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Convergence of Nearest Neighbor Pattern Classification with Selective Sampling

arXiv.org Machine Learning

In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the function anywhere in the domain by giving the value of the nearest sample per the metric. More generally, one may use the modal value of the m nearest samples, where m is a fixed positive integer (although m=1 is known to be admissible in the sense that no larger value is asymptotically superior in terms of prediction error). The nearest neighbor rule is nonparametric and extremely general, requiring in principle only that the domain be a metric space. The classic paper on the technique, proving convergence under independent, identically-distributed (iid) sampling, is due to Cover and Hart (1967). Because taking samples is costly, there has been much research in recent years on selective sampling, in which each sample is selected from a pool of candidates ranked by a heuristic; the heuristic tries to guess which candidate would be the most "informative" sample. Lindenbaum et al. (2004) apply selective sampling to the nearest neighbor rule, but their approach sacrifices the austere generality of Cover and Hart; furthermore, their heuristic algorithm is complex and computationally expensive. Here we report recent results that enable selective sampling in the original Cover-Hart setting. Our results pose three selection heuristics and prove that their nearest neighbor rule predictions converge to the true pattern. Two of the algorithms are computationally cheap, with complexity growing linearly in the number of samples. We believe that these results constitute an important advance in the art.


Supervised Learning Approach to Approximate Nearest Neighbor Search

arXiv.org Machine Learning

Approximate nearest neighbor search is a classic algorithmic problem where the goal is to design an efficient index structure for fast approximate nearest neighbor queries. We show that it can be framed as a classification problem and solved by training a suitable multi-label classifier and using it as an index. Compared to the existing algorithms, this supervised learning approach has several advantages: it enables adapting an index to the query distribution when the query distribution and the corpus distribution differ; it allows using training sets larger than the corpus; and in principle it enables using any multi-label classifier for approximate nearest neighbor search. We demonstrate these advantages on multiple synthetic and real-world data sets by using a random forest and an ensemble of random projection trees as the base classifiers. Introduction In k -nearest neighbor ( k -nn) search, k points that are nearest to the query point are retrieved from the corpus. Approximate nearest neighbor search is used to speed up k -nn search in applications where fast response times are critical, such as in computer vision, robotics, and recommendation systems. Traditionally, approximate nearest neighbor search is approached as a problem in algorithms and data structures. Space-partitioning methods--trees, hashing, and quantization--divide the space according to a geometric criterion. For instance, k -d trees (Bentley 1975) and principal component trees (McNames 2001) are grown by hierarchically partitioning the space along the maximum variance directions of the corpus.


Jiang

AAAI Conferences

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a symmetric strategy to learn one deep hash function for both query points and database (retrieval) points. The training of these symmetric deep supervised hashing methods is typically time-consuming, which makes them hard to effectively utilize the supervised information for cases with large-scale database. In this paper, we propose a novel deep supervised hashing method, called asymmetric deep supervised hashing (ADSH), for large-scale nearest neighbor search. ADSH treats the query points and database points in an asymmetric way. More specifically, ADSH learns a deep hash function only for query points, while the hash codes for database points are directly learned. The training of ADSH is much more efficient than that of traditional symmetric deep supervised hashing methods. Experiments show that ADSH can achieve state-of-the-art performance in real applications.


Balanced k-Nearest Neighbors

AAAI Conferences

Classic k-Nearest Neighbor (kNN) algorithms approximate a regression or classification function at a query point based on the k-nearest training observations. In real-world datasets, however, the set of k neighbors is frequently not uniformly distributed around a given query point. This can result in a locally biased estimate and thus in degraded regression or classification results. This paper presents two new kNN algorithms that adjust the weight of the k-nearest neighbors to achieve a more balanced distribution. Experiments on real-world datasets and a range of synthetic training distributions and noise levels identify conditions under which the algorithms can improve accuracy with minimal increase in computation time.


LeadLag LDA: Estimating Topic Specific Leads and Lags of Information Outlets

AAAI Conferences

Identifying which outlet in social media leads the rest in disseminating novel information on specific topics is an interesting challenge for information analysts and social scientists. In this work, we hypothesize that novel ideas are disseminated through the creation and propagation of new or newly emphasized key words, and therefore lead/lag of outlets can be estimated by tracking word usage across these outlets. First, we demonstrate the validaty of our hypothesis by showing that a simple TF-IDF based nearest-neighbors approach can recover generally accepted lead/lag behavior on the outlets pair of ACM journal articles and conference papers. Next, we build a new topic model called LeadLag LDA that estimates the lead/lag of the outlets on specific topics. We validate the topic model using the lead/lag results from the TF-IDF nearest neighbors approach. Finally, we present results from our model on two different outlet pairs of blogs vs. news media and grant proposals vs. research publications that reveal interesting patterns.