Related papers: Quantifying the Conceptual Error in Dimensionality…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…

How can one meaningfully make a measurement, if the meter does not conform to any standard and its scale expands or shrinks depending on what is measured? In the present work it is argued that current evaluation practices for…

A plethora of dimension reduction methods have been developed to visualize high-dimensional data in low dimensions. However, different dimension reduction methods often output different and possibly conflicting visualizations of the same…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

Concept probing has recently garnered increasing interest as a way to help interpret artificial neural networks, dealing both with their typically large size and their subsymbolic nature, which ultimately renders them unfeasible for direct…

Data quality describes the degree to which data meet specific requirements and are fit for use by humans and/or downstream tasks (e.g., artificial intelligence). Data quality can be assessed across multiple high-level concepts called…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…

Identifying meaningful concepts in large data sets can provide valuable insights into engineering design problems. Concept identification aims at identifying non-overlapping groups of design instances that are similar in a joint space of…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

Precise perception of the environment is essential in highly automated driving systems, which rely on machine learning tasks such as object detection and segmentation. Compression of sensor data is commonly used for data handling, while…

Classification models are a key component of structural digital twin technologies used for supporting asset management decision-making. An important consideration when developing classification models is the dimensionality of the input, or…

Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…

The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity…

The advent of compact, handheld devices has given us a pool of tracked movement data that could be used to infer trends and patterns that can be made to use. With this flooding of various trajectory data of animals, humans, vehicles, etc.,…

The community lacks theory-informed guidelines for building good data sets. We analyse theoretical directions relating to what aspects of the data matter and conclude that the intuitions derived from the existing literature are incorrect…

We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…

Dimensionality Reduction (DR) is widely used for visualizing high-dimensional data, often with the goal of revealing expected cluster structure. However, such a structure may not always appear in the projections. Existing DR quality metrics…