6 research outputs found
Estimation of the Success Probability of Random Sampling by the Gram-Charlier Approximation
The lattice basis reduction algorithm is a method for solving the
Shortest Vector Problem (SVP) on lattices. There are many variants of
the lattice basis reduction algorithm such as LLL, BKZ, and RSR. Though
BKZ has been used most widely, it is shown recently that some variants
of RSR are quite efficient for solving a high-dimensional SVP (they
achieved many best scores in TU Darmstadt SVP challenge). RSR repeats
alternately the generation of new very short lattice vectors from the
current basis (we call this procedure ``random sampling\u27\u27) and the
improvement of the current basis by utilizing the generated very short
lattice vectors. Therefore, it is important for investigating and
ameliorating RSR to estimate the success probability of finding very
short lattice vectors by combining the current basis. In this paper,
we propose a new method for estimating the success probability by the
Gram-Charlier approximation, which is a basic asymptotic expansion of
any probability distribution by utilizing the higher order cumulants
such as the skewness and the kurtosis. The proposed method uses a
``parametric\u27\u27 model for estimating the probability, which gives a
closed-form expression with a few parameters. Therefore, the proposed
method is much more efficient than the previous methods using the
non-parametric estimation. This enables us to investigate the lattice
basis reduction algorithm intensively in various situations and clarify
its properties. Numerical experiments verified that the Gram-Charlier
approximation can estimate the actual distribution quite accurately.
In addition, we investigated RSR and its variants by the proposed
method. Consequently, the results showed that the weighted random
sampling is useful for generating shorter lattice vectors. They also
showed that it is crucial for solving the SVP to improve the current
basis periodically
Improved System for Identification of Live Music Performances by Dynamic Time Warping
The identification of a song performed at a concert, called the "live version," is not yet a popular search among users because of the song possibly having a different arrangement or other modifications, unlike audio searches for an exactly matching song. For live song identification, we examined the application of dynamic time warping to chroma feature series extracted from both studio and live versions of a song. In this paper, we especially focused on measuring the linearity of the warping path. It was evaluated using datasets collected from the internet and the results were compared to those of an existing search service, which showed that the proposed method has the highest accuracy
Linear multilayer independent component analysis using stochastic gradient algorithm
In this paper, linear multilayer ICA (LMICA) is proposed for extracting independent components from quite high-dimensional observed signals such as large-size natural scenes. There are two phases in each layer of LMICA. One is the mapping phase, where a one-dimensional mapping is formed by a stochastic gradient algorithm which makes more highlycorrelated (non-independent) signals be nearer incrementally. Another is the local-ICA phase, where each neighbor (namely, highly-correlated) pair of signals in the mapping is separated by the MaxKurt algorithm. Because LMICA separates only the highly-correlated pairs instead of all ones, it can extract independent components quite efficiently from appropriate observed signals. In addition, it is proved that LMICA always converges. Some numerical experiments verify that LMICA is quite efficient and effective in large-size natural image processing.