Kernel-Free Quadratic Surface Regression for Multi-Class Classification

For multi-class classification problems, a new kernel-free nonlinear classifier is presented, called the hard quadratic surface least squares regression (HQSLSR). It combines the benefits of the least squares loss function and quadratic kernel-free trick. The optimization problem of HQSLSR is convex and unconstrained, making it easy to solve. Further, to improve the generalization ability of HQSLSR, a softened version (SQSLSR) is proposed by introducing an ε-dragging technique, which can enlarge the between-class distance. The optimization problem of SQSLSR is solved by designing an alteration iteration algorithm. The convergence, interpretability and computational complexity of our methods are addressed in a theoretical analysis. The visualization results on five artificial datasets demonstrate that the obtained regression function in each category has geometric diversity and the advantage of the ε-dragging technique. Furthermore, experimental results on benchmark datasets show that our methods perform comparably to some state-of-the-art classifiers.

Past and Future Perspectives for Hepatitis B and C in Pakistan

Background

Hepatitis B and C are viral infections of the liver transmitted by blood contamination. These infections are endemic in Pakistan and put a tremendous burden on its healthcare system. We conducted this study to assess the prevalence of hepatitis B virus (HBV) and hepatitis C virus (HCV) infections in Gujranwala, Pakistan, from 2010 to 2015 and determine the trend of future infections for a prediction of the disease burden by 2030 so policymakers can make informed decisions.

Methods

We conducted a retrospective cross-sectional study of 66,308 healthy blood donor samples at District Headquarters Teaching Hospital in Gujranwala from January 2010 to December 2015. Samples were screened for HBV and HCV using the kit method, and data were analyzed using IBM SPSS Statistics for Windows, version 20.0 (IBM Corp., Armonk, NY). We applied a least squares regression to our results to predict HBV and HCV incidence in 2030.

Results

A total of 715 samples (1.08%) were positive for HBV and 1,846 samples (2.78%) were positive for HCV. Our projections indicate that 3.25% of patients in Pakistan will be positive for HBV, and 6.36% will be positive for HBC by 2030.

Conclusion

We found an unexpectedly greater burden of HBV and HCV in the recent past than at current levels. The predicted percentages of future burden over the next decade were alarmingly high. These data necessitate implementing preventive and therapeutic measures by policymakers to reduce the disease burden and mortality in Pakistan.

Noise-insensitive discriminative subspace fuzzy clustering

Discriminative subspace clustering (DSC) can make full use of linear discriminant analysis (LDA) to reduce the dimension of data and achieve effective clustering high-dimension data by clustering low-dimension data in discriminant subspace. However, most existing DSC algorithms do not consider the noise and outliers that may be contained in data sets, and when they are applied to the data sets with noise or outliers, and they often obtain poor performance due to the influence of noise and outliers. In this paper, we address the problem of the sensitivity of DSC to noise and outlier. Replacing the Euclidean distance in the objective function of LDA by an exponential non-Euclidean distance, we first develop a noise-insensitive LDA (NILDA) algorithm. Then, combining the proposed NILDA and a noise-insensitive fuzzy clustering algorithm: AFKM, we propose a noise-insensitive discriminative subspace fuzzy clustering (NIDSFC) algorithm. Experiments on some benchmark data sets show the effectiveness of the proposed NIDSFC algorithm.

Autoregressive linear least square single scanning electron microscope image signal-to-noise ratio estimation

A technique based on linear Least Squares Regression (LSR) model is applied to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. In order to test the accuracy of this technique on SNR estimation, a number of SEM images are initially corrupted with white noise. The autocorrelation function (ACF) of the original and the corrupted SEM images are formed to serve as the reference point to estimate the SNR value of the corrupted image. The LSR technique is then compared with the previous three existing techniques known as nearest neighbourhood, first-order interpolation, and the combination of both nearest neighborhood and first-order interpolation. The actual and the estimated SNR values of all these techniques are then calculated for comparison purpose. It is shown that the LSR technique is able to attain the highest accuracy compared to the other three existing techniques as the absolute difference between the actual and the estimated SNR value is relatively small. SCANNING 38:771-782, 2016. © 2016 Wiley Periodicals, Inc.