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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.


Papers
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Proceedings Article
07 Jul 2001
TL;DR: A novel technique for determining a useful dimension for a time-delay embedding of an arbitrary time series, along with the individual time delays for each dimension is described.
Abstract: This paper describes a novel technique for determining a useful dimension for a time-delay embedding of an arbitrary time series, along with the individual time delays for each dimension. A binary-string genetic algorithm is designed to search for a variable number of time delays that minimize the standard deviation of the distance between each embedded data point and the centroid of the set of all data points, relative to the mean distance between each data point and the centroid. The geometric transformations of rotation and scaling are added to the algorithm to allow it to identify attractors that are not aligned with the data axes. Several artificial and real-world attractors and time series are analyzed to describe the types of attractors favorable to the use of this technique.

13 citations

Journal ArticleDOI
TL;DR: It is found that the joint action descriptor shows the best performance among the proposed descriptors due to its high discriminative power and also outperforms state-of-the-art approaches.
Abstract: In this paper, we present action descriptors that are capable of performing single- and two-person simultaneous action recognition. In order to exploit the shape information of action silhouettes, we detect junction points and geometric patterns at the silhouette boundary. The motion information is exploited by using optical flow points. We compute centroid distance signatures to construct the junction points and optical flow-based action descriptors. By taking advantage of the distinct poses, we extract key frames and construct geometric pattern action descriptor, which is based on histograms of the geometric patterns classes obtained by a distance-based classification method. In order to exploit the shape and motion information simultaneously, we follow the information fusion strategy and construct a joint action descriptor by combining geometric patterns and optical flow descriptors. We evaluate the performance of these descriptors on the two widely used action datasets, i.e., Weizmann dataset (single-person actions) and SBU Kinect interaction dataset, clean and noisy versions (two-person actions). The experimental outcomes demonstrate the ability of the individual descriptors to give satisfactory performance on average. It is found that the joint action descriptor shows the best performance among the proposed descriptors due to its high discriminative power and also outperforms state-of-the-art approaches.

13 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that Busemann's 2-volume density is convex, which was recently shown by Burago-Ivanov et al. They also showed how the new volume definition is related to the centroid body and proved affine isoperimetric inequalities.
Abstract: We introduce a new volume definition on normed vector spaces. We show that the induced $k$-area functionals are convex for all $k$. In the particular case $k = 2$, our theorem implies that Busemann’s 2-volume density is convex, which was recently shown by Burago-Ivanov. We also show how the new volume definition is related to the centroid body and prove some affine isoperimetric inequalities.

12 citations

Journal ArticleDOI
TL;DR: In the present paper, comparisons between models with different topologies are made possible by further specifying the prior of the centroid parameters with an additionalhyperparameter, and a fast hyperparameter-search algorithm using the derivatives of evidence is presented.
Abstract: A topology-selection method for self-organizing maps (SOMs) based on empirical Bayesian inference is presented. This method is a natural extension of the hyperparameter-selection method presented earlier, in which the SOM algorithm is regarded as an estimation algorithm for a Gaussian mixture model with a Gaussian smoothing prior on the centroid parameters, and optimal hyperparameters are obtained by maximizing their evidence. In the present paper, comparisons between models with different topologies are made possible by further specifying the prior of the centroid parameters with an additional hyperparameter. In addition, a fast hyperparameter-search algorithm using the derivatives of evidence is presented. The validity of the methods presented is confirmed by simulation experiments.

12 citations

Journal ArticleDOI
TL;DR: The complexity of SRC is reduced by reducing the number of train samples for the classification of the test sample by sparse representation and the processing speed of the proposed algorithm is significantly improved in comparison with the conventional SRC which is due to the reduced number of training samples.
Abstract: In this paper, an efficient finger vein recognition algorithm based on the combination of the nearest centroid neighbor and sparse representation classification techniques ( ${k}$ NCN-SRC) is presented. The previously proposed recognition algorithms are mainly based on distance computation. In the proposed method, the distance, as well as the spatial distribution, are considered to achieve a better recognition rate. The proposed method consists of two stages: first, the ${k}$ nearest neighbors of the test sample are selected based on the nearest centroid neighbor, and then, in the second stage, based on the selected number of closest nearest centroid neighbors ( ${k}$ ), the test sample is classified by sparse representation. Findings from the proposed method ${k}$ NCN-SRC demonstrated an increased recognition rate. This improvement can be attributed to the selection of the train samples, where the train samples are selected by considering the spatial and distance distribution. In addition, the complexity of SRC is reduced by reducing the number of train samples for the classification of the test sample by sparse representation and the processing speed of the proposed algorithm is significantly improved in comparison with the conventional SRC which is due to the reduced number of training samples. It can be concluded that the ${k}$ NCN-SRC classification method is efficient for finger vein recognition. An increase in the recognition rate of 3.35% , 9.07% , 20.23% , and 0.81% is obtained for the proposed ${k}$ NCN-SRC method in comparison with the conventional SRC for the four tested public finger vein databases.

12 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023492
20221,001
2021184
2020202
2019269
2018271