New modifications of the Cohen-Sutherland algorithm for clipping lines and line segments in E-2 are presented. The suggested algorithms are based on a technique of coding the line direction together with the end point...
详细信息
New modifications of the Cohen-Sutherland algorithm for clipping lines and line segments in E-2 are presented. The suggested algorithms are based on a technique of coding the line direction together with the end points of the clipped line segment. They solve all cases more effectively. The algorithms are convenient for clippings lines or line segments by rectangle. Theoretical considerations and experimental results are also presented.
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the tr...
详细信息
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.
A new algorithm for clipping a line segment against a pyramid in E-3 is presented. This algorithm avoids computation of intersection points that are not end points of the output line segment. It also solves all cases ...
详细信息
A new algorithm for clipping a line segment against a pyramid in E-3 is presented. This algorithm avoids computation of intersection points that are not end points of the output line segment. It also solves all cases more effectively. The performance of this algorithm is shown to be consistently better than that of existing algorithms, including the Cohen-Sutherland, Liang-Barsky, and Cyrus-Beck algorithms.
Decision trees have been found very effective for classification especially in data mining. Although classification is a well studied problem, most of the current classification algorithms need an in-memory data struc...
详细信息
暂无评论