Kensuke Onishi

Voronoi diagram in statistical parametric space by Kullback-Leibler divergence

Voronoi diagram has been a main theme in computational geometry, and the theory of generalized Voronoi diagrams for various applications in robotics, VLSI CAD, etc., has been developed in terms of arrangements, Davenport-Schinzel sequences and lower envelopes. In this paper, we propose a new direction of research towards introducing discrete proximity structures in statistical parametric spaces by Voronoi diagrams defined by statistically meaningful distance, partially based on information geometry (Amari [1]), and the Voronoi diagram in the upper half space is constructed for canonical normal distributions by revealing its relation with the Euclidean Voronoi diagram. This paper investigates the statistical parametric space of normal distributions by adopting the Kullback-Leibler divergence as a distance to generate the Voronoi diagram. The KullbackLeibler divergence is the most fundamental divergence in information theory (e.g., see [3, 5]), and similarity of the diagram obtained from this divergence with that in [6, 7] is shown. Due to relative simplicity, the Kullback-Leibler divergence allows us to compute the Voronoi diagram for general normal distribution. Linearization technique as well as lower envelope arguments is fully made use of in deriving bounds of this paper. Voronoi diagrams for other divergences in the statistical parametric space of probability distribution of a discrete variable taking d values are also touched upon.

Voronoi diagrams by divergences with additive weights

We introduce the Voronoi diagram by the divergence determincd by a convex function with additive weights. This class of Voronoi diagrams includes the Euclidean case and further the Voronoi diagram for normal distributions in a statistically meaningful setting. With the additive weights, the Voronoi diagram for circles is also included, These Voronoi diagrams can be handled in a unified way via appropriate potential functions and its tangent hypcrsurfaces. 1 Divcrgcnco Voronoi diagram In this acction, we define the Voronoi diagram by the divergence determined by a given convex function. The following preliminary results in sections 1.1 and 1.2 may be found in [9] and [l, 21, respectively. 1.1 Conjugacy of convex functions Let S be an open convex set in Rd. Let

A feature independent of bit rate for twinvq audio retrieval

J be a twice differentiable and strictly convex function on S which diverges to &co at the infinity/boundary. Define ai

A method for retrieving music data with different bit rates using MPEG-4 TwinVQ audio compression

= a<+(0) for 0 = [O’] E S’ by and denote [B&l in Rd by &,!J. Define S+ c Rd by s

Indoor Position Detection Using BLE Signals Based on Voronoi Diagram

= {&b(e) ] e E S} Lemma 1 When 111 is twice differentiable and strictly convex, S” is an open convex set. Define a function 4: SG + R by for 1 E S

mm-GNAT: index structure for arbitrary L p norm

, The supremum is attained for 8 with a

Cover Ratio of Absolute Neighbor

= 7, and so define v(0) by 71(e) = w(e). ‘Tbc tanaor notation is used. Pcmksion to m&e digits1 or hard copies of all or part of this work for psrconal or clnmoom WC is gnu&d without fee provided that copies nro not mnde or dislribukd for profit or wmmercial advantage snd th3t copies bear Ohio notice end the full cifetion on the fti page. To copy oU~crv~i~, to republish, to post on servers or to redistribute to Iii require3 prior spccilic pcmksion andlor s fee. ~CCI 98 Minneapolis Minnesota USA Copyright ACM 1998 0-89791.973-4/98/6...

Adjacency of Optimal Regions for Huffman Trees

5.00 Then, Lemma 2 (p is a twice diflerentiable and strictly convex function on 9. I

Construction of Voronoi Diagram on the Upper Half-Plane

is called the conjugate function of 111.

A new method for extracting a period of beat of music in compressed domain of TwinVQ audio compression

In this paper we propose an audio feature for TwinVQ audio retrieval. For making effective audio database, we consider that these two techniques (compression and feature extraction) are dealt with on one platform. The proposed audio feature satisfies the following requirements: 1) independent of bit rate; 2) extractable from compressed data without decoding; 3) computable in the framework of TwinVQ. We show that the autocorrelation coefficient is theoretically independent of bit rate and confirm experimentally that the feature computed from CD audio data is actually independent of bit rate.