We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

Measuring statistical dependence with Hilbert-Schmidt norms

Pattern recognition

The lithium-ion battery of an electric vehicle continues to have available capacity even after it is retired, thus representing good echelon utilization value The ideal regrouping form for echelon utilization is conducted at the module level However, existing sorting methods are generally only suitable at the cell level To address this issue, a fast sorting and regrouping method is proposed at the module level based on a machine learning algorithm First, the correlation between the charging curve and the remaining useful capacity of the battery is investigated The charging curves of cells in a module are translated and supplemented to extract the capacity characteristics without disassembling the modules Next, a rapid sorting model based on the support vector machine is proposed to estimate the capacity Then, a regrouping method based on an improved K-means algorithm that considers different echelon utilization scenarios at the module level is proposed Finally, simulations and experiments are conducted to verify the effectiveness of the proposed method The results show that the capacity prediction accuracy is within 3%, and the consistency of the echelon utilization battery system obtained by the proposed regrouping method is higher than that obtained by the conventional method

Rapid Sorting and Regrouping of Retired Lithium-Ion Battery Modules for Echelon Utilization Based on Partial Charging Curves

Multiple Kernel Learning (MKL) algorithms have recently demonstrated their effectiveness for classifying the data with numerous features. These algorithms aim at learning an optimal composite kernel through combining the basis kernels constructed from different features. Despite their satisfactory results, MKL algorithms assume that the basis kernels are a priori computed. Moreover, they adopt complex optimization methods to train the combination of the basis kernels, which are usually hard to solve and can only handle the binary classification problems. In this paper, a novel MKL framework was introduced in order to address all these issues. This framework optimizes a data-dependent kernel evaluation measure in order to learn both the basis kernels and their combination. The kernel evaluation measure should be able to estimate the goodness of the composite kernel for a multiclass classification problem. In this paper, we defined such a measure based on the similarity between the composite kernel and an ideal kernel. To this end, three different kernel-based similarity measures, namely kernel alignment (KA), centered kernel alignment (CKA), and Hilbert-Schmidt independence criterion (HSIC), were presented. For solving the optimization problem of the proposed MKL framework, we used the metaheuristic optimization algorithms, which in addition to being accurate algorithms can be easily implemented. The performance of the proposed framework was evaluated by classifying the features extracted from two multispectral and hyperspectral datasets. The results showed that this framework outperformed the other state-of-the-art MKL algorithms in terms of both classification accuracy and the computational time.

A Novel Multiple Kernel Learning Framework for Multiple Feature Classification

Centered kernel alignment inspired fuzzy support vector machine

An efficient Gaussian kernel optimization based on centered kernel polarization criterion

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An efficient Gaussian kernel optimization based on centered kernel polarization criterion