Nonsmooth ICA contrast minimization using a Riemannian Nelder-Mead method

Postboosting Using Extended G-Mean for Online Sequential Multiclass Imbalance Learning

In this paper, a novel learning method called postboosting using extended G-mean (PBG) is proposed for online sequential multiclass imbalance learning (OS-MIL) in neural networks. PBG is effective due to three reasons. 1) Through postadjusting a classification boundary under extended G-mean, the challenging issue of imbalanced class distribution for sequentially arriving multiclass data can be effectively resolved. 2) A newly derived update rule for online sequential learning is proposed, which produces a high G-mean for current model and simultaneously possesses almost the same information of its previous models. 3) A dynamic adjustment mechanism provided by extended G-mean is valid to deal with the unresolved challenging dense-majority problem and two dynamic changing issues, namely, dynamic changing data scarcity (DCDS) and dynamic changing data diversity (DCDD). Compared to other OS-MIL methods, PBG is highly effective on resolving DCDS, while PBG is the only method to resolve dense-majority and DCDD. Furthermore, PBG can directly and effectively handle unscaled data stream. Experiments have been conducted for PBG and two popular OS-MIL methods for neural networks under massive binary and multiclass data sets. Through the analyses of experimental results, PBG is shown to outperform the other compared methods on all data sets in various aspects including the issues of data scarcity, dense-majority, DCDS, DCDD, and unscaled data.

Constrained Null Space Component Analysis for Semiblind Source Separation Problem

The blind source separation (BSS) problem extracts unknown sources from observations of their unknown mixtures. A current trend in BSS is the semiblind approach, which incorporates prior information on sources or how the sources are mixed. The constrained independent component analysis (ICA) approach has been studied to impose constraints on the famous ICA framework. We introduced an alternative approach based on the null space component (NCA) framework and referred to the approach as the c-NCA approach. We also presented the c-NCA algorithm that uses signal-dependent semidefinite operators, which is a bilinear mapping, as signatures for operator design in the c-NCA approach. Theoretically, we showed that the source estimation of the c-NCA algorithm converges with a convergence rate dependent on the decay of the sequence, obtained by applying the estimated operators on corresponding sources. The c-NCA can be formulated as a deterministic constrained optimization method, and thus, it can take advantage of solvers developed in optimization society for solving the BSS problem. As examples, we demonstrated electroencephalogram interference rejection problems can be solved by the c-NCA with proximal splitting algorithms by incorporating a sparsity-enforcing separation model and considering the case when reference signals are available.

Post-boosting of classification boundary for imbalanced data using geometric mean

In this paper, a novel imbalance learning method for binary classes is proposed, named as Post-Boosting of classification boundary for Imbalanced data (PBI), which can significantly improve the performance of any trained neural networks (NN) classification boundary. The procedure of PBI simply consists of two steps: an (imbalanced) NN learning method is first applied to produce a classification boundary, which is then adjusted by PBI under the geometric mean (G-mean). For data imbalance, the geometric mean of the accuracies of both minority and majority classes is considered, that is statistically more suitable than the common metric accuracy. PBI also has the following advantages over traditional imbalance methods: (i) PBI can significantly improve the classification accuracy on minority class while improving or keeping that on majority class as well; (ii) PBI is suitable for large data even with high imbalance ratio (up to 0.001). For evaluation of (i), a new metric called Majority loss/Minority advance ratio (MMR) is proposed that evaluates the loss ratio of majority class to minority class. Experiments have been conducted for PBI and several imbalance learning methods over benchmark datasets of different sizes, different imbalance ratios, and different dimensionalities. By analyzing the experimental results, PBI is shown to outperform other imbalance learning methods on almost all datasets.

A Derivative-Free Riemannian Powell's Method, Minimizing Hartley-Entropy-Based ICA Contrast

Even though the Hartley-entropy-based contrast function guarantees an unmixing local minimum, the reported nonsmooth optimization techniques that minimize this nondifferentiable function encounter computational bottlenecks. Toward this, Powell's derivative-free optimization method has been extended to a Riemannian manifold, namely, oblique manifold, for the recovery of quasi-correlated sources by minimizing this contrast function. The proposed scheme has been demonstrated to converge faster than the related algorithms in the literature, besides the impressive source separation results in simulations involving synthetic sources having finite-support distributions and correlated images.