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Register a new userA Distance-preserving Matrix Sketch
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Added by
Hengrui Luo
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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No Arabic abstract
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An important aspect of these methods is how to preserve relative distances between points in the higher-dimensional space after reducing rows and columns to fit in a lower dimensional space. This aspect is important because conclusions based on faulty visual reasoning can be harmful. Judging dissimilar points as similar or similar points as dissimilar on the basis of a visualization can lead to false conclusions. To ameliorate this bias and to make visualizations of very large datasets feasible, we introduce two new algorithms that respectively select a subset of rows and columns of a rectangular matrix. This selection is designed to preserve relative distances as closely as possible. We compare our matrix sketch to more traditional alternatives on a variety of artificial and real datasets.
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This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks.
Learning data storytelling involves a complex web of skills. Professional and academic educational offerings typically focus on the computational literacies required, but professionals in the field employ many non-technical methods; sketching by hand on paper is a common practice. This paper introduces and classifies a corpus of 101 data sketches produced by participants as part of a guided learning activity in informal and formal settings. We manually code each sketch against 12 metrics related to visual encodings, representations, and story structure. We find evidence for preferential use of positional and shape-based encodings, frequent use of symbolic and textual representations, and a high prevalence of stories comparing subsets of data. These findings contribute to our understanding of how learners sketch with data. This case study can inform tool design for learners, and help create educational programs that introduce novices to sketching practices used by experts.
We show that a simple randomized sketch of the matrix multiplicative weight (MMW) update enjoys (in expectation) the same regret bounds as MMW, up to a small constant factor. Unlike MMW, where every step requires full matrix exponentiation, our steps require only a single product of the form $e^A b$, which the Lanczos method approximates efficiently. Our key technique is to view the sketch as a $textit{randomized mirror projection}$, and perform mirror descent analysis on the $textit{expected projection}$. Our sketch solves the online eigenvector problem, improving the best known complexity bounds by $Omega(log^5 n)$. We also apply this sketch to semidefinite programming in saddle-point form, yielding a simple primal-dual scheme with guarantees matching the best in the literature.
Developing fully parametric building models for performance-based generative design tasks often requires proficiency in many advanced 3D modeling and visual programming, limiting its use for many building designers. Moreover, iterations of such models can be time-consuming tasks and sometimes limiting, as major changes in the layout design may result in remodeling the entire parametric definition. To address these challenges, we introduce a novel automated generative design system, which takes a basic floor plan sketch as an input and provides a parametric model prepared for multi-objective building optimization as output. Furthermore, the user-designer can assign various design variables for its desired building elements by using simple annotations in the drawing. The system would recognize the corresponding element and define variable constraints to prepare for a multi-objective optimization problem.
We propose an interactive GAN-based sketch-to-image translation method that helps novice users create images of simple objects. As the user starts to draw a sketch of a desired object type, the network interactively recommends plausible completions, and shows a corresponding synthesized image to the user. This enables a feedback loop, where the user can edit their sketch based on the networks recommendations, visualizing both the completed shape and final rendered image while they draw. In order to use a single trained model across a wide array of object classes, we introduce a gating-based approach for class conditioning, which allows us to generate distinct classes without feature mixing, from a single generator network. Video available at our website: https://arnabgho.github.io/iSketchNFill/.
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