Centroid

About: Centroid is a research topic. Over the lifetime, 4110 publications have been published within this topic receiving 53637 citations. The topic is also known as: barycenter (geometry) & geometric center of a plane figure.

Supervised term weighting centroid-based classifiers for text categorization

Abstract: In this paper, we study the theoretical properties of the class feature centroid (CFC) classifier by considering the rate of change of each prototype vector with respect to individual dimensions (terms). We show that CFC is inherently biased toward the larger (dominant majority) classes, which invariably leads to poor performance on class-imbalanced data. CFC also aggressively prune terms that appear across all classes, discarding some non-exclusive but useful terms. To overcome these CFC limitations while retaining its intrinsic and worthy design goals, we propose an improved centroid-based classifier that uses precise term-class distribution properties instead of presence or absence of terms in classes. Specifically, terms are weighted based on the Kullback–Leibler (KL) divergence measure between pairs of class-conditional term probabilities; we call this the CFC–KL centroid classifier. We then generalize CFC–KL to handle multi-class data by replacing the KL measure with the multi-class Jensen–Shannon (JS) divergence, called CFC–JS. Our proposed supervised term weighting schemes have been evaluated on 5 datasets; KL and JS weighted classifiers consistently outperformed baseline CFC and unweighted support vector machines (SVM). We also devise a word cloud visualization approach to highlight the important class-specific words picked out by our KL and JS term weighting schemes, which were otherwise obscured by unsupervised term weighting. The experimental and visualization results show that KL and JS term weighting not only notably improve centroid-based classifiers, but also benefit SVM classifiers as well.

Small-object location utilizing centroid accumulation

Abstract: In the disclosed image-analysis scheme, a processing window of M by N pixels is successively scanned in single-pixel steps over a sensed image, with the centroid of the image data contained in each window position then being determined. When a pixel-by-pixel tabulation is made of the number of times each pixel has been determined to be the windowed-data centroid, those pixels having the higher tabulated centroid counts will tend to be the intra-image locations of any objects which are smaller than about M/2 by N/2 pixels.

Coincidences of simplex centers and related facial structures

Abstract: We investigate the geometric properties of simplices in Euclidean d-dimensional space for which two or more of the analogues of the classical triangle centers (including the centroid, circumcenter, incenter, orthocenter or Monge point, and the Fermat-Torricelli point) coincide. We also investigate the geometric significance of the cevian line segments through a given center having the same length. We give a unified presentation, including known results for d=2 and d=3.

Centroid mutation-based Search and Rescue optimization algorithm for feature selection and classification

Abstract: Massive data is generated as a result of technological innovations in various fields. Medical data sets often have extremely complex dimensions with limited sample sizes. The researchers face a difficult problem in classifying this high-dimensional data. We present a novel optimization approach for better feature selection in medical data classification in this research. We call this approach a centroid mutation-based Search and Rescue optimization algorithm (cmSAR) based on a k-Nearest Neighbor (kNN) classifier for disease classification. The use of cmSAR in feature selection is to find the optimal group of features that show strong separability between two classes, solving premature convergence and improves the local search ability of the SAR algorithm. We use a fuzzy logic as a logical system, which is an extension of multi-valued logic to generate a fuzzy set and apply a centroid mutation operator on it. The statistical results of cmSAR were either identical or superior to those of well-known metaheuristic algorithms, including the Slime Mould Algorithm (SMA), Particle Swarm Optimization (PSO) algorithm, Sine Cosine Algorithm (SCA), Moth–Flame Optimization (MFO) algorithm, Whale Optimization Algorithm (WOA), Genetic Algorithm (GA), and the original SAR algorithm on 15 disease data sets with different feature sizes extracted from UCI. In addition, cmSAR outperformed the other algorithms in CEC-C06 2019 single-objective benchmark functions as well as in performance evaluation metrics for classification according to Friedman test and Bonferroni–Dunn test for statistical verification. The proposed cmSAR achieved superior performance on all the medical data sets.