计算学习理论中最早的理论之一--样本压缩理论--断言概念类（等价集合系统）在其VC维度上允许大小线性的压缩方案。到目前为止，这一说法是正确的最大类--那些拥有最大的基数为他们的VC维。最有前途的方法，积极解决的猜想是通过嵌入一般的VC类到最大类没有超线性增加的VC维度，因为这样的嵌入将扩展到所有的VC类的压缩方案。我们表明，最大类的特点是通过查看类作为一个立方复杂的图的局部连通性。最大VC类的这种几何特征被应用于证明一个否定的嵌入结果，该结果表明VC-d类不能嵌入到VC维低于2d的任何最大类中。另一方面，我们证明了每个VC-d类C嵌入到VC-（d+D）最大类中，其中D是C的亏数，即，最大VC-d类的基数与C的基数之间的差。对于VC-2类的二元n-立方体4 <= n <= 6，我们给出了最好的结果嵌入到最大类。对于一些特殊的布尔函数类，研究了它们与最大类的关系。最后给出了一个将VC-d类嵌入到VC-（d+k）极大类中的一般递归过程。
英文摘要：
One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinality for their VC dimension. The most promising approach to positively resolving the conjecture is by embedding general VC classes into maximum classes without super-linear increase to their VC dimensions, as such embeddings would extend the known compression schemes to all VC classes. We show that maximum classes can be characterised by a local-connectivity property of the graph obtained by viewing the class as a cubical complex. This geometric characterisation of maximum VC classes is applied to prove a negative embedding result which demonstrates VC-d classes that cannot be embedded in any maximum class of VC dimension lower than 2d. On the other hand, we show that every VC-d class C embeds in a VC-(d+D) maximum class where D is the deficiency of C, i.e., the difference between the cardinalities of a maximum VC-d class and of C. For VC-2 classes in binary n-cubes for 4 <= n <= 6, we give best possible results on embedding into maximum classes. For some special classes of Boolean functions, relationships with maximum classes are investigated. Finally we give a general recursive procedure for embedding VC-d classes into VC-(d+k) maximum classes for smallest k.
Learning Adaptive Embedding Considering Incremental Class
Nanjing University of Science and Technology（南京理工大学）；Nanjing Normal University（南京师范大学）；Baidu Talent Intelligence Center, Baidu Inc（百度公司人才智库）；Missouri University of Science and Technology（密苏里科技大学）；Rutgers University（罗格斯大学）
DIRECT: Deep Discriminative Embedding for Clustering of LIGO Data
Northwestern University（西北大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Center for Interdisciplinary Exploration and Research in Astrophysics（天体物理学跨学科探索与研究中心）
Zero-Shot Image Classification Using Coupled Dictionary Embedding
USC Information Sciences Institute（南加州大学信息科学研究所）；Vanderbilt University（范德堡大学）；Wayve；HRL Laboratories（HRL实验室）；University of Pennsylvania（宾夕法尼亚大学）；SK Telecom（SK电信）
