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 any of them. The paper proposes another improvement to the basic k-NNC where the weights to nearest neighbors are given based on Gaussian distribution (instead of linear interpolation as done in weighted k-NNC) which is also independent of any space reduction and classification time reduction technique. We formally show that our proposed method is closely related to non-parametric density estimation using a Gaussian kernel. We experimentally demonstrate using various standard data-sets that the proposed method is better than the existing ones in most cases.
Yahoo! Labs（雅虎实验室）；Binghamton University, State University of New York（纽约州立大学宾汉姆顿分校）；Purdue University（普渡大学）；Princeton University（普林斯顿大学）
The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classification instability (CIS) to quantify the sampling variability of the prediction made by a classification method. Interestingly, the asymptotic CIS of any weighted nearest neighbor classifier turns out to be proportional to the Euclidean norm of its weight vector. Based on this c…
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…
In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also consider to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyzed two real example where two different manifolds are considered.
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…
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.
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each class is modeled by a union of of a finite number ofaffine subspaces of the feature space. The affine subspaces have a common dimension, which is assumed to be much less than the dimension of the feature space. The subspaces are found using regression based on the L0-norm. The proposed method is a generalisation of classical NN (Nearest Neighbor), NFL (Neares…
Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the dimensionality of data grows, while hashing based methods usually lack efficiency in practice. Recently, the graph based methods have drawn considerable attention. The main idea is that \emph{a neighbor of a neighbor is also likely to be a neighbor}, which we refer as \emph{NN-expansion}. These methods construct a $k$-nearest neighbor ($k$NN) graph offline. And at online…
Microsoft Research（微软研究院）；University of California, Berkeley（加州大学伯克利分校）
We explore a variety of nearest neighbor baseline approaches for image captioning. These approaches find a set of nearest neighbor images in the training set from which a caption may be borrowed for the query image. We select a caption for the query image by finding the caption that best represents the "consensus" of the set of candidate captions gathered from the nearest neighbor images. When measured by automatic evaluation metrics on the MS COCO caption evaluation server, these approaches perform as well as many recent approaches that generate novel captions. However, human studies show tha…
A number of authors have described randomized algorithms for solving the epsilon-approximate nearest neighbor problem. In this note I point out that the epsilon-approximate nearest neighbor property often fails to be a useful approximation property, since epsilon-approximate solutions fail to satisfy the necessary preconditions for using nearest neighbors for classification and related tasks.
The present paper deals with optimisation of Nearest Neighbour rule Classifiers via Genetic Algorithms. The methodology consists on implement a Genetic Algorithm capable of search the input feature space used by the NNR classifier. Results show that is adequate to perform feature reduction and simultaneous improve the Recognition Rate. Some practical examples prove that is possible to Recognise Portuguese Granites in 100%, with only 3 morphological features (from an original set of 117 features), which is well suited for real time applications. Moreover, the present method represents a robust …
Cornell University（康奈尔大学）；Ohio State University（俄亥俄州立大学）；Facebook AI Research（脸书人工智能研究院）
Few-shot learners aim to recognize new object classes based on a small number of labeled training examples. To prevent overfitting, state-of-the-art few-shot learners use meta-learning on convolutional-network features and perform classification using a nearest-neighbor classifier. This paper studies the accuracy of nearest-neighbor baselines without meta-learning. Surprisingly, we find simple feature transformations suffice to obtain competitive few-shot learning accuracies. For example, we find that a nearest-neighbor classifier used in combination with mean-subtraction and L2-normalization …
Fujian Key Laboratory of Sensing and Computing for Smart City, Xiamen University（厦门大学福建省智慧城市感知与计算重点实验室）；City University of Hong Kong（香港城市大学）
Nearest neighbor search and k-nearest neighbor graph construction are two fundamental issues arise from many disciplines such as multimedia information retrieval, data-mining and machine learning. They become more and more imminent given the big data emerge in various fields in recent years. In this paper, a simple but effective solution both for approximate k-nearest neighbor search and approximate k-nearest neighbor graph construction is presented. These two issues are addressed jointly in our solution. On the one hand, the approximate k-nearest neighbor graph construction is treated as a se…
The problem of optical character recognition, OCR, has been widely discussed in the literature. Having a hand-written text, the program aims at recognizing the text. Even though there are several approaches to this issue, it is still an open problem. In this paper we would like to propose an approach that uses K-nearest neighbors algorithm, and has the accuracy of more than 90%. The training and run time is also very short.
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences（奥地利科学院约翰·拉东计算与应用数学研究所（RICAM））；Linköping University（林雪平大学）；RISE Research Institutes of Sweden AB（瑞典RISE研究院AB）
A windowed version of the Nearest Neighbour (WNN) classifier for images is described. While its construction is inspired by the architecture of Artificial Neural Networks, the underlying theoretical framework is based on approximation theory. We illustrate WNN on the datasets MNIST and EMNIST of images of handwritten digits. In order to calibrate the parameters of WNN, we first study it on the classical MNIST dataset. We then apply WNN with these parameters to the challenging EMNIST dataset. It is demonstrated that WNN misclassifies 0.42% of the images of EMNIST and therefore significantly out…
Query Expansion (QE) is a well established method for improving retrieval metrics in image search applications. When using QE, the search is conducted on a new query vector, constructed using an aggregation function over the query and images from the database. Recent works gave rise to QE techniques in which the aggregation function is learned, whereas previous techniques were based on hand-crafted aggregation functions, e.g., taking the mean of the query's nearest neighbors. However, most QE methods have focused on aggregation functions that work directly over the query and its immediate near…
To denoise a reference patch, the Non-Local-Means denoising filter processes a set of neighbor patches. Few Nearest Neighbors (NN) are used to limit the computational burden of the algorithm. Here here we show analytically that the NN approach introduces a bias in the denoised patch, and we propose a different neighbors' collection criterion, named Statistical NN (SNN), to alleviate this issue. Our approach outperforms the traditional one in case of both white and colored noise: fewer SNNs generate images of higher quality, at a lower computational cost.
In this study, we present a novel ranking model based on learning neighborhood relationships embedded in the index space. Given a query point, conventional approximate nearest neighbor search calculates the distances to the cluster centroids, before ranking the clusters from near to far based on the distances. The data indexed in the top-ranked clusters are retrieved and treated as the nearest neighbor candidates for the query. However, the loss of quantization between the data and cluster centroids will inevitably harm the search accuracy. To address this problem, the proposed model ranks clu…
Nearest neighbor search is known as a challenging issue that has been studied for several decades. Recently, this issue becomes more and more imminent in viewing that the big data problem arises from various fields. In this paper, a scalable solution based on hill-climbing strategy with the support of k-nearest neighbor graph (kNN) is presented. Two major issues have been considered in the paper. Firstly, an efficient kNN graph construction method based on two means tree is presented. For the nearest neighbor search, an enhanced hill-climbing procedure is proposed, which sees considerable perf…
Measuring the similarity between patches in images is a fundamental building block in various tasks. Naturally, the patch-size has a major impact on the matching quality, and on the consequent application performance. We try to use large patches instead of relatively small patches so that each patch contains more information. We use different feature extraction mechanisms to extract the features of each individual image patches which forms a feature matrix and find out the nearest neighbor patches in the image. The nearest patches are calculated using two different nearest neighbor algorithms …
