Related papers: Uncovering Temporal Patterns in Visualizations of …

A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…

While deep learning surpasses human-level performance in narrow and specific vision tasks, it is fragile and over-confident in classification. For example, minor transformations in perspective, illumination, or object deformation in the…

Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

t-SNE has gained popularity as a dimension reduction technique, especially for visualizing data. It is well-known that all dimension reduction techniques may lose important features of the data. We provide a mathematical framework for…

Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional…

With the rapid development of machine learning applications on time-series data, accurately assessing the value of training samples has become essential for data selection, noise detection, and model optimization. However, traditional data…

In video analysis, understanding the temporal context is crucial for recognizing object interactions, event patterns, and contextual changes over time. The proposed model leverages adjacency and semantic similarities between objects from…

We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…

Pattern extraction algorithms are enabling insights into the ever-growing amount of today's datasets by translating reoccurring data properties into compact representations. Yet, a practical problem arises: With increasing data volumes and…

Dimensionality reduction (DR) techniques help analysts to understand patterns in high-dimensional spaces. These techniques, often represented by scatter plots, are employed in diverse science domains and facilitate similarity analysis among…

It has become standard to use gradient-based dimensionality reduction (DR) methods like tSNE and UMAP when explaining what AI models have learned. This makes sense: these methods are fast, robust, and have an uncanny ability to find…

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…

Historically, researchers in the field have spent a great deal of effort to create image representations that have scale invariance and retain spatial location information. This paper proposes to encode equivalent temporal characteristics…

This paper contributes a set of quality metrics for identification and visual analysis of structured missingness in high-dimensional data. Missing values in data are a frequent challenge in most data generating domains and may cause a range…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

Dimensionality reduction algorithms are often used to visualise high-dimensional data. Previously, studies have used prior information to enhance or suppress expected patterns in projections. In this paper, we adapt such techniques for…

The visualization of multi-dimensional data with interpretable methods remains limited by capabilities for both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized…