We introduce a new supervised learning model using a discriminative regression approach. This new model estimates a regression vector to represent the similarity between a test example and training examples while seamlessly integrating the class information in the similarity estimation. This distinguishes our model from usual regression models and locally linear embedding approaches, rendering our method suitable for supervised learning problems in high-dimensional settings. Our model is easily extensible to account for nonlinear relationship and applicable to general data, including both high- and low-dimensional data. The objective function of the model is convex, for which two optimization algorithms are provided. These two optimization approaches induce two scalable solvers that are of mathematically provable, linear time complexity. Experimental results verify the effectiveness of the proposed method on various kinds of data. For example, our method shows comparable performance on low-dimensional data and superior performance on high-dimensional data to several widely used classifiers; also, the linear solvers obtain promising performance on large-scale classification.

Matrix factorization is a useful technique for data representation in many data mining and machine learning tasks. Particularly, for data sets with all nonnegative entries, matrix factorization often requires that factor matrices be nonnegative, leading to nonnegative matrix factorization (NMF). One important application of NMF is for clustering with reduced dimensions of the data represented in the new feature space. In this paper, we propose a new graph regularized NMF method capable of feature learning and apply it to clustering. Unlike existing NMF methods that treat all features in the original feature space equally, our method distinguishes features by incorporating a feature-wise sparse approximation error matrix in the formulation. It enables important features to be more closely approximated by the factor matrices. Meanwhile, the graph of the data is constructed using cleaner features in the feature learning process, which integrates feature learning and manifold learning procedures into a unified NMF model. This distinctly differs from applying the existing graph-based NMF models after feature selection in that, when these two procedures are independently used, they often fail to align themselves toward obtaining a compact and most expressive data representation. Comprehensive experimental results demonstrate the effectiveness of the proposed method, which outperforms state-of-the-art algorithms when applied to clustering.

Matrix factorization is often used for data representation in many data mining and machine-learning problems. In particular, for a dataset without any negative entries, nonnegative matrix factorization (NMF) is often used to find a low-rank approximation by the product of two nonnegative matrices. With reduced dimensions, these matrices can be effectively used for many applications such as clustering. The existing methods of NMF are often afflicted with their sensitivity to outliers and noise in the data. To mitigate this drawback, in this paper, we consider integrating NMF into a robust principal component model, and design a robust formulation that effectively captures noise and outliers in the approximation while incorporating essential nonlinear structures. A set of comprehensive empirical evaluations in clustering applications demonstrates that the proposed method has strong robustness to gross errors and superior performance to current state-of-the-art methods.

This paper introduces a minimax framework for multiclass classification, which is applicable to general data including, in particular, imagery and other types of high-dimensional data. The framework consists of estimating a representation model that minimizes the fitting errors under a class of distortions of interest to an application, and deriving subsequently categorical information based on the estimated model. A variety of commonly used regression models, including lasso, elastic net and ridge regression, can be regarded as special cases that correspond to specific classes of distortions. Optimal decision rules are derived for this classification framework. By using kernel techniques the framework can account for nonlinearity in the input space. To demonstrate the power of the framework we consider a class of signal-dependent distortions and build a new family of classifiers as new special cases. This family of new methods-minimax classification with generalized multiplicative distortions-often outperforms the state-of-the-art classification methods such as the support vector machine in accuracy. Extensive experimental results on images, gene expressions and other types of data verify the effectiveness of the proposed framework.

This paper develops a novel supervised method for predicting earthquake ground motions in the wavelet domain. The training input is a set of seismological predictors related to seismic source, path and local site conditions, and the training output consists of the weights from a multiway analysis of ground motions. We treat wavelet transforms of acceleration records as images and extract essential patterns from them using tensor decomposition. The decomposition weights of these patterns are then linked to seismological variables using general regression neural network (GRNN). The resulting nonparametric model is then used to predict the wavelet image of an accelerogram for a given set of seismological variables. The predicted image can be transformed back to the time domain using inverse wavelet transform for subsequent processing to match a given design spectrum. Unlike conventional ground motion models, the proposed approach retains the time domain characteristics of ground motions. Pearson's correlation coefficient between the vectorized forms of actual and predicted wavelet images has been used as the similarity metric in assessing the prediction capability of the resulting model. Experimental results demonstrate the ability of the proposed model to predict significant patterns in the seismic energy distribution.

Selecting features for multiclass classification is a critically important task for pattern recognition and machine learning applications. Especially challenging is selecting an optimal subset of features from high-dimensional data, which typically have many more variables than observations and contain significant noise, missing components, or outliers. Existing methods either cannot handle high-dimensional data efficiently or scalably, or can only obtain local optimum instead of global optimum. Toward the selection of the globally optimal subset of features efficiently, we introduce a new selector--which we call the Fisher-Markov selector--to identify those features that are the most useful in describing essential differences among the possible groups. In particular, in this paper we present a way to represent essential discriminating characteristics together with the sparsity as an optimization objective. With properly identified measures for the sparseness and discriminativeness in possibly high-dimensional settings, we take a systematic approach for optimizing the measures to choose the best feature subset. We use Markov random field optimization techniques to solve the formulated objective functions for simultaneous feature selection. Our results are noncombinatorial, and they can achieve the exact global optimum of the objective function for some special kernels. The method is fast; in particular, it can be linear in the number of features and quadratic in the number of observations. We apply our procedure to a variety of real-world data, including mid--dimensional optical handwritten digit data set and high-dimensional microarray gene expression data sets. The effectiveness of our method is confirmed by experimental results. In pattern recognition and from a model selection viewpoint, our procedure says that it is possible to select the most discriminating subset of variables by solving a very simple unconstrained objective function which in fact can be obtained with an explicit expression.

This brief presents a dynamical system approach to vector quantization or clustering based on ordinary differential equations with the potential for real-time implementation. Two examples of different pattern clusters demonstrate that the model can successfully quantize different types of input patterns. Furthermore, we analyze and study the stability of our dynamical system. By discovering the equilibrium points for certain input patterns and analyzing their stability, we have shown the quantizing behavior of the system with respect to its vigilance parameter. The proposed system is applied to two real-world problems, providing comparable results to the best reported findings. This validates the effectiveness of our proposed approach.

We develop principal components analysis for the optimal SNR phased-array magnetic resonance (MR) image recombination. As shown in our analysis, we can achieve the best possible SNR in both weak-noise and noisy cases, without needing to estimate the coil sensitivities or to remove noise effects using polynomial fitting or filtering. We provide both analysis and reconstruction techniques. Our results shed light on the performance of the phased-array image combination and give new insight into good image formation schemes.