8 papers
The geometry of monarch matrix approximation
Shintaro Yoshizawa
Helmke and Shayman showed that, for generic targets, least-squares distance to the manifold of rank-r matrices is a nondegenerate Morse function whose indices are governed by Bruha…
A Homotopical Geometry of the Multinomial and Negative-Multinomial Potentials
Shintaro Yoshizawa
We study the one-parameter family of Hessian metrics , , formed by convexly combining the log-partition functions (not the densities) of the multinomi…
Halley's Method for Rectangular Matrix Variables and the Matrix Schwarzian Derivative
Shintaro Yoshizawa
Alefeld (1981) recast Halley's cubic convergence as Newton's method on , linked to the Schwarzian derivative. We generalize this to matrix gradient fields $F=\nablaϕ…
A Generalized Ridge Regression and Convolutional LASSO
Shintaro Yoshizawa
We derive the complete duality theory underlying the Hodrick--Prescott filter, whose rank-deficient second-difference penalty admits infinitely many equivalent trend representation…
Information Geometry of Gradient Flows
Shintaro Yoshizawa
Taking classical information geometry as its point of departure, this paper investigates, through gradient flows, how dually flat geometry extends beyond regular convexity, non-deg…
A Power Geometry and Hypergeometric Functions
Shintaro Yoshizawa
This paper is a corrected English translation of an original Japanese work introducing "power geometry," a research programme centred on power transformations, deformations and dua…
CLIP-Loc: Multi-modal Landmark Association for Global Localization in Object-based Maps
Shigemichi Matsuzaki, Takuma Sugino, Kazuhito Tanaka +4
This paper describes a multi-modal data association method for global localization using object-based maps and camera images. In global localization, or relocalization, using objec…
Dynamical systems for eigenvalue problems of axisymmetric matrices with positive eigenvalues
Shintaro Yoshizawa
We consider the eigenvalues and eigenvectors of an axisymmetric matrix with some special structures. We propose S-Oja-Brockett equation where $X(t)…