Optimized Cartesian KK-Means

Product quantization-based approaches are effective to encode high-dimensional data points for approximate nearest neighbor search. The space is decomposed into a Cartesian product of low-dimensional subspaces, each of which generates a sub codebook. Data points are encoded as compact binary codes using these sub codebooks, and the distance between two data points can be approximated efficiently from their codes by the precomputed lookup tables. Traditionally, to encode a subvector of a data point in a subspace, only one sub codeword in the corresponding sub codebook is selected, which may impose strict restrictions on the search accuracy. In this paper, we propose a novel approach, named Optimized Cartesian $K$-Means (OCKM), to better encode the data points for more accurate approximate nearest neighbor search. In OCKM, multiple sub codewords are used to encode the subvector of a data point in a subspace. Each sub codeword stems from different sub codebooks in each subspace, which are optimally generated with regards to the minimization of the distortion errors. The high-dimensional data point is then encoded as the concatenation of the indices of multiple sub codewords from all the subspaces. This can provide more flexibility and lower distortion errors than traditional methods. Experimental results on the standard real-life datasets demonstrate the superiority over state-of-the-art approaches for approximate nearest neighbor search.Comment: to appear in IEEE TKDE, accepted in Apr. 201

Study of interpolation methods for high-accuracy computations on overlapping grids

Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section

Precoding for Outage Probability Minimization on Block Fading Channels

The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, full diversity on a block fading channel can be achieved without error-correcting code. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. Using a geometric approach, this paper establishes simple upper bounds on the outage probability, the minimization of which yields to precoding matrices that achieve very good performance. For discrete alphabets, it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing the coding gain.Comment: Submitted to Transactions on Information Theory on March 23, 201

Performance and storage requirements of topology-conserving maps for robot manipulator control

A new programming paradigm for the control of a robot manipulator by learning the mapping between the Cartesian space and the joint space (inverse Kinematic) is discussed. It is based on a Neural Network model of optimal mapping between two high-dimensional spaces by Kohonen. This paper describes the approach and presents the optimal mapping, based on the principle of maximal information gain. It is shown that Kohonens mapping in the 2-dimensional case is optimal in this sense. Furthermore, the principal control error made by the learned mapping is evaluated for the example of the commonly used PUMA robot, the trade-off between storage resources and positional error is discussed and an optimal position encoding resolution is proposed