Approximate Nearest Neighbor Search (ANNS) in high dimensional spaces is crucial for many real-life applications (e.g., e-commerce, web, multimedia, etc.) dealing with an abundance of data. This paper proposes an end-to-end learning framework that couples the partitioning (one critical step of ANNS) and learning-to-search steps using a custom loss function. A key advantage of our proposed solution is that it does not require any expensive pre-processing of the dataset, which is one of the critical limitations of the state-of-the-art approach. We achieve the above edge by formulating a multi-objective custom loss function that does not need ground truth labels to quantify the quality of a given data-space partition, making it entirely unsupervised. We also propose an ensembling technique by adding varying input weights to the loss function to train an ensemble of models to enhance the search quality. On several standard benchmarks for ANNS, we show that our method beats the state-of-the-art space partitioning method and the ubiquitous K-means clustering method while using fewer parameters and shorter offline training times. We also show that incorporating our space-partitioning strategy into state-of-the-art ANNS techniques such as ScaNN can improve their performance significantly. Finally, we present our unsupervised partitioning approach as a promising alternative to many widely used clustering methods, such as K-means clustering and DBSCAN.
University of Helsinki（赫尔辛基大学）；Helsinki Institute for Information Technology (HIIT)（赫尔辛基信息技术研究所）；Carnegie Mellon University（卡内基梅隆大学）
Both supervised and unsupervised machine learning algorithms have been used to learn partition-based index structures for approximate nearest neighbor (ANN) search. Existing supervised algorithms formulate the learning task as finding a partition in which the nearest neighbors of a training set point belong to the same partition element as the point itself, so that the nearest neighbor candidates can be retrieved by naive lookup or backtracking search. We formulate candidate set selection in ANN search directly as a multilabel classification problem where the labels correspond to the nearest n…
University of Applied Sciences Osnabrück（奥斯纳布吕克应用科学大学）；Leibniz University Hannover（莱布尼茨汉诺威大学）
When applying outlier detection in settings where data is sensitive, mechanisms which guarantee the privacy of the underlying data are needed. The $k$-nearest neighbors ($k$-NN) algorithm is a simple and one of the most effective methods for outlier detection. So far, there have been no attempts made to develop a differentially private ($ε$-DP) approach for $k$-NN based outlier detection. Existing approaches often relax the notion of $ε$-DP and employ other methods than $k$-NN. We propose a method for $k$-NN based outlier detection by separating the procedure into a fitting step on reference i…
In this paper, we compare the performances of FAISS and FENSHSES on nearest neighbor search in Hamming space--a fundamental task with ubiquitous applications in nowadays eCommerce. Comprehensive evaluations are made in terms of indexing speed, search latency and RAM consumption. This comparison is conducted towards a better understanding on trade-offs between nearest neighbor search systems implemented in main memory and the ones implemented in secondary memory, which is largely unaddressed in literature.
This paper analyzes k nearest neighbor classification with training data anonymized using anatomy. Anatomy preserves all data values, but introduces uncertainty in the mapping between identifying and sensitive values. We first study the theoretical effect of the anatomized training data on the k nearest neighbor error rate bounds, nearest neighbor convergence rate, and Bayesian error. We then validate the derived bounds empirically. We show that 1) Learning from anatomized data approaches the limits of learning through the unprotected data (although requiring larger training data), and 2) near…
This paper computationally demonstrates a sharp improvement in predictive performance for $k$ nearest neighbors thanks to an efficient forward selection of the predictor variables. We show both simulated and real-world data that this novel repeatedly approaches outperformance regression models under stepwise selection
Carl von Ossietzky Universität Oldenburg（卡尔·冯·奥西茨基奥尔登堡大学）
In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It is based on fitting K-nearest neighbor regression to the unsupervised regression framework for learning of low-dimensional manifolds. Similar to related approaches that are mostly based on kernel methods, unsupervised K-nearest neighbor (UNN) regression optimizes latent variables w.r.t. the data space reconstruction error employing the K-nearest neighbor he…
Nearest neighbors is a successful and long-standing technique for anomaly detection. Significant progress has been recently achieved by self-supervised deep methods (e.g. RotNet). Self-supervised features however typically under-perform Imagenet pre-trained features. In this work, we investigate whether the recent progress can indeed outperform nearest-neighbor methods operating on an Imagenet pretrained feature space. The simple nearest-neighbor based-approach is experimentally shown to outperform self-supervised methods in: accuracy, few shot generalization, training time and noise robustnes…
University of Copenhagen（哥本哈根大学）；Delft University of Technology（代尔夫特理工大学）
Importance weighting is widely applicable in machine learning in general and in techniques dealing with data covariate shift problems in particular. A novel, direct approach to determine such importance weighting is presented. It relies on a nearest neighbor classification scheme and is relatively straightforward to implement. Comparative experiments on various classification tasks demonstrate the effectiveness of our so-called nearest neighbor weighting (NNeW) scheme. Considering its performance, our procedure can act as a simple and effective baseline method for importance weighting.
The nearest neighbor method together with the dynamic time warping (DTW) distance is one of the most popular approaches in time series classification. This method suffers from high storage and computation requirements for large training sets. As a solution to both drawbacks, this article extends learning vector quantization (LVQ) from Euclidean spaces to DTW spaces. The proposed LVQ scheme uses asymmetric weighted averaging as update rule. Empirical results exhibited superior performance of asymmetric generalized LVQ (GLVQ) over other state-of-the-art prototype generation methods for nearest n…
We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual $k$-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for target value estimates and the framework to select the hyperparameters. It is shown that both the proposed methods asymptotically converge to kernel and mutual $k$-nearest neighbor regression methods, respectively. The simulation results show that the proposed methods can select proper hyperparameters and are better than or comparable to the former methods for…
Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor classification has not fully reflected these subtle properties. We analyze the behavior of these estimators in metric spaces and provide finite-sample, distribution-dependent rates of convergence under minimal assumptions. As a by-product, we are able to establish the universal consistency of nearest neighbor in a broader range of data spaces than was previo…
This work deals with the problem of classifying uncertain data. With this aim the Uncertain Nearest Neighbor (UNN) rule is here introduced, which represents the generalization of the deterministic nearest neighbor rule to the case in which uncertain objects are available. The UNN rule relies on the concept of nearest neighbor class, rather than on that of nearest neighbor object. The nearest neighbor class of a test object is the class that maximizes the probability of providing its nearest neighbor. It is provided evidence that the former concept is much more powerful than the latter one in t…
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One possible explanation is that for many modern machine learning algorithms, over-fitting can greatly reduce the estimation bias, while not increasing the estimation variance too much. To illustrate the above idea, we prove that the proposed interpolated nearest neighbor algorithm achieves the minimax optimal rate in both regression and classification regimes, an…
Toulouse School of Economics (TSE)（图卢兹经济学院（TSE））；Artificial and Natural Intelligence Toulouse Institute (ANITI)（图卢兹人工智能与自然智能研究所（ANITI））；Istituto Italiano di Tecnologia（意大利技术研究院）；Università degli Studi di Milano（米兰大学）
The property of almost every point being a Lebesgue point has proven to be crucial for the consistency of several classification algorithms based on nearest neighbors. We characterize Lebesgue points in terms of a 1-Nearest Neighbor regression algorithm for pointwise estimation, fleshing out the role played by tie-breaking rules in the corresponding convergence problem. We then give an application of our results, proving the convergence of the risk of a large class of 1-Nearest Neighbor classification algorithms in general metric spaces where almost every point is a Lebesgue point.
This paper presents the local best model of PSO for partition-based clustering. The proposed model gets rid off the drawbacks of gbest PSO for clustering. The model uses a pre-specified number of clusters K. The LPOSC has K neighborhoods. Each neighborhood represents one of the clusters. The goal of the particles in each neighborhood is optimizing the position of the centroid of the cluster. The performance of the proposed algorithms is measured using adjusted rand index. The results is compared with k-means and global best model of PSO.
Space partitions of $\mathbb{R}^d$ underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn, Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space partitions reducing the problem to balanced graph partitioning followed by supervised classification. We instantiate this general approach with the KaHIP graph partitioner [Sanders, Schulz SEA 2013] and neural networks, respectively, to obtain a new partitioning procedure called Neural Locali…
Nearest neighbor has always been one of the most appealing non-parametric approaches in machine learning, pattern recognition, computer vision, etc. Previous empirical studies partly shows that nearest neighbor is resistant to noise, yet there is a lack of deep analysis. This work presents the finite-sample and distribution-dependent bounds on the consistency of nearest neighbor in the random noise setting. The theoretical results show that, for asymmetric noises, k-nearest neighbor is robust enough to classify most data correctly, except for a handful of examples, whose labels are totally mis…
This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object q in a database of n objects. In contrast with most existing approaches, we can only access the ``hidden'' space in which the objects live through a similarity oracle. The oracle, given two reference objects and a query object, returns the reference object closest to the query object. The oracle attempts to model the behavior of human users, capable of making statements about similarity, but not of assigning meaningful numerical values to distances between objects.
We present a novel method of stacking decision trees by projection into an ordered time split out-of-fold (OOF) one nearest neighbor (1NN) space. The predictions of these one nearest neighbors are combined through a linear model. This process is repeated many times and averaged to reduce variance. Generalized Linear Tree Space Nearest Neighbor (GLTSNN) is competitive with respect to Mean Squared Error (MSE) compared to Random Forest (RF) on several publicly available datasets. Some of the theoretical and applied advantages of GLTSNN are discussed. We conjecture a classifier based upon the GLTS…
Verizon（威瑞森）；LinkedIn（领英）；Sorin Capital Management（索林资本管理）
We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.
Department of Statistics, University of California, Berkeley, CA 94720, USA（加州大学伯克利分校统计系）；Department of Biostatistics, University of California, Berkeley, CA 94720, USA（加州大学伯克利分校生物统计学系）
NRI Institute of Technology-Guntur（NRI理工学院（贡图尔校区））
K-Nearest neighbor classifier (k-NNC) is simple to use and has little design time like finding k values in k-nearest neighbor classifier, hence these are suitable to work with dynamically varying data-sets. There exists some fundamental improvements over the basic k-NNC, like weighted k-nearest neighbors classifier (where weights to nearest neighbors are given based on linear interpolation), using artificially generated training set called bootstrapped training set, etc. These improvements are orthogonal to space reduction and classification time reduction techniques, hence can be coupled with…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the problem of finding a subset of O(k) points in a given set of points that contains the set of k nearest neighbors of a given query point. We propose an algorithm based on adaptively estimating the distances, and show that it is essentially optimal out of algorithms that are only all…
The nearest neighbor rule is a classic yet essential classification model, particularly in problems where the supervising information is given by pairwise dissimilarities and the embedding function are not easily obtained. Prototype selection provides means of generalization and improving efficiency of the nearest neighbor model, but many existing methods assume and rely on the analyses of the input vector space. In this paper, we explore a dissimilarity-based, parametrized model of the nearest neighbor rule. In the proposed model, the selection of the nearest prototypes is influenced by the p…
Ariel University（阿里埃勒大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Tel-Aviv University（特拉维夫大学）
We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented.
In pattern recognition or machine learning, it is a very fundamental task to find nearest neighbors of a given point. All the methods for the task work basically by comparing the given point to all the points in the data set. That is why the computational cost increases with the number of data points. However, the human visual system seems to work in a different way. When the human visual system tries to find the neighbors of one point on a map, it directly focuses on the area around the point and actively searches the neighbors by looking or zooming in and out around the point. In this paper,…
Using naive Bayes for email classification has become very popular within the last few months. They are quite easy to implement and very efficient. In this paper we want to present empirical results of email classification using a combination of naive Bayes and k-nearest neighbor searches. Using this technique we show that the accuracy of a Bayes filter can be improved slightly for a high number of features and significantly for a small number of features.
São Paulo State University（圣保罗州立大学）；University of Wolverhampton（伍尔弗汉普顿大学）
Demands for minimum parameter setup in machine learning models are desirable to avoid time-consuming optimization processes. The $k$-Nearest Neighbors is one of the most effective and straightforward models employed in numerous problems. Despite its well-known performance, it requires the value of $k$ for specific data distribution, thus demanding expensive computational efforts. This paper proposes a $k$-Nearest Neighbors classifier that bypasses the need to define the value of $k$. The model computes the $k$ value adaptively considering the data distribution of the training set. We compared …
In this paper, we present an overview of Nearest neighbor (NN) methods, which are frequently employed for solving classification problems using supervised learning. The article concisely introduces the theoretical background, algorithmic, and implementation aspects along with the key applications. From an application standpoint, this article explores the challenges related to the 5G and beyond wireless networks which can be solved using NN classification techniques.
