The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Ludwig Schmidt - One of the best experts on this subject based on the ideXlab platform.
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NIPS - Practical and optimal LSH for Angular Distance
2015Co-Authors: Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig SchmidtAbstract:We show the existence of a Locality-Sensitive Hashing (LSH) family for the Angular Distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [1, 2]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [3] in practice. We also introduce a multiprobe version of this algorithm and conduct an experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for Angular Distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
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practical and optimal lsh for Angular Distance
Neural Information Processing Systems, 2015Co-Authors: Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig SchmidtAbstract:We show the existence of a Locality-Sensitive Hashing (LSH) family for the Angular Distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [1, 2]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [3] in practice. We also introduce a multiprobe version of this algorithm and conduct an experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for Angular Distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
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Practical and Optimal LSH for Angular Distance
arXiv: Data Structures and Algorithms, 2015Co-Authors: Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig SchmidtAbstract:We show the existence of a Locality-Sensitive Hashing (LSH) family for the Angular Distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for Angular Distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
Mohammad Sal Moslehian - One of the best experts on this subject based on the ideXlab platform.
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p-Angular Distance orthogonality
Aequationes Mathematicae, 2019Co-Authors: Jamal Rooin, Setareh Rajabi, Mohammad Sal MoslehianAbstract:We present a new orthogonality which is based on p-Angular Distance in normed linear spaces. This orthogonality generalizes the Singer and isosceles orthogonalities to a vast extent. Some important properties of this orthogonality, such as the $$\alpha $$-existence and the $$\alpha $$-diagonal existence, are established with giving some natural bounds for $$\alpha $$. It is shown that a real normed linear space is an inner product space if and only if the p-Angular Distance orthogonality is either homogeneous or additive. Several examples are presented to illustrate the results.
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Geometric aspects of $p$-Angular and skew $p$-Angular Distances
arXiv: Functional Analysis, 2017Co-Authors: Jamal Rooin, S. Habibzadeh, Mohammad Sal MoslehianAbstract:Corresponding to the concept of $p$-Angular Distance $\alpha_p[x,y]:=\left\lVert\lVert x\rVert^{p-1}x-\lVert y\rVert^{p-1}y\right\rVert$, we first introduce the notion of skew $p$-Angular Distance $\beta_p[x,y]:=\left\lVert \lVert y\rVert^{p-1}x-\lVert x\rVert^{p-1}y\right\rVert$ for non-zero elements of $x, y$ in a real normed linear space and study some of significant geometric properties of the $p$-Angular and the skew $p$-Angular Distances. We then give some results comparing two different $p$-Angular Distances with each other. Finally, we present some characterizations of inner product spaces related to the $p$-Angular and the skew $p$-Angular Distances. In particular, we show that if $p>1$ is a real number, then a real normed space $\mathcal{X}$ is an inner product space, if and only if for any $x,y\in \mathcal{X}\smallsetminus{\lbrace 0\rbrace}$, it holds that $\alpha_p[x,y]\geq\beta_p[x,y]$.
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Dunkl--Williams inequality for operators \\ associated with $p$-Angular Distance
arXiv: Operator Algebras, 2010Co-Authors: Farzad Dadipour, Masatoshi Fujii, Mohammad Sal MoslehianAbstract:We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-Angular Distance for operators. More precisely, we show that if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible, $\frac{1}{r}+\frac{1}{s}=1\,\,(r>1)$ and $p\in\mathbb{R}$, then \begin{equation*} |A|A|^{p-1}-B|B|^{p-1}|^{2} \leq |A|^{p-1}(r|A-B|^{2}+s||A|^{1-p}|B|^{p}-|B||^2)|A|^{p-1}.%\nonumber \end{equation*} In the case that $0 0$, then $$|(U|A|^{p}-V|B|^{p})|A|^{1-p}|^{2}\leq (1+t)|A-B|^{2}+(1+\frac{1}{t})||B|^{p}|A|^{1-p}-|B||^2 \,.$$ We obtain several equivalent conditions, when the case of equalities hold.
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dunkl williams inequality for operators associated with p Angular Distance
arXiv: Operator Algebras, 2010Co-Authors: Farzad Dadipour, Masatoshi Fujii, Mohammad Sal MoslehianAbstract:We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-Angular Distance for operators. More precisely, we show that if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible, $\frac{1}{r}+\frac{1}{s}=1\,\,(r>1)$ and $p\in\mathbb{R}$, then \begin{equation*} |A|A|^{p-1}-B|B|^{p-1}|^{2} \leq |A|^{p-1}(r|A-B|^{2}+s||A|^{1-p}|B|^{p}-|B||^2)|A|^{p-1}.%\nonumber \end{equation*} In the case that $0 0$, then $$|(U|A|^{p}-V|B|^{p})|A|^{1-p}|^{2}\leq (1+t)|A-B|^{2}+(1+\frac{1}{t})||B|^{p}|A|^{1-p}-|B||^2 \,.$$ We obtain several equivalent conditions, when the case of equalities hold.
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A characterization of inner product spaces related to the p-Angular Distance
arXiv: Functional Analysis, 2010Co-Authors: Farzad Dadipour, Mohammad Sal MoslehianAbstract:In this paper we present a new characterization of inner product spaces related to the p-Angular Distance. We also generalize some results due to Dunkl, Williams, Kirk, Smiley and Al-Rashed by using the notion of p-Angular Distance.
Nynke Hofstra - One of the best experts on this subject based on the ideXlab platform.
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spatial variability in correlation decay Distance and influence on Angular Distance weighting interpolation of daily precipitation over europe
International Journal of Climatology, 2009Co-Authors: Nynke Hofstra, Mark NewAbstract:Angular-Distance weighting (ADW) is a common approach for interpolation of an irregular network of meteorological observations to a regular grid. A widely used version of ADW employs the correlation decay Distance (CDD) to (1) select stations that should contribute to each grid-point estimate and (2) define the Distance component of the station weights. We show, for Europe, that the CDD of daily precipitation varies spatially, as well as by season and synoptic state, and is also anisotropic. However, ADW interpolation using CDDs that varies spatially by season or synoptic state yield only small improvements in interpolation skill, relative to the use of a fixed CDD across the entire domain. If CDDs are optimized through cross validation, a larger improvement in interpolation skill is achieved. Improvements are larger for the determination of the state of precipitation (wet/dry) than for the magnitude. These or other attempts to improve interpolation skill appear to be fundamentally limited by the available station network
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Spatial variability in correlation decay Distance and influence on Angular‐Distance weighting interpolation of daily precipitation over Europe
International Journal of Climatology, 2008Co-Authors: Nynke Hofstra, Mark NewAbstract:Angular-Distance weighting (ADW) is a common approach for interpolation of an irregular network of meteorological observations to a regular grid. A widely used version of ADW employs the correlation decay Distance (CDD) to (1) select stations that should contribute to each grid-point estimate and (2) define the Distance component of the station weights. We show, for Europe, that the CDD of daily precipitation varies spatially, as well as by season and synoptic state, and is also anisotropic. However, ADW interpolation using CDDs that varies spatially by season or synoptic state yield only small improvements in interpolation skill, relative to the use of a fixed CDD across the entire domain. If CDDs are optimized through cross validation, a larger improvement in interpolation skill is achieved. Improvements are larger for the determination of the state of precipitation (wet/dry) than for the magnitude. These or other attempts to improve interpolation skill appear to be fundamentally limited by the available station network
Guangjun Zhang - One of the best experts on this subject based on the ideXlab platform.
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Observation Angular Distance error modeling and matching threshold optimization for terrestrial star tracker.
Optics Express, 2019Co-Authors: Zhen Wang, Jie Jiang, Guangjun ZhangAbstract:Observation Angular Distance error, as the difference between the actual observation Angular Distance and the reference Angular Distance, is an important parameter that affects the identification success rate, attitude measurement accuracy, and real-time performance of a terrestrial star tracker. It is the criterion to determine whether stars are identified in star identification but is still unclarified to date. To resolve the problem, the observation Angular error model is presented in this work. This model determines the variation range of the observation Angular Distance error by analyzing the factors of astrometric transformations. Then, the optimal Angular Distance matching threshold expression for a terrestrial star tracker is presented on the basis of the proposed model for the optimal efficiency in star identification. Numerical simulations and a night sky experiment demonstrate that the differences between the theoretical model, simulation and actual experiment results are less than 0.5'' and thereby validate the reliability of our conclusions.
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Star Identification Utilizing Star Patterns
Star Identification, 2016Co-Authors: Guangjun ZhangAbstract:Traditionally, most star identification algorithms are based on the characteristics of Angular Distance, such as polygon match algorithms, triangle algorithms and group match algorithms. Though they are easy to use, these algorithms require a relatively large storage capacity because their matching features are line segments (Angular Distances) or triangles.
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Global calibration of unleveled theodolite using Angular Distance constraints.
Applied Optics, 2016Co-Authors: Xuehan Zheng, Zhenzhong Wei, Guangjun ZhangAbstract:The theodolite is an important optical measurement instrument in application. Its global calibration, including position and orientation, is a prerequisite for measurement. Most global calibration methods require the theodolite to be leveled precisely, which is time-consuming and susceptible to error. We propose a global calibration method without leveling: it solves position results using the Angular Distance of control points by nonlinear optimization and then computes orientation parameters (rotation matrix) linearly based on position results. Furthermore, global calibration of multiple theodolites is also introduced. In addition, we introduced a method that can compute the dip direction and tilt angle by decomposing the rotation matrix. We evaluate the calibration algorithms on both computer simulation and real data experiments, demonstrating the effectiveness of the techniques.
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Angular Distance constraints calibration for outdoor zoom camera
Optics Express, 2016Co-Authors: Xuehan Zheng, Zhenzhong Wei, Guangjun ZhangAbstract:Based on 2-D protractor property of camera, we proposed a flexible calibration method for zoom camera that used outdoors. It only requires the camera to observe control points once for given zooming settings, when there are several control points at infinity and known the Angular Distances. Under constraints of image points, the Angular Distance between their re-projecting vectors and the image of absolute conic (IAC), nonlinear optimization is used to solve parameters of IAC. Then IAC can be uniquely decomposed by the Cholesky factorization, and consequently the intrinsic parameters can be obtained. Towards the factors that affect the accuracy of the calibration, theoretical analysis and computer simulation are carried out respectively consequence in qualitative analysis and quantitative result. On the issues of inaccuracy of principal point, the zooming center is selected to improve the accuracy of calibration. Real data demonstrated the effectiveness of the techniques.
Alexandr Andoni - One of the best experts on this subject based on the ideXlab platform.
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NIPS - Practical and optimal LSH for Angular Distance
2015Co-Authors: Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig SchmidtAbstract:We show the existence of a Locality-Sensitive Hashing (LSH) family for the Angular Distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [1, 2]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [3] in practice. We also introduce a multiprobe version of this algorithm and conduct an experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for Angular Distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
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practical and optimal lsh for Angular Distance
Neural Information Processing Systems, 2015Co-Authors: Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig SchmidtAbstract:We show the existence of a Locality-Sensitive Hashing (LSH) family for the Angular Distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [1, 2]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [3] in practice. We also introduce a multiprobe version of this algorithm and conduct an experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for Angular Distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
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Practical and Optimal LSH for Angular Distance
arXiv: Data Structures and Algorithms, 2015Co-Authors: Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig SchmidtAbstract:We show the existence of a Locality-Sensitive Hashing (LSH) family for the Angular Distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for Angular Distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.
