning. Moreover, we present preliminary results which confirm that our approach can be easily trained to obtain complex structures.

Shahin Mahdizadehaghdam, Ashkan Panahi, Hamid Krim et al.

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The dictionaries and classification parameters are trained by a classification objective, and the sparse features are extracted by reducing a reconstruction loss in each layer. The reconstruction objectives in some sense regularize the classification problem and inject source signal information in the extracted features. The performance of the proposed hierarchical method increases by adding more layers, which consequently makes this model easier to tune and adapt. The proposed algorithm furthermore, shows remarkably lower fooling rate in presence of adversarial perturbation. The validation of the proposed approach is based on its classification performance using four benchmark datasets and is compared to a CNN of similar size.

Hui Guan, Thanos Gentimis, Hamid Krim et al.

We introduce the idea of Data Readiness Level (DRL) to measure the relative richness of data to answer specific questions often encountered by data scientists. We first approach the problem in its full generality explaining its desired mathematical properties and applications and then we propose and study two DRL metrics. Specifically, we define DRL as a function of at least four properties of data: Noisiness, Believability, Relevance, and Coherence. The information-theoretic based metrics, Cosine Similarity and Document Disparity, are proposed as indicators of Relevance and Coherence for a piece of data. The proposed metrics are validated through a text-based experiment using Twitter data.

Saba Emrani, Hamid Krim

We propose a geometric model-free causality measurebased on multivariate delay embedding that can efficiently detect linear and nonlinear causal interactions between time series with no prior information. We then exploit the proposed causal interaction measure in real MEG data analysis. The results are used to construct effective connectivity maps of brain activity to decode different categories of visual stimuli. Moreover, we discovered that the MEG-based effective connectivity maps as a response to structured images exhibit more geometric patterns, as disclosed by analyzing the evolution of toplogical structures of the underlying networks using persistent homology. Extensive simulation and experimental result have been carried out to substantiate the capabilities of the proposed approach.

Xiao Bian, Hamid Krim

Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying structure may be affected by sparse errors and/or outliers. In this paper, we propose a bi-sparse model as a framework to analyze this problem and provide a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We further show the effectiveness of our method by experiments on both synthetic data and real-world vision data.