Modified mean shift algorithm

• Published in: IET image processing Vol. 12; no. 12; pp. 2172 - 2177
• Main Authors: Aliyari Ghassabeh, Youness, Rudzicz, Frank
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.12.2018
• Subjects: convergence of numerical methods; convergent sequence; density estimate values; generated sequence; iterative methods; kernel density estimate; machine learning; matrix algebra; mean shift algorithm; modified MS algorithm; nonparametric iterative method; original MS algorithm; probability; probability density function; Research Article; upper bound; weight matrix; iterative methods; nonparametric iterative method; probability; mean shift algorithm; kernel density estimate; upper bound; convergence of numerical methods; weight matrix; machine learning; matrix algebra; generated sequence; modified MS algorithm; convergent sequence; density estimate values; original MS algorithm; probability density function
• ISSN: 1751-9659; 1751-9667
• DOI: 10.1049/iet-ipr.2018.5600

The mean shift (MS) algorithm is an iterative method introduced for locating modes of a probability density function. Although the MS algorithm has been widely used in many applications, the convergence of the algorithm has not yet been proven. In this study, the authors modify the MS algorithm in order to guarantee its convergence. The authors prove that the generated sequence using the proposed modified algorithm is a convergent sequence and the density estimate values along the generated sequence are monotonically increasing and convergent. In contrast to the MS algorithm, the proposed modified version does not require setting a stopping criterion a priori; instead, it guarantees the convergence after a finite number of iterations. The proposed modified version defines an upper bound for the number of iterations which is missing in the MS algorithm. The authors also present the matrix form of the proposed algorithm and show that, in contrast to the MS algorithm, the weight matrix is required to be computed once in the first iteration. The performance of the proposed modified version is compared with the MS algorithm and it was shown through the simulations that the proposed version can be used successfully to estimate cluster centres.