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This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…

Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…

Data imputation is an effective way to handle missing data, which is common in practical applications. In this study, we propose and test a novel data imputation process that achieve two important goals: (1) preserve the row-wise…

Sentiment analysis, mostly based on text, has been rapidly developing in the last decade and has attracted widespread attention in both academia and industry. However, the information in the real world usually comes from multiple…

Temporal graph classification plays a critical role in applications such as cybersecurity, brain connectivity analysis, social dynamics, and traffic monitoring. Despite its significance, this problem remains underexplored compared to…

In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially…

Missing value imputation in machine learning is the task of estimating the missing values in the dataset accurately using available information. In this task, several deep generative modeling methods have been proposed and demonstrated…

We address prediction problems on tabular categorical data, where each instance is defined by multiple categorical attributes, each taking values from a finite set. These attributes are often referred to as fields, and their categorical…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

I introduce a continuous-variable quantum topological data algorithm. The goal of the quantum algorithm is to calculate the Betti numbers in persistent homology which are the dimensions of the kernel of the combinatorial Laplacian. I…

Diffusion tensor imaging (DTI) is a prevalent neuroimaging tool in analyzing the anatomical structure. The distinguishing feature of DTI is that the voxel-wise variable is a 3x3 positive definite matrix other than a scalar, describing the…

A methodology is proposed for inferring the topology underlying point cloud data. The approach employs basic elements of Morse Theory, and is capable of producing not only a point estimate of various topological quantities (e.g., genus),…

This paper investigates the optimal selection and fusion of feature encoders across multiple modalities and combines these in one neural network to improve sentiment detection. We compare different fusion methods and examine the impact of…

Many adaptations of transformers have emerged to address the single-modal vision tasks, where self-attention modules are stacked to handle input sources like images. Intuitively, feeding multiple modalities of data to vision transformers…

Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…

Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…

Emotion recognition plays a vital role in enhancing human-computer interaction. In this study, we tackle the MER-SEMI challenge of the MER2025 competition by proposing a novel multimodal emotion recognition framework. To address the issue…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

Change detection process has recently progressed from a post-classification method to an expert knowledge interpretation process of the time-series data. The technique finds applications mainly in remote sensing images and can be utilized…