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In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions. However, it has a large computational cost, especially when the input data has many dimensions. Many use t-SNE to embed the output of a neural…
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
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…
Over the years, various algorithms were developed, attempting to imitate the Human Visual System (HVS), and evaluate the perceptual image quality. However, for certain image distortions, the functionality of the HVS continues to be an…
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
Current work in planning with preferences assume that the user's preference models are completely specified and aim to search for a single solution plan. In many real-world planning scenarios, however, the user probably cannot provide any…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…
Machine learning (ML) has employed various discretization methods to partition numerical attributes into intervals. However, an effective discretization technique remains elusive in many ML applications, such as association rule mining.…
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…
Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic…
Methods for Projection Pursuit aim to facilitate the visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge is the design of a suitable quality metric of projections, commonly…
Despite their output being ultimately consumed by human viewers, 3D Gaussian Splatting (3DGS) methods often rely on ad-hoc combinations of pixel-level losses, resulting in blurry renderings. To address this, we systematically explore…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data. However, reasoning dynamically about the results of a dimensionality reduction is difficult. Dimensionality-reduction algorithms use complex…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
We propose a new method for the visual quality assessment of 360-degree (omnidirectional) videos. The proposed method is based on computing multiple spatio-temporal objective quality features on viewports extracted from 360-degree videos. A…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…