Flexible ranking extreme learning machine based on matrix-centering transformation

Chen, Shizhao; Chen, Kai; Xu, Chuanfu; Lan, Long

doi:10.1109/ijcnn.2018.8489418

Cited by 2 publications

(3 citation statements)

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“…In addition, the centering matrix has important simplified role in the ranking algorithms in information retrieval [4,19,20]. For instance, in [19], T. Pahikkala et al introduced the centering matrix to construct a block diagonal matrix as weighted matrix, express the loss function, obtain the matrix notation of a least squares problem, and conveniently find the linear solution of RankRLS algorithm.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…It is a symmetric idempotent matrix and has been successfully applied in various fields, such as transfer learning [1,2], feature learning [3], extreme learning [4], ensemble learning [5][6][7][8][9], dictionary learning [10,11], and multivariate statistical analysis (MVA) [12][13][14][15][16]. e practical applications involve a wide range of aspects (e.g., data-driven fault diagnosis and prognosis [3,17,18], sentiment analysis [7,8], web page classification [9], information retrieval [4,19,20], image denoising [10], and signal processing of electronics [11], theoretical chemistry and graph theory [21], and rank data analysis [22]). For instance, Chen S. Z. et al [4] proposed a flexible ranking extreme learning machine (ELM) method based on matrix-centering transformation to replace the traditional graph Laplacian matrix-based methods.…”

Section: Introductionmentioning

confidence: 99%

“…e practical applications involve a wide range of aspects (e.g., data-driven fault diagnosis and prognosis [3,17,18], sentiment analysis [7,8], web page classification [9], information retrieval [4,19,20], image denoising [10], and signal processing of electronics [11], theoretical chemistry and graph theory [21], and rank data analysis [22]). For instance, Chen S. Z. et al [4] proposed a flexible ranking extreme learning machine (ELM) method based on matrix-centering transformation to replace the traditional graph Laplacian matrix-based methods.…”

Section: Introductionmentioning

confidence: 99%

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The Simplified Expression of Machine Learning and Multivariate Statistical Analysis Based on the Centering Matrix

Xue

Zhang

2021

Mathematical Problems in Engineering

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In machine learning (ML) algorithms and multivariate statistical analysis (MVA) problems, it is usually necessary to center (zero centered or mean subtraction) the original data. The centering matrix plays an important role in this process. The full consideration and use of its properties may contribute to the speed or stability improvement of some related ML algorithms. Therefore, in this paper, we discussed in detail the properties of the centering matrix, proved some previously known properties, and deduced some new properties. The involved properties mainly consisted of the centering, quadratic form, spectral decomposition, null space, projection, exchangeability, Kronecker square, and so on. Based on this, we explored the simplified expression role of the centering matrix in the principal component analysis (PCA) and regression analysis theory. The results show that the sum of deviation squares which is widely used in regression theory and variance analysis can be expressed by the quadratic form with the centering matrix as the kernel matrix. The ML algorithms introducing the centering matrix can greatly simplify the learning process and improve predictive ability.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Simplified Expression of Machine Learning and Multivariate Statistical Analysis Based on the Centering Matrix

Xue

Zhang

2021

Mathematical Problems in Engineering

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Data Mining and Machine Learning Techniques for Aerodynamic Databases: Introduction, Methodology and Potential Benefits

Andrés-Pérez

2020

Energies

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Machine learning and data mining techniques are nowadays being used in many business sectors to exploit the data in order to detect trends, discover certain features and patters, or even predict the future. However, in the field of aerodynamics, the application of these techniques is still in the initial stages. This paper focuses on exploring the benefits that machine learning and data mining techniques can offer to aerodynamicists in order to extract knowledge from the CFD data and to make quick predictions of aerodynamic coefficients. For this purpose, three aerodynamic databases (NACA0012 airfoil, RAE2822 airfoil and 3D DPW wing) have been used and results show that machine-learning and data-mining techniques have a huge potential also in this field.

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Flexible ranking extreme learning machine based on matrix-centering transformation

Cited by 2 publications

References 25 publications

The Simplified Expression of Machine Learning and Multivariate Statistical Analysis Based on the Centering Matrix

The Simplified Expression of Machine Learning and Multivariate Statistical Analysis Based on the Centering Matrix

Data Mining and Machine Learning Techniques for Aerodynamic Databases: Introduction, Methodology and Potential Benefits

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