Adaptive data embedding framework for multiclass classification

Generalized Embedding Regression: A Framework for Supervised Feature Extraction

Sparse discriminative projection learning has attracted much attention due to its good performance in recognition tasks. In this article, a framework called generalized embedding regression (GER) is proposed, which can simultaneously perform low-dimensional embedding and sparse projection learning in a joint objective function with a generalized orthogonal constraint. Moreover, the label information is integrated into the model to preserve the global structure of data, and a rank constraint is imposed on the regression matrix to explore the underlying correlation structure of classes. Theoretical analysis shows that GER can obtain the same or approximate solution as some related methods with special settings. By utilizing this framework as a general platform, we design a novel supervised feature extraction approach called jointly sparse embedding regression (JSER). In JSER, we construct an intrinsic graph to characterize the intraclass similarity and a penalty graph to indicate the interclass separability. Then, the penalty graph Laplacian is used as the constraint matrix in the generalized orthogonal constraint to deal with interclass marginal points. Moreover, the L_2,1 -norm is imposed on the regression terms for robustness to outliers and data's variations and the regularization term for jointly sparse projection learning, leading to interesting semantic interpretability. An effective iterative algorithm is elaborately designed to solve the optimization problem of JSER. Theoretically, we prove that the subproblem of JSER is essentially an unbalanced Procrustes problem and can be solved iteratively. The convergence of the designed algorithm is also proved. Experimental results on six well-known data sets indicate the competitive performance and latent properties of JSER.

Simultaneously Learning Neighborship and Projection Matrix for Supervised Dimensionality Reduction

Explicitly or implicitly, most dimensionality reduction methods need to determine which samples are neighbors and the similarities between the neighbors in the original high-dimensional space. The projection matrix is then learnt on the assumption that the neighborhood information, e.g., the similarities, are known and fixed prior to learning. However, it is difficult to precisely measure the intrinsic similarities of samples in high-dimensional space because of the curse of dimensionality. Consequently, the neighbors selected according to such similarities and the projection matrix obtained according to such similarities and the corresponding neighbors might not be optimal in the sense of classification and generalization. To overcome this drawback, in this paper, we propose to let the similarities and neighbors be variables and model these in a low-dimensional space. Both the optimal similarity and projection matrix are obtained by minimizing a unified objective function. Nonnegative and sum-to-one constraints on the similarity are adopted. Instead of empirically setting the regularization parameter, we treat it as a variable to be optimized. It is interesting that the optimal regularization parameter is adaptive to the neighbors in a low-dimensional space and has an intuitive meaning. Experimental results on the YALE B, COIL-100, and MNIST data sets demonstrate the effectiveness of the proposed method.

Sequential projection pursuit with kernel matrix update and symbolic model selection

This paper proposes a novel way for generating reliable low-dimensional features with improved class separability in a kernel-induced feature space. The feature projections rely on a very efficient sequential projection pursuit method, adapted to support nonlinear projections using a new kernel matrix update scheme. This enables the gradual removal of structure from the space of residual dimensions to allow the recovery of multiple projections. An adaptive kernel function is employed to unfold different types of data characteristics. We follow a holistic model selection procedure that, together with the optimal projections, dimensionality, and kernel parameters, additionally optimizes symbolically the projection index that controls the actual measurement of the data interestingness without user interaction. We tackle the underlying complex bi-level optimization model as a mixture of evolutionary and gradient search. The effectiveness of the proposed algorithm over existing approaches is demonstrated with benchmark evaluations and comparisons.

Automated induction of heterogeneous proximity measures for supervised spectral embedding

Spectral embedding methods have played a very important role in dimensionality reduction and feature generation in machine learning. Supervised spectral embedding methods additionally improve the classification of labeled data, using proximity information that considers both features and class labels. However, these calculate the proximity information by treating all intraclass similarities homogeneously for all classes, and similarly for all interclass samples. In this paper, we propose a very novel and generic method which can treat all the intra- and interclass sample similarities heterogeneously by potentially using a different proximity function for each class and each class pair. To handle the complexity of selecting these functions, we employ evolutionary programming as an automated powerful formula induction engine. In addition, for computational efficiency and expressive power, we use a compact matrix tree representation equipped with a broad set of functions that can build most currently used similarity functions as well as new ones. Model selection is data driven, because the entire model is symbolically instantiated using only problem training data, and no user-selected functions or parameters are required. We perform thorough comparative experimentations with multiple classification datasets and many existing state-of-the-art embedding methods, which show that the proposed algorithm is very competitive in terms of classification accuracy and generalization ability.

Quantum-based algorithm for optimizing artificial neural networks

This paper presents a quantum-based algorithm for evolving artificial neural networks (ANNs). The aim is to design an ANN with few connections and high classification performance by simultaneously optimizing the network structure and the connection weights. Unlike most previous studies, the proposed algorithm uses quantum bit representation to codify the network. As a result, the connectivity bits do not indicate the actual links but the probability of the existence of the connections, thus alleviating mapping problems and reducing the risk of throwing away a potential candidate. In addition, in the proposed model, each weight space is decomposed into subspaces in terms of quantum bits. Thus, the algorithm performs a region by region exploration, and evolves gradually to find promising subspaces for further exploitation. This is helpful to provide a set of appropriate weights when evolving the network structure and to alleviate the noisy fitness evaluation problem. The proposed model is tested on four benchmark problems, namely breast cancer and iris, heart, and diabetes problems. The experimental results show that the proposed algorithm can produce compact ANN structures with good generalization ability compared to other algorithms.

Dynamic sampling approach to training neural networks for multiclass imbalance classification

Class imbalance learning tackles supervised learning problems where some classes have significantly more examples than others. Most of the existing research focused only on binary-class cases. In this paper, we study multiclass imbalance problems and propose a dynamic sampling method (DyS) for multilayer perceptrons (MLP). In DyS, for each epoch of the training process, every example is fed to the current MLP and then the probability of it being selected for training the MLP is estimated. DyS dynamically selects informative data to train the MLP. In order to evaluate DyS and understand its strength and weakness, comprehensive experimental studies have been carried out. Results on 20 multiclass imbalanced data sets show that DyS can outperform the compared methods, including pre-sample methods, active learning methods, cost-sensitive methods, and boosting-type methods.