Related papers: A Distance-preserving Matrix Sketch
Extensions of earlier algorithms and enhanced visualization techniques for approximating a correlation matrix are presented. The visualization problems that result from using column or colum--and--row adjusted correlation matrices, which…
We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls,…
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…
Visualizations are frequently used as a means to understand trends and gather insights from datasets, but often take a long time to generate. In this paper, we focus on the problem of rapidly generating approximate visualizations while…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
Time series visualization plays a crucial role in identifying patterns and extracting insights across various domains. However, as datasets continue to grow in size, visualizing them effectively becomes challenging. Downsampling, which…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…
One of the primary challenges faced by deep learning is the degree to which current methods exploit superficial statistics and dataset bias, rather than learning to generalise over the specific representations they have experienced. This is…
Machine learning algorithms using deep architectures have been able to implement increasingly powerful and successful models. However, they also become increasingly more complex, more difficult to comprehend and easier to fool. So far, most…
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…
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…
Building successful recommender systems requires uncovering the underlying dimensions that describe the properties of items as well as users' preferences toward them. In domains like clothing recommendation, explaining users' preferences…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Dealing with visualizations containing large data set is a challenging issue and, in the field of Information Visualization, almost every visual technique reveals its drawback when visualizing large number of items. To deal with this…
Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so…
In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15]. A projection-cost-preserving sketch is a matrix…
High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…
Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a…