Multiple rank multi-linear kernel support vector machine for matrix data classification

Gao, Xizhan; Li, Fan; Xu, Haitao

doi:10.1007/s13042-015-0383-0

Cited by 26 publications

(12 citation statements)

References 16 publications

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“…In this section, we use synthetic and real-world data to evaluate the performance of the proposed classifier with other methodologies (DuSK (He et al, 2014), SVM, STM, MRMLKSVM (Gao et al, 2018), SMM (Luo et al, 2015)), since they have been proven successful in various applications. We first introduce the date sets constructed and describe how we conduct the experiments.…”

Section: Methodsmentioning

confidence: 99%

“…Since W = UΣV ⊺ , factorization technique have been introduced to explore nonlinear relationships of matrix data in kernel space (Hao et al, 2013;He et al, 2014;Gao et al, 2018). Another intuitive way to leverage the structural information of matrix data is by imposing the low-rank constraint.…”

Section: Problem Formulation and Related Workmentioning

confidence: 99%

“…To address these issues, researches have been exploited on classifying data in matrix form directly. Gao et al (2018) proposed a multiple rank multi-linear kernel SVM (MRMLKSVM), which introduced the left and right projecting vectors to construct decision boundary and establish margin function. Another typical structure information is the correlation between columns or rows in the data matrix which is commonly leveraged by a regression matrix.…”

Section: Introductionmentioning

confidence: 99%

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Multi-distance support matrix machines

Han

2019

Pattern Recognition Letters

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Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression matrix to be low-rank or sparse. Some other methodologies introduce factorization technique to explore nonlinear relationships of matrix data in kernel space. In this paper, we propose a multi-distance support matrix machine (MDSMM), which provides a principled way of solving matrix classification problems. The multi-distance is introduced to capture the correlation within matrix data, by means of an array which contains the products of columns and rows of the sample and the regression matrix. A complex hyperplane is constructed upon weighting the relative importance of the entries of the multii-distance. We further study the generalization bounds for i.i.d. processes and non i.i.d. process based on SVM, SMM and MDSMM classifiers. For typical hypothesis classes where matrix norms are constrained, MDSMM achieves a faster learning rate than traditional classifiers. We also provide a more general approach for samples without prior knowledge. We demonstrate the merits of the proposed method by conducting exhaustive experiments on both simulation study and a number of real-word datasets.

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Section: Methodsmentioning

confidence: 99%

Section: Problem Formulation and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-distance support matrix machines

Han

2019

Pattern Recognition Letters

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“…SVM projects training data vectors to locate in space in order to expand the distance between any categories as much as possible. The test data vectors are then projected into the same specified area and classified according to which part of the space they stand on [36]. Figure 3 shows the functionality of SVM in a two-dimensional space.…”

Section: Support Vector Machine Classifiermentioning

confidence: 99%

Machine Learning-Based Fault Location for Smart Distribution Networks Equipped with Micro-PMU

Mirshekali

Dashti

Keshavarz

et al. 2022

Sensors

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Faults in distribution networks occur unpredictably, causing a threat to public safety and resulting in power outages. Automated, efficient, and precise detection of faulty sections could be a major element in immediately restoring networks and avoiding further financial losses. Distributed generations (DGs) are used in smart distribution networks and have varied current levels and internal impedances. However, fault characteristics are completely unknown because of their stochastic nature. Therefore, in these circumstances, locating the fault might be difficult. However, as technology advances, micro-phasor measurement units (micro-PMU) are becoming more extensively employed in smart distribution networks, and might be a useful tool for reducing protection uncertainties. In this paper, a new machine learning-based fault location method is proposed for use regardless of fault characteristics and DG performance using recorded data of micro-PMUs during a fault. This method only uses the recorded voltage at the sub-station and DGs. The frequency component of the voltage signals is selected as a feature vector. The neighborhood component feature selection (NCFS) algorithm is utilized to extract more informative features and lower the feature vector dimension. A support vector machine (SVM) classifier is then applied to the decreased dimension training data. The simulations of various fault types are performed on the 11-node IEEE standard feeder equipped with three DGs. Results reveal that the accuracy of the proposed fault section identification algorithm is notable.

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“…Analyzed results derived from multiple DEA specifications and DFCM can be fed into an emerging artificial intelligence (AI) technique -namely, extreme support vector machine (ESVM), which is developed from extreme learning machine (ELM) and support vector machine (SVM) -to construct the forecasting model [16,28]. It not only preserves the benefit of ELM, such as extremely fast learning speed, but also has better generalization capability than conventional ELM due to its output bias term and regularization scheme [13,49]. One of the critical challenges of ESVM is a lack of comprehensibility.…”

Section: Introductionmentioning

confidence: 99%

An emerging online business decision making architecture in a dynamic economic environment

Lin

Chang

Hsu

2019

IFS

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It is widely acknowledged that a corporate's profitability that decreases dramatically not only threatens both potential and current investors, but also can freeze stock market transactions as well as deteriorate the flow of economic resources. However, far too little attention has been paid to this issue, which also has been deemed as a main trigger for a financial crisis. To confront this problem, a decision support system can be built up to evaluate a corporate's operating performance. Thus, this study introduces a novel architecture for forecasting the online operating performance of a firm when entering data at different time intervals. The introduced architecture is grounded on multiple data envelopment analysis specifications, dynamic fuzzy c-means (DFCM), and extreme support vector machine (ESVM). Because obtaining a comprehensible architecture is essential for achieving high accuracy in today's knowledge-based economy, this study advances the opaque nature of the introduced architecture and extracts the inherent knowledge to represent it in a transparent, human-readable format. The decision logics can be judged or examined by users, which will increase the acceptance rate of the architecture as well as enhance its practical application. Our built-up architecture, tested by real cases, is a promising alternative for financial performance forecasting.

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Multiple rank multi-linear kernel support vector machine for matrix data classification

Cited by 26 publications

References 16 publications

Multi-distance support matrix machines

Multi-distance support matrix machines

Machine Learning-Based Fault Location for Smart Distribution Networks Equipped with Micro-PMU

An emerging online business decision making architecture in a dynamic economic environment

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