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Volume 1, 2018

Mathematical Foundations of Computing

February 2019 , Volume 2 , Issue 1

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Kernel-based online gradient descent using distributed approach
Xiaming Chen
2019, 2(1): 1-9 doi: 10.3934/mfc.2019001 +[Abstract](268) +[HTML](162) +[PDF](336.95KB)

In this paper we study the kernel-based online gradient descent with least squares loss without an explicit regularization term. Our approach is novel by controlling the expectation of the K-norm of \begin{document}$ f_t $\end{document} using an iterative process. Then we use distributed learning to improve our result.

Comparisons of different methods for balanced data classification under the discrete non-local total variational framework
Shixiu Zheng, Zhilei Xu, Huan Yang, Jintao Song and Zhenkuan Pan
2019, 2(1): 11-28 doi: 10.3934/mfc.2019002 +[Abstract](264) +[HTML](156) +[PDF](2696.4KB)

Because balanced constraints can overcome the problems of trivial solutions of data classification via minimum cut method, many techniques with different balanced strategies have been proposed to improve data classification accuracy. However, their performances have not been compared comprehensively so far. In this paper, we investigate seven balanced classification methods under the discrete non-local total variational framework and compare their accuracy performances on graph. The two-class classification problem with equality constraints, inequality constraints and Ratio Cut, Normalized Cut, Cheeger Cut models are investigated. For cases of equality constraint, we firstly compare the Penalty Function Method (PFM) and the Augmented Lagrangian Method (ALM), which can transform the constrained problems into unconstrained ones, to show the advantages of ALM. The other cases are all solved using the ALM also. In order to make the comparison fairly, we solve all models using ALM method and using the same proportion of fidelity points and the same neighborhood size on graph. Experimental results demonstrate ALM with the equality balanced constraint has the best classification accuracy compared with other six constraints. 200 words.

SEMANTIC-RTAB-MAP (SRM): A semantic SLAM system with CNNs on depth images
Mingyuan Mao, Hewei Zhang, Simeng Li and Baochang Zhang
2019, 2(1): 29-41 doi: 10.3934/mfc.2019003 +[Abstract](293) +[HTML](273) +[PDF](1868.4KB)

SLAM (simultaneous localization and mapping) system can be implemented based on monocular, RGB-D and stereo cameras. RTAB-MAP is a SLAM system, which can build dense 3D map. In this paper, we present a novel method named SEMANTIC-RTAB-MAP (SRM) to implement a semantic SLAM system based on RTAB-MAP and deep learning. We use YOLOv2 network to detect target objects in 2D images, and then use depth information for precise localization of the targets and finally add semantic information into 3D point clouds. We apply SRM in different scenes, and the results show its higher running speed and accuracy.

Eliminating other-race effect for multi-ethnic facial expression recognition
Mingliang Xue, Xiaodong Duan and Wanquan Liu
2019, 2(1): 43-53 doi: 10.3934/mfc.2019004 +[Abstract](199) +[HTML](175) +[PDF](317.51KB)

It has been noticed that the performance of multi-ethnic facial expression recognition is affected by other-race effect significantly. Though this phenomenon has been noticed by psychologists and computer vision researchers for decades, the mechanism of other-race effect is still unknown and few work has been done to compensate or remove this effect. This work proposes an ICA-based method to eliminate the other-race effect in automatic 3D facial expression recognition. Firstly, the depth features are extracted from 3D local facial patches, and independent component analysis is applied to project the features into a subspace in which the projected features are mutually independent. The ethnic-related features and expression-related features are supposed to be separated in ICA subspace. Hence, ethnic-sensitive features are then determined by an entropy-based feature selection method and discarded to depress their influence on facial expression recognition. The proposed method is evaluated on benchmark BU-3DFE database, and the experimental results reveal that the influence caused by other-race effect can be suppressed effectively with the proposed method.

Online optimization for residential PV-ESS energy system scheduling
Zhenhuan Yang, Yiming Ying and Qilong Min
2019, 2(1): 55-71 doi: 10.3934/mfc.2019005 +[Abstract](210) +[HTML](141) +[PDF](569.43KB)

This paper studies a residential PV-ESS energy system scheduling problem with electricity purchase cost, storage degradation cost and surplus PV generated cost [2]. This problem can be viewed as an online optimization problem in time \begin{document}$ t \in [1, T] $\end{document} with switching costs between decision at \begin{document}$ t-1 $\end{document} and \begin{document}$ t $\end{document}. We reformulate the problem into a single variable problem with \begin{document}$ {\bf{s}} = (s_1, ..., s_T)^T $\end{document}, which denotes the storage energy content. We then propose a new algorithm, named Average Receding Horizon Control (ARHC) to solve the PV-ESS energy system scheduling problem. ARHC is an online control algorithm exploiting the prediction information with \begin{document}$ W $\end{document}-steps look-ahead. We proved an upper bound on the dynamic regret for ARHC of order \begin{document}$ O(nT/W) $\end{document}, where \begin{document}$ n $\end{document} is the dimension of decision space. This bound can be converted to a competitive ratio of order \begin{document}$ 1+O(1/W) $\end{document}. This result overcomes the drawback of the classical algorithm Receding Horizon Control (RHC), which has been proved [11] that it may perform bad even with large look ahead \begin{document}$ W $\end{document}. We also provide a lower bound for ARHC of order \begin{document}$ O(nT/W^2) $\end{document} on the dynamic regret. ARHC is then used to study a real world case in residential PV-ESS energy system scheduling.

A classification algorithm with Linear Discriminant Analysis and Axiomatic Fuzzy Sets
Wenjuan Jia, Yingjie Deng, Chenyang Xin, Xiaodong Liu and Witold Pedrycz
2019, 2(1): 73-81 doi: 10.3934/mfc.2019006 +[Abstract](238) +[HTML](190) +[PDF](681.93KB)

In exploratory data mining, most classifiers pay more attention on the accuracy and speed of learned models, but they are lacking of the interpretability. In this paper, an interpretable and comprehensible classifier is proposed based on Linear Discriminant Analysis (LDA) and Axiomatic Fuzzy Sets (AFS). The algorithm utilizes LDA to extract features with the largest inter-class variance. Besides, the proposed approach aims to explore a transformation from the selected feature space to a semantic space where the samples in the same class are made as close as possible to one another, whereas the samples in the different class are as far as possible from one another. Moreover, the descriptions of each class can be obtained by the proposed approach. When compared with well-known classifiers such as LogisticR, C4.5Tree, SVM and KNN, the proposed method not only can achieve better performance in terms of accuracy but also has the capability of interpretability and comprehension.




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