Canonical correlation analysis (CCA) is a widely used multivariate analysis technique for explaining the relation between two sets of variables. It achieves this goal by finding linear combinations of the variables with maximal correlation. Recently, under the assumption that leading canonical directions are sparse, various penalized CCA procedures have been proposed for high dimensional data applications. However, all these procedures have the inconvenience of not preserving the sparsity among the retained leading canonical directions. To address this issue, two new sparse CCA methods are proposed in this paper. The first method is obtained by diagonal thresholding of two square matrices derived from the cross-covariance matrix of the two sets of variables where each matrix characterizes one set of variables. A model selection criterion is used to select the number of variables to retain from each matrix diagonal. The second method is derived within an adaptive alternating penalized least squares framework where the 1 2-norm is used as a penalty promoting block sparsity. Compared to existing sparse CCA methods, the proposed methods have the advantage of preserving the sparsity across the retained canonical loading vectors. Their performance are illustrated in an extended experimental study which shows the superior performance of the proposed methods.

Domain adaptation is a well-studied field in machine learning. Distribution shift between train (source) and test (target) datasets is a common problem encountered in machine learning applications. One approach to resolve this issue is to use the Unsupervised Domain Adaptation (UDA) technique that carries out knowledge transfer from a label-rich source domain to an unlabeled target domain. Outliers that exist in either source or target datasets can introduce additional challenges when using UDA in practice. In this article, \(\alpha\) -divergence is used as a measure to minimize the discrepancy between the source and target distributions while inheriting robustness, adjustable with a single parameter \(\alpha\) , as the prominent feature of this measure. Here, it is shown that the other well-known divergence-based UDA techniques can be derived as special cases of the proposed method. Furthermore, a theoretical upper bound is derived for the loss in the target domain in terms of the source loss and the \(\alpha\) -divergence between the joint distributions in the two domains. The robustness of the proposed method is validated through testing on several benchmarked datasets in open-set and partial UDA setups where extra classes existing in target and source datasets are considered as outliers. The code is publicly available at https://github.com/rashidis/IT-RUDA .

Detecting small objects in optical images and videos is a significant challenge in numerous intelligent transportation and autonomous systems. State-of-the-art generic object detection methods fail to accurately localize and identify such small objects (e.g., pedestrians, small vehicles, obstacles). Because small objects occupy only a small area in the input image (e.g.,$32 \times 32$pixels or less), the information extracted from such a small area is not always rich enough to support decision-making. Multidisciplinary strategies are being developed by researchers working at the interface of deep learning and computer vision to enhance the performance of Small Object Detection (SOD). In this paper, we provide a comprehensive review of over 160 research papers published between 2017 and 2022 in order to survey this growing subject. This paper summarizes the existing literature and provides a taxonomy that illustrates the broad picture of current research. We further explore methods to boost the performance of small object detection in maritime settings, where enhanced performance is crucial for ensuring safety and managing traffic. Detecting small objects in the maritime environment requires additional considerations and the current survey aims to review the advanced techniques addressing those aspects. In addition, the popular SOD datasets for generic and maritime applications are discussed, and also well-known evaluation metrics for the state-of-the-art methods on some of the datasets are provided. The link to these datasets appears inhttps://github.com/arekavandi/Datasets_SOD.

While latent diffusion models (LDMs) excel at creating imaginative images, they often lack precision in semantic fidelity and spatial control over where objects are generated. To address these deficiencies, we introduce the Box-it-to-Bind-it (B2B) module—a novel, training-free approach for improving spatial control and semantic accuracy in text-to-image (T2I) diffusion models. B2B targets three key challenges in T2I: catastrophic neglect, attribute binding, and layout guidance. The process encompasses two main steps: (i)Object generation, which adjusts the latent encoding to guarantee object generation and directs it within specified bounding boxes, and (ii)Attribute binding, ensuring that generated objects adhere to their specified attributes in the prompt. B2B is designed as a compatible plug-and-play module for existing T2I models like Stable Diffusion and Gligen, markedly enhancing models’ performance in addressing these key challenges. We assess our technique on the well-established CompBench and TIFA score benchmarks, and HRS dataset where B2B not only surpasses methods specialized in either attribute binding or layout guidance but also uniquely excels by integrating these capabilities to deliver enhanced overall performance.

In this paper, novel robust principal component analysis (RPCA) methods are proposed to exploit the local structure of datasets. The proposed methods are derived by minimizing the α -divergence between the sample distribution and the Gaussian density model. The α- divergence is used in different frameworks to represent variants of RPCA approaches including orthogonal, non-orthogonal, and sparse methods. We show that the classical PCA is a special case of our proposed methods where the α- divergence is reduced to the Kullback-Leibler (KL) divergence. It is shown in simulations that the proposed approaches recover the underlying principal components (PCs) by down-weighting the importance of structured and unstructured outliers. Furthermore, using simulated data, it is shown that the proposed methods can be applied to fMRI signal recovery and Foreground-Background (FB) separation in video analysis. Results on real world problems of FB separation as well as image reconstruction are also provided.

In this paper, we generalize the well-known Expectation Maximization (EM) algorithm using the α−divergence for Gaussian Mixture Model (GMM). This approach is used in robust subspace detection when the number of parameters is kept small to avoid overfitting and large estimation variances. The level of robustness can be tuned by the parameter α. When α → 1, our method is equivalent to the standard EM approach and for α < 1 the method is robust against potential outliers. Simulation results show that the method outperforms the standard EM when it comes to mismatches between noise models and their realizations. In addition, we use the proposed method to detect active brain areas using collected functional Magnetic Resonance Imaging (fMRI) data during task-related experiments.

We studied the problem of robust subspace tracking (RST) in contaminated environments. Leveraging the fast approximated power iteration and α-divergence, a novel robust algorithm called αFAPI was developed for tracking the underlying principal subspace of streaming data over time. αFAPI is fast and it outperforms many RST methods while only having a low complexity linear to the data dimension. Some experiments were conducted to illustrate the performance of αFAPI.

This paper presents a novel approach for cross-domain descriptor matching between 2D and 3D modalities. The 2D-3D matching is applied to localize 2D images in 3D point clouds. Direct cross-domain matching allows our technique to localize images in any type of 3D point cloud without any constraints on the nature or mechanism by which it is obtained. We propose a learning based framework, called Desc-Matcher, to directly match features between the two modalities. A dataset of 2D and 3D features with corresponding locations in images and point clouds is generated to train the Desc-Matcher. To estimate the pose of an image in any 3D cloud, keypoints and feature descriptors are extracted from the query image and the point cloud. The trained Desc-Matcher is then used to match the features from the image and the point cloud. A robust pose estimator is used to predict the location and orientation of the query image from the corresponding positions of the matched 2D and 3D features. We carried out an extensive evaluation of the proposed method for indoor and outdoor scenarios and with different types of point clouds to verify the feasibility of our approach. Experimental results show that the proposed approach can reliably estimate the 6-DOF poses of query cameras in any type of 3D point cloud with high precision. We achieved average median errors of 1.09cm/0.27∘ and 19cm/0.39∘ on the Stanford and Cambridge datasets, respectively.

Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the α- divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter α . It is shown that when α→ 1 , these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of . Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented.

The problem of detecting a subspace signal in colored Gaussian noise with unknown covariance matrix is investigated when the training data may contain samples with target signal. The target signal is assumed that it lies in a subspace spanned by columns of a known matrix. To develop the test, an ad hoc approach, similar to the classical adaptive matched filter (AMF) is used where instead of the maximum likelihood (ML) estimator of the covariance, the minimum α-divergence based estimator is substituted in the likelihood ratio. This test just depends on the single parameter α and as a special case can be turned to the AMF. For a range of α, the proposed test has the benefits of being robust to outliers and the existence of other targets in the training data. Numerical examples illustrating that the proposed detector can achieve better detection rates in such a scenario while providing almost the same performance in a target free scenario are presented.

The problem of detecting a subspace signal in the presence of subspace interference and contaminated Gaussian noise with unknown variance is investigated. The target signal is assumed to lie in a subspace spanned by the columns of a known matrix. To develop the test, the same steps used in the generalized likelihood ratio test (GLRT) are used where instead of the maximum likelihood (ML) estimator of the parameters, the minimum α-divergence based estimator is substituted in the test to increase the robustness of the test against contaminations in noise. This test depends on the single parameter α and as the special case corresponds to the well known GLRT. Numerical examples illustrating that the proposed test can achieve better detection rates in such scenarios are presented. Moreover, the test is applied to real fMRI dataset to detect the active area of the brain for some task-related inputs.

In this paper, a new robust principal component analysis (RPCA) method which enables us to exploit the main components of a given corrupted data with non Gaussian outliers is proposed. This method is based on the α-divergence which is a parametric measure from information geometry. The proposed method is adjustable using a hyperparameter α and reduces to the classical PCA as a particular case. In order to derive the main components, the α-divergence between the empirical data distribution and the assumed model for the distribution is minimized with respect to the unknown parameters. The singular value decomposition (SVD) of the estimated covariance matrix is then used to exploit the main direction of the data. The proposed method is applied to some video and signal processing applications and the results show the superiority of the proposed method over classical PCA and other existing robust methods.

Adaptive subspace detectors (ASD) generalize matched subspace detectors (MSD) by accounting for possible correlation. Both ASD and MSD are derived using the generalized likelihood ratio test (GLRT). While MSD assumes there is no correlation between observations, ASD estimates a sample covariance matrix of possibly correlated samples using signal-free observations. In this paper, we address the performance of the ASD when the number of secondary data is insufficient and the observed signal lies in higher dimensional space. Such high dimensional spaces are frequently encountered in functional magnetic resonance imaging (fMRI) data for the analysis of brain activation detection. We propose a methodology that works based on the latent variables in a lower dimensional space. A low-rank decomposition of the sample covariance matrix is derived based on the singular value decomposition (SVD) and an adaptive basis selection method is used to decide which eigen-vectors are useful in data projection. Performing detection in the lower dimensional subspace has the benefit of reducing the number of parameters which need to be estimated. Simulation results show superiority of our proposed adaptive reduced subspace detector (ARSD) over conventional ASD in term of probability of detection.