The $k$-nearest neighbor classification method ($k$-NNC) is one of the simplest nonparametric classification methods. The mutual $k$-NN classification method (M$k$NNC) is a variant of $k$-NNC based on mutual neighborship. We propose another variant of $k$-NNC, the symmetric $k$-NN classification method (S$k$NNC) based on both mutual neighborship and one-sided neighborship. The performance of M$k$NNC and S$k$NNC depends on the parameter $k$ as the one of $k$-NNC does. We propose the ways how M$k$NN and S$k$NN classification can be performed based on Bayesian mutual and symmetric $k$-NN regression methods with the selection schemes for the parameter $k$. Bayesian mutual and symmetric $k$-NN regression methods are based on Gaussian process models, and it turns out that they can do M$k$NN and S$k$NN classification with new encodings of target values (class labels). The simulation results show that the proposed methods are better than or comparable to $k$-NNC, M$k$NNC and S$k$NNC with the parameter $k$ selected by the leave-one-out cross validation method not only for an artificial data set but also for real world data sets.
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…
When using the K-nearest neighbors method, one often ignores uncertainty in the choice of K. To account for such uncertainty, Holmes and Adams (2002) proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN (BKNN) approach uses a pseudo-likelihood function, and standard Markov chain Monte Carlo (MCMC) techniques to draw posterior samples. Holmes and Adams (2002) focused on the performance of BKNN in terms of misclassification error but did not assess its ability to quantify uncertainty. We present some evidence to show that BKNN still significantly underestimates model u…
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…
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…
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…
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…
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.
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…
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…
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…
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…
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…
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…
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.
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.
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）
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…
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 …
State Key Lab of CAD&CG, Zhejiang University（浙江大学计算机辅助设计与图形学国家重点实验室）；Zhejiang Lab（之江实验室）
Few-shot learning (FSL) aims to classify images under low-data regimes, where the conventional pooled global feature is likely to lose useful local characteristics. Recent work has achieved promising performances by using deep descriptors. They generally take all deep descriptors from neural networks into consideration while ignoring that some of them are useless in classification due to their limited receptive field, e.g., task-irrelevant descriptors could be misleading and multiple aggregative descriptors from background clutter could even overwhelm the object's presence. In this paper, we a…
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.
Technion, Israel Institute of Technology（以色列理工学院）；University of Liège（列日大学）
We devise the Unit Commitment Nearest Neighbor (UCNN) algorithm to be used as a proxy for quickly approximating outcomes of short-term decisions, to make tractable hierarchical long-term assessment and planning for large power systems. Experimental results on updated versions of IEEE-RTS79 and IEEE-RTS96 show high accuracy measured on operational cost, achieved in runtimes that are lower in several orders of magnitude than the traditional approach.
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.
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.
The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and has shown improvements over conventional methods. One important challenge in this new approach is the need to obtain, given the original dataset, a different set where the samples are distributed according to a specific product density function. This is particularly challenging when estimating CMI. In this paper, we introduce a new technique, based on k neare…
