Robust Hypersphere Fitting from Noisy Data Using an EM Algorithm

Abstract

This article studies a robust expectation maximization (EM) algorithm to solve the problem of hypersphere fitting. This algorithm relies on the introduction of random latent vectors having independent von Mises-Fisher distributions defined on the hypersphere and random latent vectors indicating the presence of potential outliers. This model leads to an inference problem that can be solved with a simple EM algorithm. The performance of the resulting robust hypersphere fitting algorithm is evaluated for circle and sphere fitting with promising results in terms of both estimation performance and computation time.

A Robust Model and its EM Algorithm for the Estimation of the Multifractality Parameter

“…Complete likelihood. In order to obtain a closed-form expression of the maximum likelihood estimator (MLE) of the unknown vector θ, in the spirit of [10], we propose to use the EM algorithm [11] using the so-called complete likelihood…”

“…To study the estimation performance of the algorithm when the data X(t) are subjected to additive or multiplicative corruptions, we conduct Monte Carlo simulations for N mc = 1000 independent copies of an MRW of size N = 2 10 , with H = 0.7, for different values for c 2 , with variance of increments normalized to the value 1. The following scenarios for data corruptions E(t), t ∈ [0, 1] are studied:…”