= 关于稀疏表示方法的整理与总结

核稀疏表示分类（KSRC）是稀疏表示分类的非线性扩展，显示了其在高光谱图像分类中的良好性能。 但是，KSRC仅考虑无序像素的光谱，而没有在空间相邻数据上合并信息。 本文提出了一种对空间光谱核稀疏表示的相邻滤波核，以增强对高光谱图像的分类。 这项工作的新颖性在于：1）提出了空间光谱KSRC框架； 2）通过核特征空间中的邻域滤波来测量空间相似度。 在几个高光谱图像上的实验证明了该方法的有效性，并且所提出的相邻滤波内核优于现有的空间光谱内核。 此外，所提出的空间光谱KSRC为将来的发展打开了广阔的领域，在其中可以轻松地合并滤波方法。

一个低秩分解的讲解，由林宙辰在北京大学做演讲时所用的材料。

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor- porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (1) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry. (3) The isomorphism theorem is proved first in an elementary way (Theorem 14.2), but later obtained again as a corollary of Serre's Theorem (18.3), which gives a presentation by generators and relations. (4) From the outset, the simple algebras of types A, B, C, D are empha- sized in the text and exercises. (5) Root systems are treated axiomatically (Chapter III), along with some of the theory of weights. (6) A conceptual approach to Weyl's character formula, based on Harish-chandra's theory of "characters" and independent of Freudenthal's multiplicity formula (22.3), is presented in 23 and 24. This is inspired by D.-N. Verma's thesis, and recent work of I. N. Bernstein, I. M. Gel'fand, S. I. Gel'fand. (7) The basic constructions in the theory of Chevalley groups are given in Chapter VII, following lecture notes of R. Steinberg. I have had to omit many standard topics (most of which I feel are better suited to a second course), e.g., cohomology, theorems of Levi and Mal'cev, theorems of Ado and Iwasawa, classification over non-algebraically closed fields, Lie algebras in prime characteristic. I hope the reader will be stirn u- lated to pursue these topics in the books and articles listed under References, especially Jacobson [1], Bourbaki [1], [2], Winter [1], Seligman [1].

机器学习方法已经广泛应用于药物发现领域，使得更强大和高效的模型成为可能。在深度模型出现之前，建模分子在很大程度上是由专家知识驱动的;为了表现分子结构的复杂性，这些手工设计的规则被证明是不够的。深度学习模型是强大的，因为它们可以学习问题的重要统计特征——但只有正确的归纳偏差。我们在两个分子问题的背景下解决这个重要的问题:表征和生成。深度学习的典型成功在于它能够将输入域映射到有意义的表示空间。这对于分子问题尤其尖锐，分子之间的“正确”关系微妙而复杂。本论文的第一部分将重点讨论分子表征，特别是性质和反应预测。在这里，我们探索了一种用于分子表示的Transformer式架构，提供了将这些模型应用于图形结构对象的新工具。抛开传统的图神经网络范式，我们展示了分子表示原型网络的有效性，它允许我们对分子的学习性质原型进行推理。最后，我们在改进反应预测的背景下研究分子表示。本论文的第二部分将集中在分子生成，这是至关重要的药物发现作为一种手段，提出有前途的药物候选人。我们开发了一种新的多性质分子生成方法，通过首先学习分子片段的分布词汇。然后，利用这个词汇，我们调查了化学空间的有效探索方法。

信号与系统英文版课件：Chap3 Fourier Series Representation of Periodic Sigs.pptx

信号与系统英文版教学课件：ch3 Fourier Series Representation of Periodic Signals.ppt

信号与系统英文版教学课件：ch8 State Model Representation.ppt

计算机科学导论课件：chap2-data-representation-new.ppt

Ch4 Internal Representation of Files高级操作系统课件PPT(UNIX).ppt