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Toshinao Akuzawa

Publications and source records attributed to Toshinao Akuzawa.

3 recordsLinked to original sources
arXiv2000

Multiplicative Nonholonomic/Newton -like Algorithm

We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has numerous merits for the rigorous treatment of the dynamics. As one consequence, the second order convergence is shown. For the cost function, functions invariant under the componentwise scaling are choosen. By identifying points which can be transformed to each other by the scaling, we assume that the dynamics is in a coset space. In our method, a point can move toward any direction in this coset. Thus, no prewhitening is required.

cs.LG↗
arXiv2000

Multiplicative Algorithm for Orthgonal Groups and Independent Component Analysis

The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the restriction to the orthogonal groups makes the problem somewhat complicated, an explicit expression for the amount of individual jumps is obtained. This algorithm is exactly second-order-convergent. The global instability inherent in the Newton method is remedied by a Levenberg-Marquardt-type variation. The method thus constructed can readily be applied to the independent component analysis. Its remarkable performance is illustrated by a numerical simulation.

cs.LG↗