The Sparse Learning of The Support Vector Machine

The sparse model plays an important role in many aeras, such as in the machine learning, image processing and signal processing. The sparse model has the ability of variable selection, so they can solve the over-fitting problem. The sparse model can be introduced into the field of support vector machine in order to get classification of the labels and sparsity of the variables simultaneously. This paper summarizes various sparse support vector machines. Finally, we revealed the research directions of the sparse support vector machines in the future.

Research of Metric Learning-Based Method for Person Re-Identification by Intelligent Computer Vision Technology

Person re-identification technology aims to establish an efficient metric model for similarity distance measurement of pedestrian images. Candidate images captured by different camera views are ranked according to their similarities to the target individual. However, the metric learning-based method, which is commonly used in similarity measurement, often failed in person re-identification tasks due to the drastic variations in appearance. The main reason for its low identification accuracy is that the metric learning method is over-fitting to the training data. Several types of metric learning methods which differ from each other by the distribution of sample pairs were summarized in this article for analysing and easing the metric learning methods’ over-fitting problem. Three different metric learning methods were tested on the VIPeR dataset. The distributions of the distance of the positive/negative training/test pairs are displayed to demonstrate the over-fitting problem. Then, a new metric model was proposed by combining the thoughts of binary classification and multi-class classification. Related verification experiments were conducted on VIPeR dataset. Besides, the semi-supervised metric learning approach was introduced to alleviate the over-fitting problem. The experimental results reflect gap between training pairs and test pairs in the metric subspace. Therefore, reducing the difference between training data and test data is a promising way to improve the identification accuracy of metric learning method.

Mathematical Modeling of the Origami Navel Shell

The well-known Nautilus shell has been modeled extensively both by mathematicians and origamists. However, there is wide disagreement on the best-fitting mathematical model — partly because there is significant variability across different Nautilus Shells found in nature, and no single model can describe all of them well. Origami structures, however, have precise repeatable folding instructions, and do not exhibit such variability. Ironically, no known mathematical models exist for these structures. In this research, we mathematically model a prominent origami design, the Navel Shell by Tomoko Fuse, believed to be based on the Nautilus. We use first-principles geometric and trigonometric constructs for developing a non-smooth Geometric Model of the ideal origami spiral. We then search for the best-fitting parametric smooth spiral approximation, by formulating the fitting problem as a minimization problem over four unknowns. We write a Python computer program for searching the space numerically. Our evaluations show that: (i) the Smooth spiral is an excellent fit for the Geometric Model; (ii) our models for Origami Navel Shell are different from prior mathematical models for the Nautilus shell, but they come close to a recent model for a rare species of Nautilus; (iii) the Geometric Model explains the outer edges of origami images quite well and helps identify construction errors in the inner edges; and (iv) the Smooth Model helps understand how well the ideal Navel Shell matches different variants of the Nautilus species. We hope our research lays the foundation for further mathematical modeling of origami structures.

A Novel Statistical Optimization Algorithm for Estimating Perfusion Curves in Susceptibility Contrast-Enhanced MRI

Dynamic susceptibility contrast-enhanced magnetic resonance imaging is an important tool for evaluating intravascular indicator dynamics, which in turn is valuable for understanding brain physiology and pathophysiology. This procedure usually involves fitting a gamma-variate function to observed concentration-time curves in order to eliminate undesired effects of recirculation and the leakage of contrast agents. Several conventional curve-fitting approaches are routinely applied. The nonlinear optimization methods typically are computationally expensive and require reliable initial values to guarantee success, whereas a logarithmic linear least-squares (LL-LS) method is more stable and efficient, and does not suffer from the initial-value problem, but it can show degraded performance, especially when a few data or outliers are present. In this paper, we demonstrate, that the original perfusion curve-fitting problem can be transformed into a gamma-distribution-fitting problem by treating the concentration-time curves as a random sample from a gamma distribution with time as the random variable. A robust maximum-likelihood estimation (MLE) algorithm can then be readily adopted to solve this problem. The performance of the proposed method is compared with the nonlinear Levenberg-Marquardt (L-M) method and the LL-LS method using both synthetic and real data. The results show that the performance of the proposed approach is far superior to those of the other two methods, while keeping the advantages of the LL-LS method, such as easy implementation, low computational load, and dispensing with the need to guess the initial values. We argue that the proposed method represents an attractive alternative option for assessing intravascular indicator dynamics in clinical applications. Moreover, we also provide valuable suggestions on how to select valid data points and set the initial values in the two traditional approaches (LL-LS and nonlinear L-M methods) to achieve more reliable estimations.

A function fitting method

In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem which can be solved using a gradient descent algorithm. We also provide qualitative analysis on fitness to data of this function fitting method. The function fitting problem is also shown to be a solution of a linear, weak partial differential equation (PDE). We describe a simple numerical solution using a gradient descent algorithm that converges uniformly to the actual solution. As the functional of the minimization problem is a quadratic form, there also exists a numerical method using linear algebra.

Assessment of the prevention and control effects on the outbreak of COVID-19 in Hunan, China: Based on a SEIAR Dynamic Model

Background A new infectious disease, Coronavirus disease 2019 (COVID-19) has been first reported during December 2019 in Wuhan, China, cases have been exported to other cities and abroad rapidly. Hunan is the neighboring province of Wuhan, a series of preventive and control measures were taken to control the outbreak of COVID-19. It is critical to assess these measures on the epidemic progression for the benefit of global expectation.Method: A Susceptible-exposed-infections/asymptomatic-removed (SEIAR) model was established to evaluate the effect of preventive measures. Berkeley Madonna 8.3.18 was employed for the model simulation and prediction, and the curve-fitting problem was solved by Runge-Kutta fourth-order method.Results In this study, we found that Rt was 2.71 from January 21 to 27 and reduced to 0.21 after January 27, 2020. If measures have not been fully launched, patients in Hunan would reach the maximum (8.96 million) on March 25, 2020, and end in about 208 days; when measures have been fully launched, patients in Hunan would just reach the maximum (699) on February 9, 2020, and end in about 56 days, which was very closed to the actual situation.Conclusion The outbreak of COVID-19 in Hunan, China has been well controlled under current measures, full implementation of measures could reduce the peak value, short the time to peak and duration of the outbreak effectively, which could provide a reference for controlling of COVID-19 for other countries.