### Abstract

We construct new algorithms, 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 chosen. 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.

Original language | English |
---|---|

Pages (from-to) | 785-793 |

Number of pages | 9 |

Journal | Chaos, Solitons and Fractals |

Volume | 12 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 Jan 3 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

*Chaos, Solitons and Fractals*,

*12*(4), 785-793. https://doi.org/10.1016/S0960-0779(00)00077-1

**Multiplicative nonholonomic/Newton-like algorithm.** / Akuzawa, Toshinao; Murata, Noboru.

Research output: Contribution to journal › Article

*Chaos, Solitons and Fractals*, vol. 12, no. 4, pp. 785-793. https://doi.org/10.1016/S0960-0779(00)00077-1

}

TY - JOUR

T1 - Multiplicative nonholonomic/Newton-like algorithm

AU - Akuzawa, Toshinao

AU - Murata, Noboru

PY - 2001/1/3

Y1 - 2001/1/3

N2 - We construct new algorithms, 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 chosen. 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.

AB - We construct new algorithms, 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 chosen. 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.

UR - http://www.scopus.com/inward/record.url?scp=0035148248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035148248&partnerID=8YFLogxK

U2 - 10.1016/S0960-0779(00)00077-1

DO - 10.1016/S0960-0779(00)00077-1

M3 - Article

VL - 12

SP - 785

EP - 793

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 4

ER -