Doubly Approximate Nearest Neighbor Classification

Nonparametric classification models, such as K-Nearest Neighbor (KNN), have become particularly powerful tools in machine learning and data mining, due to their simplicity and flexibility. However, the testing time of the KNN classi- fier becomes unacceptable and the KNN’s performance deteriorates significantly when applied to data sets with millions of dimensions. We observe that state-of-the-art approximate nearest neighbor (ANN) methods aim to either reduce the number of distance comparisons based on tree structure or decrease the cost of distance computation by dimension reduction methods. In this paper, we propose a doubly approximate nearest neighbor classification strategy, which marries the two branches which compress the dimensions for decreasing distance computation cost as well as reduce the number of distance comparison instead of full scan. Under this strategy, we build a compressed dimensional tree (CD-Tree) to avoid unnecessary distance calculations. In each decision node, we propose a novel feature selection paradigm by optimizing the feature selection vector as well as the separator (indicator variables for splitting instances) with the maximum margin. An efficient algorithm is then developed to find the globally optimal solution with convergence guarantee. Furthermore, we also provide a data-dependent generalization error bound for our model, which reveals a new insight for the design of ANN classification algorithms. Our empirical studies show that our algorithm consistently obtains competitive or better classification results on all data sets, yet we can also achieve three orders of magnitude faster than state-of-the-art libraries on very high dimensions.

Authors

• Weiwei Liu Wuhan University
• Zhuanghua Liu National University of Singapore CNRS@CREATE LTD, 1 Create Way, #08-01 CREATE Tower, Singapore 138602
• Ivor Tsang Centre for Frontier AI Research, Agency for Science, Technology and Research Institute of High Performance Computing, Agency for Science, Technology and Research
• Wenjie Zhang School of Computer Science and Artificial Intelligence, Zhengzhou University, Zhengzhou, 450001, China; Engineering Research Center of Intelligent Swarm Systems, Ministry of Education, Zhengzhou, 450001, China; National Supercomputing Center in Zhengzhou, Zhengzhou, 450001, China;
• Xuemin Lin

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