Ensemble learning methods, which combine several base classifiers, is a common technique to enhance the classification ability of ensemble models in the field of pattern recognition and machine learning. Rotation Forest, an ensemble algorithm, has been used widely in various fields with nice generalization performance. The main idea of Rotation Forest is to animate concurrently both diversity and individual accuracy within the ensemble. On the other hand, random vector functional link (RVFL) neural network, a randomized version of single layer feed-forward neural network (SLFN), is a successful model because of its universal approximation property. In this paper, we propose a novel ensemble method, known as rotated random vector functional link neural network (RoF-RVFL), which combines rotation forest (RoF) and RVFL classifiers. To verify the effectiveness of the proposed RoF- RVFL method, empirical comparisons are carried out among Rotation Forest (RoF), Random Forest (RaF), RVFL and the proposed RoF-RVFL method over 42 UCI benchmark datasets. The experimental results show that the proposed RoF-Rvflmethod is able to generate more robust network with better generalization performance.

A Novel Ensemble Method of RVFL For Classification Problem

Ecological state evaluation of lake ecosystems revisited: Latent variables with kSVM algorithm approach for assessment automatization and data comprehension

Robust kernel principal component analysis and its application in blockage detection at the turn of conveyor belt

Principal component analysis is a widely used technique. However, it is sensitive to noise and considers data samples to be linearly distributed globally. To tackle these challenges, a novel technique robust to noise termed deflated manifold embedding PCA is proposed. In this framework, we unify PCA with manifold embedding to preserve both global and local geometric structures of linear and non-linear data in sub-manifolds. Additionally, a scaling-factor is imposed in the instance space to mitigate the impact of noise in pursuing projections. By using cosine similarity and total distance approaches, we iteratively learn the relationships between instances and projections in order to discriminate between authentic and corrupt instances. Further, a deflation technique is applied to establish multi-relationships between instances and every pursued projection for thorough discrimination. Experimental evaluation of the proposed methods on five datasets show great improvements in their performances over six state-of-the-art techniques.

Deflated manifold embedding PCA framework via multiple instance factorings

Kernel principal component analysis (KPCA) is a kernelized version of principal component analysis (PCA). A kernel principal component is a superposition of kernel functions. Due to the number of kernel functions equals the number of samples, each component is not a sparse representation. Our purpose is to sparsify coefficients expressing in linear combination of kernel functions, two types of sparse kernel principal component are proposed in this paper. The method for solving sparse problem comprises two steps: (a) we start with the Pythagorean theorem and derive an explicit regression expression of KPCA and (b) two types of regularization $l_1$-norm or $l_{2,1}$-norm are added into the regression expression in order to obtain two different sparsity form, respectively. As the proposed objective function is different from elastic net-based sparse PCA (SPCA), the SPCA method cannot be directly applied to the proposed cost function. We show that the sparse representations are obtained in its iterative optimization by conducting an alternating direction method of multipliers. Experiments on toy examples and real data confirm the performance and effectiveness of the proposed method.

pdf/kernel-principal-component-analysis-allowing-sparse-2fbdrqshx3.pdf

Kernel Principal Component Analysis Allowing Sparse Representation and Sample Selection

Principal component analysis (PCA) is a widely used unsupervised method for dimensionality reduction. The kernelized version is called kernel principal component analysis (KPCA), which can capture the nonlinear data structure. KPCA is derived from the Gram matrix, which is not robust when outliers exist in the data. This may yield the principal axis in the feature space deviated by outliers, leading to misinterpretation of the principal components. In this paper, we propose a robust method for KPCA with a reformulation in Euclidean space to construct a robust KPCA method, where an error measurement is introduced into the loss function, and l
 2,1
-regularization is added to the loss function. The idea of l
 2,1
-regularization of the proposed method is motivated by sparse PCA via variable projection. However, because orthogonality is not satisfied in the proposed method, orthonormal bases are obtained by using the Gram-Schmidt orthonormalization process. In the experiments, a toy example and real data are used for outlier detection to verify the method's performance and effectiveness. In the toy example, the proposed method reduces the influence of outliers and detects more outliers than KPCA. For the real data, the proposed method improves detection in comparison to other existing methods.

/pdf/robust-kernel-principal-component-analysis-with-l-2-1-5cl4go9z2m.pdf

Robust Kernel Principal Component Analysis With ℓ 2,1 -Regularized Loss Minimization

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Robust Kernel Principal Component Analysis With ℓ 2,1 -Regularized Loss Minimization