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Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.


Papers
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Book ChapterDOI
08 Sep 2018
TL;DR: A method of learning suitable convolutional representations for camera pose retrieval based on nearest neighbour matching and continuous metric learning-based feature descriptors, which is able to generalise in a meaningful way, and outperforms related methods across several experiments.
Abstract: We propose a method of learning suitable convolutional representations for camera pose retrieval based on nearest neighbour matching and continuous metric learning-based feature descriptors. We introduce information from camera frusta overlaps between pairs of images to optimise our feature embedding network. Thus, the final camera pose descriptor differences represent camera pose changes. In addition, we build a pose regressor that is trained with a geometric loss to infer finer relative poses between a query and nearest neighbour images. Experiments show that our method is able to generalise in a meaningful way, and outperforms related methods across several experiments.

180 citations

Proceedings Article
30 Jun 2000
TL;DR: This paper defines the anchors hierarchy--a fast data structure and algorithm for localizing data based only on a triangle-inequality-obeying distance metric and shows how this structure, decorated with cached sufficient statistics, allows a wide variety of statistical learning algorithms to be accelerated even in thousands of dimensions.
Abstract: This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions, decorating kd-trees with additional "cached sufficient statistics" such as first and second moments and contingency tables can provide satisfying acceleration for a very wide range of statistical learning tasks such as kernel regression, locally weighted regression, k-means clustering, mixture modeling and Bayes Net learning. In this paper, we begin by defining the anchors hierarchy--a fast data structure and algorithm for localizing data based only on a triangle-inequality-obeying distance metric. We show how this, in its own right, gives a fast and effective clustering of data. But more importantly we show how it can produce a well-balanced structure similar to a Ball-Tree (Omohundro, 1991) or a kind of metric tree (Uhlmann, 1991; Ciaccia, Patella, & Zezula, 1997) in a way that is neither "topdown" nor "bottom-up" but instead "middleout". We then show how this structure, decorated with cached sufficient statistics, allows a wide variety of statistical learning algorithms to be accelerated even in thousands of dimensions.

179 citations

Patent
16 Dec 1998
TL;DR: In this article, a coarse placer is used in conjunction with other automatic design tools such as a detailed placer and an automatic wire router to generate coarse placement of cells on a 2-dimensional silicon chip or circuit board.
Abstract: A computer implemented process for automatic creation of integrated circuit (IC) geometry using a computer. The present invention includes a general unconstrained non-linear optimization method to generate coarse placement of cells on a 2-dimensional silicon chip or circuit board. In one embodiment, the coarse placer can also be used to automatically size cells, insert and size buffers, and aid in timing driven structuring of the placed circuit. The coarse placer is used in conjunction with other automatic design tools such as a detailed placer and an automatic wire router. A master objective function (MOF) is defined which evaluates a particular cell placement. A non-linear optimization process finds an assignment of values to the function variables which minimizes the MOF. The MOF is a weighted sum of functions which evaluate various metrics. An important metric for consideration is the density metric, which measures how well spread out the cells are in the placement. Other component functions are wire-length, which measures total linear wire-length, delay, which measures circuit timing, and power, which measures circuit power consumption. The barrier metric penalizes placements with cells outside the allowed placement region. A conjugate-gradient process utilizes both the MOF and its gradient to determine a next cell placement. The gradient is the vector of partial derivatives of the MOF with respect to all variables. The non-linear optimization process calls the MOF and gradient function subroutines and uses the results to minimize the MOF.

179 citations

Journal ArticleDOI
TL;DR: A hybrid technique, HYBICA, is described, which uses the initial characterization of the fMRI data from Independent Component Analysis and allows the experimenter to sequentially combine assumed task-related components so that one can gracefully navigate from a fully data-derived approach to a fully hypothesis-driven approach.

179 citations

Proceedings ArticleDOI
23 Jun 2003
TL;DR: This paper presents a method to estimate the number of cache misses, at compile time, using a machine independent model based on stack algorithms, which provides a very good approximation for set-associative caches and programs with non-constant dependence distances.
Abstract: Cache behavior modeling is an important part of modern optimizing compilers. In this paper we present a method to estimate the number of cache misses, at compile time, using a machine independent model based on stack algorithms. Our algorithm computes the stack histograms symbolically, using data dependence distance vectors and is totally accurate when dependence distances are uniformly generated. The stack histogram models accurately fully associative caches with LRU replacement policy, and provides a very good approximation for set-associative caches and programs with non-constant dependence distances.The stack histogram is an accurate, machine-independent metric of locality. Compilers using this metric can evaluate optimizations with respect to memory behavior. We illustrate this use of the stack histogram by comparing three locality enhancing transformations: tiling, data shackling and the product-space transformation. Additionally, the stack histogram model can be used to compute optimal parameters for data locality transformations, such as the tile size for loop tiling.

179 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202253
20213,191
20203,141
20192,843
20182,731
20172,341