28,852 research outputs found
Multi-cultural visualization : how functional programming can enrich visualization (and vice versa)
The past two decades have seen visualization flourish as a research field in its own right, with advances on the computational challenges of faster algorithms, new techniques for datasets too large for in-core processing, and advances in understanding the perceptual and cognitive processes recruited by visualization systems, and through this, how to improve the representation of data. However, progress within visualization has sometimes proceeded in parallel with that in other branches of computer science, and there is a danger that when novel solutions ossify into `accepted practice' the field can easily overlook significant advances elsewhere in the community. In this paper we describe recent advances in the design and implementation of pure functional programming languages that, significantly, contain important insights into questions raised by the recent NIH/NSF report on Visualization Challenges. We argue and demonstrate that modern functional languages combine high-level mathematically-based specifications of visualization techniques, concise implementation of algorithms through fine-grained composition, support for writing correct programs through strong type checking, and a different kind of modularity inherent in the abstractive power of these languages. And to cap it off, we have initial evidence that in some cases functional implementations are faster than their imperative counterparts
A Relational Derivation of a Functional Program
This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard quot;, but the derivation illustrates a number of points about working with relations rather than with functions
Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order Geometry
Convex optimization is a well-established research area with applications in
almost all fields. Over the decades, multiple approaches have been proposed to
solve convex programs. The development of interior-point methods allowed
solving a more general set of convex programs known as semi-definite programs
and second-order cone programs. However, it has been established that these
methods are excessively slow for high dimensions, i.e., they suffer from the
curse of dimensionality. On the other hand, optimization algorithms on manifold
have shown great ability in finding solutions to nonconvex problems in
reasonable time. This paper is interested in solving a subset of convex
optimization using a different approach. The main idea behind Riemannian
optimization is to view the constrained optimization problem as an
unconstrained one over a restricted search space. The paper introduces three
manifolds to solve convex programs under particular box constraints. The
manifolds, called the doubly stochastic, symmetric and the definite multinomial
manifolds, generalize the simplex also known as the multinomial manifold. The
proposed manifolds and algorithms are well-adapted to solving convex programs
in which the variable of interest is a multidimensional probability
distribution function. Theoretical analysis and simulation results testify the
efficiency of the proposed method over state of the art methods. In particular,
they reveal that the proposed framework outperforms conventional generic and
specialized solvers, especially in high dimensions
Explain3D: Explaining Disagreements in Disjoint Datasets
Data plays an important role in applications, analytic processes, and many
aspects of human activity. As data grows in size and complexity, we are met
with an imperative need for tools that promote understanding and explanations
over data-related operations. Data management research on explanations has
focused on the assumption that data resides in a single dataset, under one
common schema. But the reality of today's data is that it is frequently
un-integrated, coming from different sources with different schemas. When
different datasets provide different answers to semantically similar questions,
understanding the reasons for the discrepancies is challenging and cannot be
handled by the existing single-dataset solutions.
In this paper, we propose Explain3D, a framework for explaining the
disagreements across disjoint datasets (3D). Explain3D focuses on identifying
the reasons for the differences in the results of two semantically similar
queries operating on two datasets with potentially different schemas. Our
framework leverages the queries to perform a semantic mapping across the
relevant parts of their provenance; discrepancies in this mapping point to
causes of the queries' differences. Exploiting the queries gives Explain3D an
edge over traditional schema matching and record linkage techniques, which are
query-agnostic. Our work makes the following contributions: (1) We formalize
the problem of deriving optimal explanations for the differences of the results
of semantically similar queries over disjoint datasets. (2) We design a 3-stage
framework for solving the optimal explanation problem. (3) We develop a
smart-partitioning optimizer that improves the efficiency of the framework by
orders of magnitude. (4)~We experiment with real-world and synthetic data to
demonstrate that Explain3D can derive precise explanations efficiently
Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values
The stability of sparse signal reconstruction is investigated in this paper.
We design efficient algorithms to verify the sufficient condition for unique
sparse recovery. One of our algorithm produces comparable results with
the state-of-the-art technique and performs orders of magnitude faster. We show
that the -constrained minimal singular value (-CMSV) of the
measurement matrix determines, in a very concise manner, the recovery
performance of -based algorithms such as the Basis Pursuit, the Dantzig
selector, and the LASSO estimator. Compared with performance analysis involving
the Restricted Isometry Constant, the arguments in this paper are much less
complicated and provide more intuition on the stability of sparse signal
recovery. We show also that, with high probability, the subgaussian ensemble
generates measurement matrices with -CMSVs bounded away from zero, as
long as the number of measurements is relatively large. To compute the
-CMSV and its lower bound, we design two algorithms based on the
interior point algorithm and the semi-definite relaxation
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