arXiv subjects

Ljubisa Stankovic

Publications and source records attributed to Ljubisa Stankovic.

At least 19 recordsLinked to original sources

arXiv2026

GraphNNK -- Graph Classification and Interpretability

Graph Neural Networks (GNNs) have become a standard approach for learning from graph-structured data. However, their reliance on parametric classifiers (most often linear softmax layers) limits interpretability and sometimes hinders generalization. Recent work on interpolation-based methods, particularly Non-Negative Kernel regression (NNK), has demonstrated that predictions can be expressed as convex combinations of similar training examples in the embedding space, yielding both theoretical results and interpretable explanations.

cs.LG↗

arXiv2024

Fourier Analysis of Signals on Directed Acyclic Graphs (DAG) Using Graph Zero-Padding

Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix yields all eigenvalues equal to zero. This inherent property of DAGs results in an inability to differentiate between frequency components of signals on such graphs. This problem can be addressed by {alternating the Fourier basis or adding edges in a DAG}. However, these approaches change the physics of the considered problem. To address this limitation, we propose a \textit{graph zero-padding} approach. This approach involves augmenting the original DAG with additional vertices that are connected to the existing structure. The added vertices are characterized by signal values set to zero. The proposed technique enables the spectral evaluation of system outputs on DAGs (in almost all cases), that is the computation of vertex-domain convolution without the adverse effects of aliasing due to changes in a graph structure, { with the ultimate goal of preserving the output of the system on a graph as if the changes in the graph structure were not performed}.

cs.IT↗

arXiv2024

Multi-task SAR Image Processing via GAN-based Unsupervised Manipulation

Generative Adversarial Networks (GANs) have shown tremendous potential in synthesizing a large number of realistic SAR images by learning patterns in the data distribution. Some GANs can achieve image editing by introducing latent codes, demonstrating significant promise in SAR image processing. Compared to traditional SAR image processing methods, editing based on GAN latent space control is entirely unsupervised, allowing image processing to be conducted without any labeled data. Additionally, the information extracted from the data is more interpretable. This paper proposes a novel SAR image processing framework called GAN-based Unsupervised Editing (GUE), aiming to address the following two issues: (1) disentangling semantic directions in the GAN latent space and finding meaningful directions; (2) establishing a comprehensive SAR image processing framework while achieving multiple image processing functions. In the implementation of GUE, we decompose the entangled semantic directions in the GAN latent space by training a carefully designed network. Moreover, we can accomplish multiple SAR image processing tasks (including despeckling, localization, auxiliary identification, and rotation editing) in a single training process without any form of supervision. Extensive experiments validate the effectiveness of the proposed method.

cs.CV↗

arXiv2024

Graph Fourier Transform Enhancement through Envelope Extensions

Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where embedding a line digraph into a cycle digraph facilitates the powerful Discrete Fourier Transform for signal analysis, addressing the structural complexities of general digraphs can help overcome the limitations of the Graph Fourier Transform (GFT) and unlock its potential. The Discrete Fourier Transform (DFT) serves as a Graph Fourier Transform for both cycle graphs and Cayley digraphs on the finite cyclic groups $\mathbb{Z}_N$. We propose a systematic method to identify a class of such Cayley digraphs that can encompass a given directed graph. By embedding the directed graph into these Cayley digraphs and opting for envelope extensions that naturally support the Graph Fourier Transform, the GFT functionalities of these extensions can be harnessed for signal analysis. Among the potential envelopes, optimal performance is achieved by selecting one that meets key properties. This envelope's structure closely aligns with the characteristics of the original digraph. The Graph Fourier Transform of this envelope is reliable in terms of numerical stability, and its columns approximately form an eigenbasis for the adjacency matrix associated with the original digraph. It is shown that the envelope extensions possess a convolution product, with their GFT fulfilling the convolution theorem. Additionally, shift-invariant graph filters (systems) are described as the convolution operator, analogous to the classical case. This allows the utilization of systems for signal analysis.

cs.IT↗

arXiv2023

Eigenvalues of Symmetric Non-normalized Discrete Trigonometric Transforms

A comprehensive approach to the spectrum characterization (derivation of eigenvalues and the corresponding multiplicities) for non-normalized, symmetric discrete trigonometric transforms (DTT) is presented in the paper. Eight types of the DTT are analyzed. New explicit analytic expressions for the eigenvalues, together with their multiplicities, for the cases of three DTT (DCT$_{(1)}$, DCT$_{(5)}$, and DST$_{(8)}$), are the main contribution of this paper. Moreover, the presented theory is supplemented by new, original derivations for the closed-form expressions of the square and the trace of analyzed DTT matrices.

eess.SP↗

arXiv2023

Cluster-CAM: Cluster-Weighted Visual Interpretation of CNNs' Decision in Image Classification

Despite the tremendous success of convolutional neural networks (CNNs) in computer vision, the mechanism of CNNs still lacks clear interpretation. Currently, class activation mapping (CAM), a famous visualization technique to interpret CNN's decision, has drawn increasing attention. Gradient-based CAMs are efficient while the performance is heavily affected by gradient vanishing and exploding. In contrast, gradient-free CAMs can avoid computing gradients to produce more understandable results. However, existing gradient-free CAMs are quite time-consuming because hundreds of forward interference per image are required. In this paper, we proposed Cluster-CAM, an effective and efficient gradient-free CNN interpretation algorithm. Cluster-CAM can significantly reduce the times of forward propagation by splitting the feature maps into clusters in an unsupervised manner. Furthermore, we propose an artful strategy to forge a cognition-base map and cognition-scissors from clustered feature maps. The final salience heatmap will be computed by merging the above cognition maps. Qualitative results conspicuously show that Cluster-CAM can produce heatmaps where the highlighted regions match the human's cognition more precisely than existing CAMs. The quantitative evaluation further demonstrates the superiority of Cluster-CAM in both effectiveness and efficiency.

cs.CV↗

arXiv2023

Fair and skill-diverse student group formation via constrained k-way graph partitioning

Forming the right combination of students in a group promises to enable a powerful and effective environment for learning and collaboration. However, defining a group of students is a complex task which has to satisfy multiple constraints. This work introduces an unsupervised algorithm for fair and skill-diverse student group formation. This is achieved by taking account of student course marks and sensitive attributes provided by the education office. The skill sets of students are determined using unsupervised dimensionality reduction of course mark data via the Laplacian eigenmap. The problem is formulated as a constrained graph partitioning problem, whereby the diversity of skill sets in each group are maximised, group sizes are upper and lower bounded according to available resources, and `balance' of a sensitive attribute is lower bounded to enforce fairness in group formation. This optimisation problem is solved using integer programming and its effectiveness is demonstrated on a dataset of student course marks from Imperial College London.

cs.LG↗

arXiv2022

Demystifying CNNs for Images by Matched Filters

The success of convolution neural networks (CNN) has been revolutionising the way we approach and use intelligent machines in the Big Data era. Despite success, CNNs have been consistently put under scrutiny owing to their \textit{black-box} nature, an \textit{ad hoc} manner of their construction, together with the lack of theoretical support and physical meanings of their operation. This has been prohibitive to both the quantitative and qualitative understanding of CNNs, and their application in more sensitive areas such as AI for health. We set out to address these issues, and in this way demystify the operation of CNNs, by employing the perspective of matched filtering. We first illuminate that the convolution operation, the very core of CNNs, represents a matched filter which aims to identify the presence of features in input data. This then serves as a vehicle to interpret the convolution-activation-pooling chain in CNNs under the theoretical umbrella of matched filtering, a common operation in signal processing. We further provide extensive examples and experiments to illustrate this connection, whereby the learning in CNNs is shown to also perform matched filtering, which further sheds light onto physical meaning of learnt parameters and layers. It is our hope that this material will provide new insights into the understanding, constructing and analysing of CNNs, as well as paving the way for developing new methods and architectures of CNNs.

cs.CV↗

arXiv2022

VS-CAM: Vertex Semantic Class Activation Mapping to Interpret Vision Graph Neural Network

Graph convolutional neural network (GCN) has drawn increasing attention and attained good performance in various computer vision tasks, however, there lacks a clear interpretation of GCN's inner mechanism. For standard convolutional neural networks (CNNs), class activation mapping (CAM) methods are commonly used to visualize the connection between CNN's decision and image region by generating a heatmap. Nonetheless, such heatmap usually exhibits semantic-chaos when these CAMs are applied to GCN directly. In this paper, we proposed a novel visualization method particularly applicable to GCN, Vertex Semantic Class Activation Mapping (VS-CAM). VS-CAM includes two independent pipelines to produce a set of semantic-probe maps and a semantic-base map, respectively. Semantic-probe maps are used to detect the semantic information from semantic-base map to aggregate a semantic-aware heatmap. Qualitative results show that VS-CAM can obtain heatmaps where the highlighted regions match the objects much more precisely than CNN-based CAM. The quantitative evaluation further demonstrates the superiority of VS-CAM.

cs.CV↗

arXiv2022

Analytical Interpretation of Latent Codes in InfoGAN with SAR Images

Generative Adversarial Networks (GANs) can synthesize abundant photo-realistic synthetic aperture radar (SAR) images. Some recent GANs (e.g., InfoGAN), are even able to edit specific properties of the synthesized images by introducing latent codes. It is crucial for SAR image synthesis since the targets in real SAR images are with different properties due to the imaging mechanism. Despite the success of InfoGAN in manipulating properties, there still lacks a clear explanation of how these latent codes affect synthesized properties, thus editing specific properties usually relies on empirical trials, unreliable and time-consuming. In this paper, we show that latent codes are disentangled to affect the properties of SAR images in a non-linear manner. By introducing some property estimators for latent codes, we are able to provide a completely analytical nonlinear model to decompose the entangled causality between latent codes and different properties. The qualitative and quantitative experimental results further reveal that the properties can be calculated by latent codes, inversely, the satisfying latent codes can be estimated given desired properties. In this case, properties can be manipulated by latent codes as we expect.

cs.CV↗

arXiv2022

Convolutional Neural Networks Demystified: A Matched Filtering Perspective Based Tutorial

Deep Neural Networks (DNN) and especially Convolutional Neural Networks (CNN) are a de-facto standard for the analysis of large volumes of signals and images. Yet, their development and underlying principles have been largely performed in an ad-hoc and black box fashion. To help demystify CNNs, we revisit their operation from first principles and a matched filtering perspective. We establish that the convolution operation within CNNs, their very backbone, represents a matched filter which examines the input signal/image for the presence of pre-defined features. This perspective is shown to be physically meaningful, and serves as a basis for a step-by-step tutorial on the operation of CNNs, including pooling, zero padding, various ways of dimensionality reduction. Starting from first principles, both the feed-forward pass and the learning stage (via back-propagation) are illuminated in detail, both through a worked-out numerical example and the corresponding visualizations. It is our hope that this tutorial will help shed new light and physical intuition into the understanding and further development of deep neural networks.

cs.IT↗

arXiv2021

Understanding the Basis of Graph Convolutional Neural Networks via an Intuitive Matched Filtering Approach

Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation are rarely examined due to the black box nature of NNs. To this end, we revisit the operation of GCNNs and show that their convolution layers effectively perform matched filtering of input data with the chosen patterns (features). This allows us to provide a unifying account of GCNNs through a matched filter perspective, whereby the nonlinear ReLU and max-pooling layers are also discussed within the matched filtering framework. This is followed by a step-by-step guide on information propagation and learning in GCNNs. It is also shown that standard CNNs and fully connected NNs can be obtained as a special case of GCNNs. A carefully chosen numerical example guides the reader through the various steps of GCNN operation and learning both visually and numerically.

cs.LG↗

arXiv2021

Dynamic Portfolio Cuts: A Spectral Approach to Graph-Theoretic Diversification

Stock market returns are typically analyzed using standard regression, yet they reside on irregular domains which is a natural scenario for graph signal processing. To this end, we consider a market graph as an intuitive way to represent the relationships between financial assets. Traditional methods for estimating asset-return covariance operate under the assumption of statistical time-invariance, and are thus unable to appropriately infer the underlying true structure of the market graph. This work introduces a class of graph spectral estimators which cater for the nonstationarity inherent to asset price movements, and serve as a basis to represent the time-varying interactions between assets through a dynamic spectral market graph. Such an account of the time-varying nature of the asset-return covariance allows us to introduce the notion of dynamic spectral portfolio cuts, whereby the graph is partitioned into time-evolving clusters, allowing for online and robust asset allocation. The advantages of the proposed framework over traditional methods are demonstrated through numerical case studies using real-world price data.

q-fin.PM↗

arXiv2021

On the Sparsity Bound for the Existence of a Unique Solution in Compressive Sensing by the Gershgorin Theorem

Since compressive sensing deals with a signal reconstruction using a reduced set of measurements, the existence of a unique solution is of crucial importance. The most important approach to this problem is based on the restricted isometry property which is computationally unfeasible. The coherence index-based uniqueness criteria are computationally efficient, however, they are pessimistic. An approach to alleviate this problem has been recently introduced by relaxing the coherence index condition for the unique signal reconstruction using the orthogonal matching pursuit approach. This approach can be further relaxed and the sparsity bound improved if we consider only the solution existence rather than its reconstruction. One such improved bound for the sparsity limit is derived in this paper using the Gershgorin disk theorem.

cs.IT↗

arXiv2021

Improved Coherence Index-Based Bound in Compressive Sensing

Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible calculation, coherence index is one of very few CS metrics with a considerable practical importance. In this paper, we propose an improvement of the coherence based uniqueness relation for the matching pursuit algorithms. Starting from a simple and intuitive derivation of the standard uniqueness condition based on the coherence index, we derive a less conservative coherence index-based lower bound for signal sparsity. The results are generalized to the uniqueness condition of the $l_0$-norm minimization for a signal represented in two orthonormal bases.

cs.IT↗

arXiv2021

Nonstationary Portfolios: Diversification in the Spectral Domain

Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ standard time-averaging based estimators which suffer significant information loss if the market observables are non-stationary. To this end, we reformulate the portfolio optimization problem in the spectral domain to cater for the nonstationarity inherent to asset price movements and, in this way, allow for optimal capital allocations to be time-varying. Unlike existing spectral portfolio techniques, the proposed framework employs augmented complex statistics in order to exploit the interactions between the real and imaginary parts of the complex spectral variables, which in turn allows for the modelling of both harmonics and cyclostationarity in the time domain. The advantages of the proposed framework over traditional methods are demonstrated through numerical simulations using real-world price data.

q-fin.ST↗

arXiv2020

A Probabilistic Spectral Analysis of Multivariate Real-Valued Nonstationary Signals

A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity, wide-sense stationarity and cyclostationarity -- are designated respectively by the mean, Hermitian variance and pseudo-variance of the associated time-frequency representation (TFR). For rigour, the estimators of the TFR distribution parameters are derived within a maximum likelihood framework and are shown to be statistically consistent, owing to the statistical identifiability of the proposed distribution parametrization. By virtue of the assumed probabilistic model, a generalised likelihood ratio test (GLRT) for nonstationarity detection is also proposed. Intuitive examples demonstrate the utility of the derived probabilistic framework for spectral analysis in low-SNR environments.

eess.SP↗

arXiv2020

The Support Uncertainty Principle and the Graph Rihaczek Distribution: Revisited and Improved

The classical support uncertainty principle states that the signal and its discrete Fourier transform (DFT) cannot be localized simultaneously in an arbitrary small area in the time and the frequency domain. The product of the number of nonzero samples in the time domain and the frequency domain is greater or equal to the total number of signal samples. The support uncertainty principle has been extended to the arbitrary orthogonal pairs of signal basis and the graph signals, stating that the product of supports in the vertex domain and the spectral domain is greater than the reciprocal squared maximum absolute value of the basis functions. This form is then used in compressive sensing and sparse signal processing to define the reconstruction conditions. In this paper, we will revisit the graph signal uncertainty principle using the graph Rihaczek distribution as an analysis tool and derive an improved bound for the support uncertainty principle of graph signals.

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