Principal component analysis (PCA) is a workhorse of modern data science. Practitioners typically perform PCA assuming the data conforms to Euclidean geometry. However, for specific data types, such as hierarchical data, other geometrical spaces may be more appropriate. We study PCA in space forms; that is, those with constant positive (spherical) and negative (hyperbolic) curvatures, in addition to zero-curvature (Euclidean) spaces. At any point on a Riemannian manifold, one can define a Riemannian affine subspace based on a set of tangent vectors and use invertible maps to project tangent vectors to the manifold and vice versa. Finding a low-dimensional Riemannian affine subspace for a set of points in a space form amounts to dimensionality reduction because, as we show, any such affine subspace is isometric to a space form of the same dimension and curvature. To find principal components, we seek a (Riemannian) affine subspace that best represents a set of manifold-valued data points with the minimum average cost of projecting data points onto the affine subspace. We propose specific cost functions that bring about two major benefits: (1) the affine subspace can be estimated by solving an eigenequation -- similar to that of Euclidean PCA, and (2) optimal affine subspaces of different dimensions form a nested set. These properties provide advances over existing methods which are mostly iterative algorithms with slow convergence and weaker theoretical guarantees. Specifically for hyperbolic PCA, the associated eigenequation operates in the Lorentzian space, endowed with an indefinite inner product; we thus establish a connection between Lorentzian and Euclidean eigenequations. We evaluate the proposed space form PCA on data sets simulated in spherical and hyperbolic spaces and show that it outperforms alternative methods in convergence speed or accuracy, often both.

This article belongs to the series "Probabilistic Deep Learning". This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e. know what they do not know. The frequentist approach to statistics is based on the idea of repeated sampling and long-run relative frequency. It involves constructing hypotheses about a population and testing them using sample data.

The global banking industry faces heightened risks due to the evolving financial crime compliance mandates to clamp down on money laundering and sanctioned entities and maintain CDD/EDD. Among all, money laundering appears the most pernicious, with more illicit transactions evading anti-money laundering (AML) systems yearly. In tandem, screening sanctioned entities, SDNs, blocked persons, etc., is now a perennial need of financial institutions. Industry estimates place the laundered money to the tune of 2.7% of the annual global GDP, a whopping US$ 1.6 trillion loss. With an estimated 24,000 sanctions worldwide in 2022, inadequate watchlist screening and KYC (EDD/CDD) pose prodigious risks.

Breast cancer is the second most common cancer among women worldwide. Diagnosis of breast cancer by the pathologists is a time-consuming procedure and subjective. Computer aided diagnosis frameworks are utilized to relieve pathologist workload by classifying the data automatically, in which deep convolutional neural networks (CNNs) are effective solutions. The features extracted from activation layer of pre-trained CNNs are called deep convolutional activation features (DeCAF). In this paper, we have analyzed that all DeCAF features are not necessarily led to a higher accuracy in the classification task and dimension reduction plays an important role. Therefore, different dimension reduction methods are applied to achieve an effective combination of features by capturing the essence of DeCAF features. To this purpose, we have proposed reduced deep convolutional activation features (R-DeCAF). In this framework, pre-trained CNNs such as AlexNet, VGG-16 and VGG-19 are utilized in transfer learning mode as feature extractors. DeCAF features are extracted from the first fully connected layer of the mentioned CNNs and support vector machine has been used for binary classification. Among linear and nonlinear dimensionality reduction algorithms, linear approaches such as principal component analysis (PCA) represent a better combination among deep features and lead to a higher accuracy in the classification task using small number of features considering specific amount of cumulative explained variance (CEV) of features. The proposed method is validated using experimental BreakHis dataset. Comprehensive results show improvement in the classification accuracy up to 4.3% with less computational time. Best achieved accuracy is 91.13% for 400x data with feature vector size (FVS) of 23 and CEV equals to 0.15 using pre-trained AlexNet as feature extractor and PCA as feature reduction algorithm.

Exploiting image patches instead of whole images have proved to be a powerful approach to tackle various problems in image processing. Recently, Wasserstein patch priors (WPP), which are based on the comparison of the patch distributions of the unknown image and a reference image, were successfully used as data-driven regularizers in the variational formulation of superresolution. However, for each input image, this approach requires the solution of a non-convex minimization problem which is computationally costly. In this paper, we propose to learn two kind of neural networks in an unsupervised way based on WPP loss functions. First, we show how convolutional neural networks (CNNs) can be incorporated. Once the network, called WPPNet, is learned, it can be very efficiently applied to any input image. Second, we incorporate conditional normalizing flows to provide a tool for uncertainty quantification. Numerical examples demonstrate the very good performance of WPPNets for superresolution in various image classes even if the forward operator is known only approximately.

In this work we introduce a novel medical image style transfer method, StyleMapper, that can transfer medical scans to an unseen style with access to limited training data. This is made possible by training our model on unlimited possibilities of simulated random medical imaging styles on the training set, making our work more computationally efficient when compared with other style transfer methods. Moreover, our method enables arbitrary style transfer: transferring images to styles unseen in training. This is useful for medical imaging, where images are acquired using different protocols and different scanner models, resulting in a variety of styles that data may need to be transferred between. Methods: Our model disentangles image content from style and can modify an image's style by simply replacing the style encoding with one extracted from a single image of the target style, with no additional optimization required. This also allows the model to distinguish between different styles of images, including among those that were unseen in training. We propose a formal description of the proposed model. Results: Experimental results on breast magnetic resonance images indicate the effectiveness of our method for style transfer. Conclusion: Our style transfer method allows for the alignment of medical images taken with different scanners into a single unified style dataset, allowing for the training of other downstream tasks on such a dataset for tasks such as classification, object detection and others.

With modern infotainment systems, drivers are increasingly tempted to engage in secondary tasks while driving. Since distracted driving is already one of the main causes of fatal accidents, in-vehicle touchscreen Human-Machine Interfaces (HMIs) must be as little distracting as possible. To ensure that these systems are safe to use, they undergo elaborate and expensive empirical testing, requiring fully functional prototypes. Thus, early-stage methods informing designers about the implication their design may have on driver distraction are of great value. This paper presents a machine learning method that, based on anticipated usage scenarios, predicts the visual demand of in-vehicle touchscreen interactions and provides local and global explanations of the factors influencing drivers' visual attention allocation. The approach is based on large-scale natural driving data continuously collected from production line vehicles and employs the SHapley Additive exPlanation (SHAP) method to provide explanations leveraging informed design decisions. Our approach is more accurate than related work and identifies interactions during which long glances occur with 68 % accuracy and predicts the total glance duration with a mean error of 2.4 s. Our explanations replicate the results of various recent studies and provide fast and easily accessible insights into the effect of UI elements, driving automation, and vehicle speed on driver distraction. The system can not only help designers to evaluate current designs but also help them to better anticipate and understand the implications their design decisions might have on future designs.

Although machine learning on hypergraphs has attracted considerable attention, most of the works have focused on (semi-)supervised learning, which may cause heavy labeling costs and poor generalization. Recently, contrastive learning has emerged as a successful unsupervised representation learning method. Despite the prosperous development of contrastive learning in other domains, contrastive learning on hypergraphs remains little explored. In this paper, we propose TriCL (Tri-directional Contrastive Learning), a general framework for contrastive learning on hypergraphs. Its main idea is tri-directional contrast, and specifically, it aims to maximize in two augmented views the agreement (a) between the same node, (b) between the same group of nodes, and (c) between each group and its members. Together with simple but surprisingly effective data augmentation and negative sampling schemes, these three forms of contrast enable TriCL to capture both microscopic and mesoscopic structural information in node embeddings. Our extensive experiments using 13 baseline approaches, five datasets, and two tasks demonstrate the effectiveness of TriCL, and most noticeably, TriCL consistently outperforms not just unsupervised competitors but also (semi-)supervised competitors mostly by significant margins for node classification. The code and datasets are available at https://github.com/wooner49/TriCL.

In molecular and biological sciences, experiments are expensive, time-consuming, and often subject to ethical constraints. Consequently, one often faces the challenging task of predicting desirable properties from small data sets or scarcely-labeled data sets. Although transfer learning can be advantageous, it requires the existence of a related large data set. This work introduces three graph-based models incorporating Merriman-Bence-Osher (MBO) techniques to tackle this challenge. Specifically, graph-based modifications of the MBO scheme are integrated with state-of-the-art techniques, including a home-made transformer and an autoencoder, in order to deal with scarcely-labeled data sets. In addition, a consensus technique is detailed. The proposed models are validated using five benchmark data sets. We also provide a thorough comparison to other competing methods, such as support vector machines, random forests, and gradient boosting decision trees, which are known for their good performance on small data sets. The performances of various methods are analyzed using residue-similarity (R-S) scores and R-S indices. Extensive computational experiments and theoretical analysis show that the new models perform very well even when as little as 1% of the data set is used as labeled data.

Urban metabolism is an active field of research that deals with the estimation of emissions and resource consumption from urban regions. The analysis could be carried out through a manual surveyor by the implementation of elegant machine learning algorithms. In this exploratory work, we estimate the water consumption by the buildings in the region captured by satellite imagery. To this end, we break our analysis into three parts: i) Identification of building pixels, given a satellite image, followed by ii) identification of the building type (residential/non-residential) from the building pixels, and finally iii) using the building pixels along with their type to estimate the water consumption using the average per unit area consumption for different building types as obtained from municipal surveys.