Mean shift

Mean shift is a non-parametric feature-space mathematical analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm. Application domains include cluster analysis in computer vision and . The mean shift procedure is usually credited to work by Fukunaga and Hostetler in 1975. It is, however, reminiscent of earlier work by Schnell in 1964. Mean shift is a procedure for locating the maxima—the modes—of a density function given discrete data sampled from that function. This is an iterative method, and we start with an initial estimate . Let a kernel function be given. This function determines the weight of nearby points for re-estimation of the mean. Typically a Gaussian kernel on the distance to the current estimate is used, . The weighted mean of the density in the window determined by is where is the neighborhood of , a set of points for which . The difference is called mean shift in Fukunaga and Hostetler. The mean-shift algorithm now sets , and repeats the estimation until converges. Although the mean shift algorithm has been widely used in many applications, a rigid proof for the convergence of the algorithm using a general kernel in a high dimensional space is still not known. Aliyari Ghassabeh showed the convergence of the mean shift algorithm in one dimension with a differentiable, convex, and strictly decreasing profile function. However, the one-dimensional case has limited real world applications. Also, the convergence of the algorithm in higher dimensions with a finite number of the stationary (or isolated) points has been proved. However, sufficient conditions for a general kernel function to have finite stationary (or isolated) points have not been provided. Gaussian Mean-Shift is an Expectation–maximization algorithm. Let data be a finite set embedded in the -dimensional Euclidean space, . Let be a flat kernel that is the characteristic function of the -ball in , In each iteration of the algorithm, is performed for all simultaneously.

Domain knowledge-informed synthetic fault sample generation with health data map for cross-domain planetary gearbox fault diagnosis

Olga Fink, Jongmoon Ha

Extensive research has been conducted on fault diagnosis of planetary gearboxes using vibration signals and deep learning (DL) approaches. However, DL-based methods are susceptible to the domain shift problem caused by varying operating conditions of the g ...

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD2023

Hybrid Flock - Formation Control Algorithms

Alcherio Martinoli, Cyrill Silvan Baumann, Jonas Perolini, Emna Tourki

Two prominent categories for achieving coordinated multirobot displacement are flocking and navigation in formation. Both categories have their own body of literature and characteristics, including their respective advantages and disadvantages. While typic ...

2022

Domain knowledge-informed synthetic fault sample generation with health data map for cross-domain planetary gearbox fault diagnosis

Discriminative clustering with representation learning with any ratio of labeled to unlabeled data

Hybrid Flock - Formation Control Algorithms

Discriminative clustering with representation learning with any ratio of labeled to unlabeled data

Domain knowledge-informed synthetic fault sample generation with health data map for cross-domain planetary gearbox fault diagnosis

Hybrid Flock - Formation Control Algorithms