Proximal Classifier Research Articles

Seismic Random Noise Attenuation Based on PCC Classification in Transform Domain

Random noise attenuation of seismic data is an essential step in the processing of seismic signals. However, as the exploration environment is becoming more and more complicated, the energy of valid signals is weaker and the signal to noise (SNR) is much lower, which brings great difficulty to seismic data processing and interpretation. To this end, we propose an unconventional and effective seismic random noise attenuation method based on proximal classifier with consistency (PCC) in transform domain. Firstly, we analyze various transforms for seismic data from traditional wavelet transform and curvelet transform to emerging non-subsampled shearlet transform (NSST) and non-subsampled contourlet transform (NSCT). And, we select the excellent NSST to decompose the noisy seismic data into different sub-bands of frequency and orientation responses. Secondly, unlike traditional sparse transform based seismic denoising methods that often directly use a thresholding operator and corresponding inverse transform to denoise seismic data, our proposed method employs a superior performance PCC to classify the NSST coefficients of seismic data before thresholding operator. The added step can effectively divide the NSST coefficients into reflected useful signal coefficients and noise-related coefficients, which can preserve the edge of reflected signals and keep the information of events intact as much as possible. In addition, we also introduce an adaptive threshold computing method and a soft-thresholding method to achieve seismic data denoising better. Finally, the experimental results on the typical synthetic example and real seismic data show the superior performance of the proposed method.

Synchronisation correction‐based colour image watermarking using proximal classifier with consistency and multivariate generalised Gaussian model

In this Letter, a novel synchronisation correction-based colour image watermarking approach is proposed to resist geometric distortions. The Cb channel of the YCbCr colour host image is first decomposed by a two-level contourlet transform, and binary watermark image is embedded into the host image by modifying the lowpass coefficients. Then the multivariate generalised Gaussian distribution is used to capture the significant features of colour images, and the proximal classifier with consistency is employed to estimate geometric distortion parameters. Finally, the watermark image is extracted from the corrected watermarked image. Simulation results demonstrate that the presented approach shows excellent robustness against various common image processing attacks and geometric attacks while guaranteeing invisibility.

Color image segmentation using proximal classifier and quaternion radial harmonic Fourier moments

Segmentation involves separating an object from the background in a given image. Image segmentation has a variety of applications and has received considerable attention in multimedia application and computer vision. Although numerous approaches have been introduced, image segmentation is still far from being solved due to most of image segmentation algorithms are often so complicated and some unsatisfactory results appear frequently. Therefore, developing a suitable technique of image segmentation is still a challenging problem. In this article, a novel color image segmentation will be introduced based on quaternion radial harmonic Fourier moments (QRHFMs) and proximal classifier. Firstly, the image feature of pixel-level is represented by the accurate and invariant QRHFMs holistically as a vector field, which can describe sufficiently the image pixel information due to take into account the relationship among different color channels. Secondly, the image feature from pixel-level is utilized as the input of the proximal classifier with consistency (PCC), which not only has lower computation time but also has better generalization compared to traditional support vector machines classifiers. Then, we choose the training samples by Tsallis entropy thresholding to train PCC classification model. Finally, the color image is classified by the trained PCC classification model. Our algorithm can make full use of the accurate and robust local image feature, as well the quickness and generalization ability of PCC classifier. A series of experimental results shows that this algorithm has better segmentation performance than the state-of-the-art method from the literature.

A proximal classifier with positive and negative local regions

Local learning has been successfully applied in pattern recognition due to its powerful discriminating ability. The conventional local learning usually divides the feature space into a number of homogeneous local regions. By contrast, we introduce a new local strategy, which divides the feature space into two kinds of regions: positive local regions and negative local regions. Based on this strategy, a local proximal classifier (LPC) is constructed. Furthermore, to avoid overfitting, we propose a local proximal classifier with global regularizer (GLPC) by improving the LPC so that the local classifiers are smoothly glued together. In GLPC, the local correlation is modeled to capture the sample distribution among the local region, resulting in increasing the discriminating ability. Experimental results show the effectiveness of our classifiers in both classification accuracy and computation time.

A Novel Nonparallel Plane Proximal SVM for Imbalance Data Classification

The research of imbalance data classification is the hot point in the field of data mining. Conventional classifiers are not suitable to the imbalanced learning tasks since they tend to classify the instances to the majority class which is the less important class. This paper pays close attention to the uniqueness of uneven data distribution in imbalance classification problems. Without change the original imbalance training data, this paper indicated the advantages of proximal classifier for imbalance data classification. In order to improve the accuracy of classification, this paper proposed a new model named LS-NPPC, based the classical proximal SVM models which find two nonparallel planes for data classification. The LS-NPPC model is applied to six UCI datasets and one real application. The results indicate the effectiveness of the proposed model for imbalanced data classification problems.

NONPARALLEL HYPERPLANES PROXIMAL CLASSIFIERS BASED ON MANIFOLD REGULARIZATION FOR LABELED AND UNLABELED EXAMPLES

In this paper, we propose two Laplacian nonparallel hyperplane proximal classifiers (LapNPPCs) for semi-supervised and full-supervised classification problem respectively by adding manifold regularization terms. Due to the manifold regularization terms, our LapNPPCs are able to exploit the intrinsic structure of the patterns of the training set. Furthermore, our classifiers only need to solve two systems of linear equations rather than two quadratic programming (QP) problems as needed in Laplacian twin support vector machine (LapTSVM) (Z. Qi, Y. Tian and Y. Shi, Neural Netw.35 (2012) 46–53). Numerical experiments on toy and UCI benchmark datasets show that the accuracy of our LapNPPCs is comparable with other classifiers, such as the standard SVM, TWSVM and LapTSVM, etc. It is also the case that based on our LapNPPCs, some other TWSVM type classifiers with manifold regularization can be constructed by choosing different norms and loss functions to deal with semi-supervised binary and multi-class classification problems.

A proximal classifier with consistency

Note that for GEPSVM proposed in [1], the predicted class of a testing point is determined by comparing two distances between the testing point and two hyperplanes, while the optimization problems are based on comparing two distances between a hyperplane and two kinds of the training points. So there exists some inconformity between the decision process and the training process. In this paper, we propose a new proximal classifier, called PCC for short, with consistency, which is always based on comparing two distances between a point (the testing point in the decision process and the training point in the training process) and two hyperplanes. This consistency not only makes our PCC to be more reasonable logically, but also naturally leads to a simpler decision function with less computation cost. Furthermore, in our PCC two general eigenvalue problems in GEPSVM are replaced by two simple eigenvalues problems with a parameter δ. In addition, different regularization terms are introduced in the formulation of our PCC, avoiding the singular problems possibly appeared in GEPSVM. Experimental results on several benchmark data sets show that our PCC is not only faster, but also has better generalization.

Cancer Classification from Gene Expression Data by NPPC Ensemble

The most important application of microarray in gene expression analysis is to classify the unknown tissue samples according to their gene expression levels with the help of known sample expression levels. In this paper, we present a nonparallel plane proximal classifier (NPPC) ensemble that ensures high classification accuracy of test samples in a computer-aided diagnosis (CAD) framework than that of a single NPPC model. For each data set only, a few genes are selected by using a mutual information criterion. Then a genetic algorithm-based simultaneous feature and model selection scheme is used to train a number of NPPC expert models in multiple subspaces by maximizing cross-validation accuracy. The members of the ensemble are selected by the performance of the trained models on a validation set. Besides the usual majority voting method, we have introduced minimum average proximity-based decision combiner for NPPC ensemble. The effectiveness of the NPPC ensemble and the proposed new approach of combining decisions for cancer diagnosis are studied and compared with support vector machine (SVM) classifier in a similar framework. Experimental results on cancer data sets show that the NPPC ensemble offers comparable testing accuracy to that of SVM ensemble with reduced training time on average.

Newton's method for nonparallel plane proximal classifier with unity norm hyperplanes

In our previous research we observed that the nonparallel plane proximal classifier (NPPC) obtained by minimizing two related regularized quadratic optimization problems performs equally with that of other support vector machine classifiers but with a very lower computational cost. NPPC classifies binary patterns by the proximity of it to one of the two nonparallel hyperplanes. Thus to calculate the distance of a pattern from any hyperplane we need the Euclidean norm of the normal vector of the hyperplane. Alternatively, this should be equal to unity. But in the formulation of NPPC these equality constraints were not considered. Without these constraints the solutions of the objective functions do not guarantee to satisfy the constraints. In this work we have reformulated NPPC by considering those equality constraints and solved it by Newton's method and the solution is updated by solving a system of linear equations by conjugate gradient method. The performance of the reformulated NPPC is verified experimentally on several bench mark and synthetic data sets for both linear and nonlinear classifiers. Apart from the technical improvement of adding those constraints in the NPPC formulation, the results indicate enhanced computational efficiency of nonlinear NPPC on large data sets with the proposed NPPC framework.

Nonparallel plane proximal classifier

We observed that the two costly optimization problems of twin support vector machine (TWSVM) classifier can be avoided by introducing a technique as used in proximal support vector machine (PSVM) classifier. With this modus operandi we formulate a much simpler nonparallel plane proximal classifier (NPPC) for speeding up the training of it by reducing significant computational burden over TWSVM. The formulation of NPPC for binary data classification is based on two identical mean square error (MSE) optimization problems which lead to solving two small systems of linear equations in input space. Thus it eliminates the need of any specialized software for solving the quadratic programming problems (QPPs). The formulation is also extended for nonlinear kernel classifier. Our computations show that a MATLAB implementation of NPPC can be trained with a data set of 3 million points with 10 attributes in less than 3 s. Computational results on synthetic as well as on several bench mark data sets indicate the advantages of the proposed classifier in both computational time and test accuracy. The experimental results also indicate that performances of classifiers obtained by MSE approach are sufficient in many cases than the classifiers obtained by standard SVM approach.

Screening of knee-joint vibroarthrographic signals using the strict 2-surface proximal classifier and genetic algorithm

We propose the strict 2-surface proximal (S2SP) classifier, by seeking two cross proximal planes to fit the distribution of the given samples in a corresponding feature space. The method is applied to screen knee-joint vibration or vibroarthrographic (VAG) signals based on statistical parameters derived from signals and selected by the genetic algorithm. A database of 89 VAG signals was studied. With the leave-one-out procedure, the linear S2SP classifier provided an efficiency of 0.82 in terms of the area under the receiver operating characteristics curve ( A z ); the nonlinear S2SP classifier provided 0.95 in A z value using the Gaussian kernel, and possessed good robustness around the selected kernel parameter.

Classification of Breast Masses Using Selected Shape, Edge-sharpness, and Texture Features with Linear and Kernel-based Classifiers

Breast masses due to benign disease and malignant tumors related to breast cancer differ in terms of shape, edge-sharpness, and texture characteristics. In this study, we evaluate a set of 22 features including 5 shape factors, 3 edge-sharpness measures, and 14 texture features computed from 111 regions in mammograms, with 46 regions related to malignant tumors and 65 to benign masses. Feature selection is performed by a genetic algorithm based on several criteria, such as alignment of the kernel with the target function, class separability, and normalized distance. Fisher's linear discriminant analysis, the support vector machine (SVM), and our strict two-surface proximal (S2SP) classifier, as well as their corresponding kernel-based nonlinear versions, are used in the classification task with the selected features. The nonlinear classification performance of kernel Fisher's discriminant analysis, SVM, and S2SP, with the Gaussian kernel, reached 0.95 in terms of the area under the receiver operating characteristics curve. The results indicate that improvement in classification accuracy may be gained by using selected combinations of shape, edge-sharpness, and texture features.