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Kernel logistic regression (KLR) is a conventional nonlinear classifier in machine learning. With the explosive growth of data size, the storage and computation of large dense kernel matrices is a major challenge in scaling KLR. Even the nystr\"{o}m approximation is applied to solve KLR, it also faces the time complexity of $O(nc^2)$ and the space complexity of $O(nc)$, where $n$ is the number of training instances and $c$ is the sampling size. In this paper, we propose a fast Newton method efficiently solving large-scale KLR problems by exploiting the storage and computing advantages of multilevel circulant matrix (MCM). Specifically, by approximating the kernel matrix with an MCM, the storage space is reduced to $O(n)$, and further approximating the coefficient matrix of the Newton equation as MCM, the computational complexity of Newton iteration is reduced to $O(n \log n)$. The proposed method can run in log-linear time complexity per iteration, because the multiplication of MCM (or its inverse) and vector can be implemented the multidimensional fast Fourier transform (mFFT). Experimental results on some large-scale binary-classification and multi-classification problems show that the proposed method enables KLR to scale to large scale problems with less memory consumption and less training time without sacrificing test accuracy.

Suchi Chang,1 Jindong Shi,2 Cuiping Fu,1 Xu Wu,1 Shanqun Li1 1Department of Respiratory Medicine, Zhongshan Hospital, Fudan University, Shanghai, 2Department of Respiratory Medicine, The Fifth People’s Hospital of Shanghai, Fudan University, Shanghai, People’s Republic of China Background: COPD is the third leading cause of death worldwide. Acute exacerbations of COPD may cause respiratory failure, requiring intensive care unit admission and mechanical ventilation. Intensive care unit patients with acute exacerbations of COPD requiring mechanical ventilation have higher mortality rates than other hospitalized patients. Although mechanical ventilation is the most effective intervention for these conditions, invasive ventilation techniques have yielded variable effects. Objective: We evaluated pressure-regulated volume control (PRVC) ventilation treatment efficacy and preventive effects on pulmonary barotrauma in elderly COPD patients with respiratory failure. Patients and methods: Thirty-nine intubated patients were divided into experimental and control groups and treated with the PRVC and synchronized intermittent mandatory ventilation – volume control methods, respectively. Vital signs, respiratory mechanics, and arterial blood gas analyses were monitored for 2–4 hours and 48 hours. Results: Both groups showed rapidly improved pH, partial pressure of oxygen (PaO2), and PaO2 per fraction of inspired O2 levels and lower partial pressure of carbon dioxide (PaCO2) levels. The pH and PaCO2 levels at 2–4 hours were lower and higher, respectively, in the test group than those in the control group (P<0.05 for both); after 48 hours, blood gas analyses showed no statistical difference in any marker (P>0.05). Vital signs during 2–4 hours and 48 hours of treatment showed no statistical difference in either group (P>0.05). The level of peak insp