KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data grows KNN suffers from slowness in making decisions since it needs to search nearest neighbors within the entire dataset at each decision making. This paper proposes a new technique that enables the selection of nearest neighbors directly in the neighborhood of a given observation. The proposed approach consists of dividing the data space into subcells of a virtual grid built on top of data space. The mapping between the data points and subcells is performed using hashing. When it comes to select the nearest neighbors of a given observation, we firstly identify the cell the observation belongs by using hashing, and then we look for nearest neighbors from that central cell and cells around it layer by layer. From our experiment performance analysis on publicly available datasets, our algorithm outperforms the original KNN in time efficiency with a prediction quality as good as that of KNN it also offers competitive performance with solutions like KDtree
Learning from set-structured data is an essential problem with many applications in machine learning and computer vision. This paper focuses on non-parametric and data-independent learning from set-structured data using approximate nearest neighbor (ANN) solutions, particularly locality-sensitive hashing. We consider the problem of set retrieval from an input set query. Such retrieval problem requires: 1) an efficient mechanism to calculate the distances/dissimilarities between sets, and 2) an appropriate data structure for fast nearest neighbor search. To that end, we propose Sliced-Wasserste…
Columbia University（哥伦比亚大学）；IBM T. J. Watson Research Center（IBM T. J. 沃森研究中心）；Google Research（谷歌研究中心）
Hyperplane hashing aims at rapidly searching nearest points to a hyperplane, and has shown practical impact in scaling up active learning with SVMs. Unfortunately, the existing randomized methods need long hash codes to achieve reasonable search accuracy and thus suffer from reduced search speed and large memory overhead. To this end, this paper proposes a novel hyperplane hashing technique which yields compact hash codes. The key idea is the bilinear form of the proposed hash functions, which leads to higher collision probability than the existing hyperplane hash functions when using random p…
Along with data on the web increasing dramatically, hashing is becoming more and more popular as a method of approximate nearest neighbor search. Previous supervised hashing methods utilized similarity/dissimilarity matrix to get semantic information. But the matrix is not easy to construct for a new dataset. Rather than to reconstruct the matrix, we proposed a straightforward CNN-based hashing method, i.e. binarilizing the activations of a fully connected layer with threshold 0 and taking the binary result as hash codes. This method achieved the best performance on CIFAR-10 and was comparable…
Ocean University of China（中国海洋大学）；State Key Laboratory of Integrated Services Networks (Xidian University)（综合业务网理论及关键技术国家重点实验室（西安电子科技大学））；Southeast University（东南大学）；Purple Mountain Laboratories（紫金山实验室）
Hashing has been widely researched to solve the large-scale approximate nearest neighbor search problem owing to its time and storage superiority. In recent years, a number of online hashing methods have emerged, which can update the hash functions to adapt to the new stream data and realize dynamic retrieval. However, existing online hashing methods are required to update the whole database with the latest hash functions when a query arrives, which leads to low retrieval efficiency with the continuous increase of the stream data. On the other hand, these methods ignore the supervision relatio…
Wuhan University（武汉大学）；Sun Yat-Sen University（中山大学）；University of South Carolina（南卡罗来纳大学）
Hash coding has been widely used in approximate nearest neighbor search for large-scale image retrieval. Given semantic annotations such as class labels and pairwise similarities of the training data, hashing methods can learn and generate effective and compact binary codes. While some newly introduced images may contain undefined semantic labels, which we call unseen images, zeor-shot hashing techniques have been studied. However, existing zeor-shot hashing methods focus on the retrieval of single-label images, and cannot handle multi-label images. In this paper, for the first time, a novel t…
University of Waterloo（滑铁卢大学）；University of Tehran（德黑兰大学）；Vector Institute（向量研究所）
In the era of big data, methods for improving memory and computational efficiency have become crucial for successful deployment of technologies. Hashing is one of the most effective approaches to deal with computational limitations that come with big data. One natural way for formulating this problem is spectral hashing that directly incorporates affinity to learn binary codes. However, due to binary constraints, the optimization becomes intractable. To mitigate this challenge, different relaxation approaches have been proposed to reduce the computational load of obtaining binary codes and sti…
Universidad de Antioquia（安蒂奥基亚大学）；Universidad Politécnica de Madrid（马德里理工大学）
Training of Machine Learning (ML) models in real contexts often deals with big data sets and high-class imbalance samples where the class of interest is unrepresented (minority class). Practical solutions using classical ML models address the problem of large data sets using parallel/distributed implementations of training algorithms, approximate model-based solutions, or applying instance selection (IS) algorithms to eliminate redundant information. However, the combined problem of big and high imbalanced datasets has been less addressed. This work proposes three new methods for IS to be able…
Nearest neighbors search is a fundamental problem in various research fields like machine learning, data mining and pattern recognition. Recently, hashing-based approaches, e.g., Locality Sensitive Hashing (LSH), are proved to be effective for scalable high dimensional nearest neighbors search. Many hashing algorithms found their theoretic root in random projection. Since these algorithms generate the hash tables (projections) randomly, a large number of hash tables (i.e., long codewords) are required in order to achieve both high precision and recall. To address this limitation, we propose a …
Computing approximate nearest neighbors in high dimensional spaces is a central problem in large-scale data mining with a wide range of applications in machine learning and data science. A popular and effective technique in computing nearest neighbors approximately is the locality-sensitive hashing (LSH) scheme. In this paper, we aim to develop LSH schemes for distance functions that measure the distance between two probability distributions, particularly for f-divergences as well as a generalization to capture mutual information loss. First, we provide a general framework to design LHS scheme…
Given a large dataset of binary codes and a binary query point, we address how to efficiently find $K$ codes in the dataset that yield the largest cosine similarities to the query. The straightforward answer to this problem is to compare the query with all items in the dataset, but this is practical only for small datasets. One potential solution to enhance the search time and achieve sublinear cost is to use a hash table populated with binary codes of the dataset and then look up the nearby buckets to the query to retrieve the nearest neighbors. However, if codes are compared in terms of cosi…
Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error or other objective functions tailored to the retrieval problem. In this paper, we re-interpret popular methods such as binary hashing or product quantizers as auto-encoders, and point out that they implicitly make suboptimal assumptions on the form of the decoder. We design backward-compatible decoders that improve the reconstruction of the vectors from the…
We propose a new class of data-independent locality-sensitive hashing (LSH) algorithms based on the fruit fly olfactory circuit. The fundamental difference of this approach is that, instead of assigning hashes as dense points in a low dimensional space, hashes are assigned in a high dimensional space, which enhances their separability. We show theoretically and empirically that this new family of hash functions is locality-sensitive and preserves rank similarity for inputs in any `p space. We then analyze different variations on this strategy and show empirically that they outperform existing …
Alibaba Group（阿里巴巴集团）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Google Research（谷歌研究院）；Columbia University（哥伦比亚大学）
The explosive growth in big data has attracted much attention in designing efficient indexing and search methods recently. In many critical applications such as large-scale search and pattern matching, finding the nearest neighbors to a query is a fundamental research problem. However, the straightforward solution using exhaustive comparison is infeasible due to the prohibitive computational complexity and memory requirement. In response, Approximate Nearest Neighbor (ANN) search based on hashing techniques has become popular due to its promising performance in both efficiency and accuracy. Pr…
Columbia University（哥伦比亚大学）；Google Research（谷歌研究院）
Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how difficult is (approximate) nearest neighbor search in a given data set? And which data properties affect the difficulty of nearest neighbor search and how? This paper introduces the first concrete measure called Relative Contrast that can be used to evaluate the influence of several crucial data characteristics such as dimensionality, sparsity, and database si…
We present a simple but powerful reinterpretation of kernelized locality-sensitive hashing (KLSH), a general and popular method developed in the vision community for performing approximate nearest-neighbor searches in an arbitrary reproducing kernel Hilbert space (RKHS). Our new perspective is based on viewing the steps of the KLSH algorithm in an appropriately projected space, and has several key theoretical and practical benefits. First, it eliminates the problematic conceptual difficulties that are present in the existing motivation of KLSH. Second, it yields the first formal retrieval perf…
In large scale systems, approximate nearest neighbour search is a crucial algorithm to enable efficient data retrievals. Recently, deep learning-based hashing algorithms have been proposed as a promising paradigm to enable data dependent schemes. Often their efficacy is only demonstrated on data sets with fixed, limited numbers of classes. In practical scenarios, those labels are not always available or one requires a method that can handle a higher input variability, as well as a higher granularity. To fulfil those requirements, we look at more flexible similarity measures. In this work, we p…
Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization…
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…
Youtu Lab, Tencent（腾讯优图实验室）；Department of Computer Science and Engineering, The Chinese University of Hong Kong（香港中文大学计算机科学与工程学系）；Shenzhen Research Institute, The Chinese University of Hong Kong（香港中文大学深圳研究院）；Meitu (China)（美图（中国））；Department of Computing, Hang Seng University of Hong Kong（香港恒生大学计算机系）
Data-dependent hashing methods have demonstrated good performance in various machine learning applications to learn a low-dimensional representation from the original data. However, they still suffer from several obstacles: First, most of existing hashing methods are trained in a batch mode, yielding inefficiency for training streaming data. Second, the computational cost and the memory consumption increase extraordinarily in the big data setting, which perplexes the training procedure. Third, the lack of labeled data hinders the improvement of the model performance. To address these difficult…
Laboratory for Information and Decision Systems（信息与决策系统实验室）；Massachusetts Institute of Technology（麻省理工学院）
We consider model-free reinforcement learning for infinite-horizon discounted Markov Decision Processes (MDPs) with a continuous state space and unknown transition kernel, when only a single sample path under an arbitrary policy of the system is available. We consider the Nearest Neighbor Q-Learning (NNQL) algorithm to learn the optimal Q function using nearest neighbor regression method. As the main contribution, we provide tight finite sample analysis of the convergence rate. In particular, for MDPs with a $d$-dimensional state space and the discounted factor $γ\in (0,1)$, given an arbitrary…
Hashing has been widely studied for big data retrieval due to its low storage cost and fast query speed. Zero-shot hashing (ZSH) aims to learn a hashing model that is trained using only samples from seen categories, but can generalize well to samples of unseen categories. ZSH generally uses category attributes to seek a semantic embedding space to transfer knowledge from seen categories to unseen ones. As a result, it may perform poorly when labeled data are insufficient. ZSH methods are mainly designed for single-modality data, which prevents their application to the widely spread multi-modal…
Finding similar data in high-dimensional spaces is one of the important tasks in multimedia applications. Approaches introduced to find exact searching techniques often use tree-based index structures which are known to suffer from the curse of the dimensionality problem that limits their performance. Approximate searching techniques prefer performance over accuracy and they return good enough results while achieving a better performance. Locality Sensitive Hashing (LSH) is one of the most popular approximate nearest neighbor search techniques for high-dimensional spaces. One of the most time-…
Binary codes can be used to speed up nearest neighbor search tasks in large scale data sets as they are efficient for both storage and retrieval. In this paper, we propose a robust auto-encoder model that preserves the geometric relationships of high-dimensional data sets in Hamming space. This is done by considering a noise-removing function in a region surrounding the manifold where the training data points lie. This function is defined with the property that it projects the data points near the manifold into the manifold wisely, and we approximate this function by its first order approximat…
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity search. This paper aims at bridging these realms: to reap the advantages of fast evaluation time while maintaining Bayes consistency, and further without sacrificing too much in the risk decay rate. We combine the locality-sensitive hashing (LSH) technique with a novel missing-mass argument to obtain a fast and Bayes-consistent classifier. Our algorithm's pre…
Southwest University（西南大学）；Shandong University（山东大学）；George Mason University（乔治梅森大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Due to the advantage of reducing storage while speeding up query time on big heterogeneous data, cross-modal hashing has been extensively studied for approximate nearest neighbor search of multi-modal data. Most hashing methods assume that training data is class-balanced.However, in practice, real world data often have a long-tailed distribution. In this paper, we introduce a meta-learning based cross-modal hashing method (MetaCMH) to handle long-tailed data. Due to the lack of training samples in the tail classes, MetaCMH first learns direct features from data in different modalities, and the…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We devise a new strategy that avoids partitioning the vector space and present a novel randomized algorithm that runs in time linear in dimensionality of the space and sub-linear in the intrinsic dimensionality and the size of the dataset and takes space constant in dimensionality of the space and linear in the size of the dataset. The proposed algorithm allow…
IT University of Copenhagen（哥本哈根信息技术大学）；BARC；University of Copenhagen（哥本哈根大学）
Kernel Density Estimation (KDE) is a nonparametric method for estimating the shape of a density function, given a set of samples from the distribution. Recently, locality-sensitive hashing, originally proposed as a tool for nearest neighbor search, has been shown to enable fast KDE data structures. However, these approaches do not take advantage of the many other advances that have been made in algorithms for nearest neighbor algorithms. We present an algorithm called Density Estimation from Approximate Nearest Neighbors (DEANN) where we apply Approximate Nearest Neighbor (ANN) algorithms as a…
Hashing is an efficient method for nearest neighbor search in large-scale data space by embedding high-dimensional feature descriptors into a similarity preserving Hamming space with a low dimension. However, large-scale high-speed retrieval through binary code has a certain degree of reduction in retrieval accuracy compared to traditional retrieval methods. We have noticed that multi-view methods can well preserve the diverse characteristics of data. Therefore, we try to introduce the multi-view deep neural network into the hash learning field, and design an efficient and innovative retrieval…
Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership limitations, we consider the divide and conquer scheme: the entire data set is divided into small subsamples, on which nearest neighbor predictions are made, and then a final decision is reached by aggregating the predictions on subsamples by majority voting. We name this method the big Nearest Neighbor (bigNN) classifier, and provide its rates of convergence under m…
Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We here develop a new clustering algorithm for large data of mixed type, aiming at improving the applicability and efficiency of the peak-finding technique. The improvements are threefold: (1) the new algorithm is applicable to mixed data; (2) the algorithm is capable of detecting outliers and clusters of relatively lower density values; (3) the algorithm is co…
Discovering Data Structures: Nearest Neighbor Search and Beyond
Université de Montréal（蒙特利尔大学）；Mila；HEC Montréal（蒙特利尔高等商学院）；Microsoft Research（微软研究院）；University of Southern California（南加州大学）；Stanford University（斯坦福大学）
The facility location problem is widely used for summarizing large datasets and has additional applications in sensor placement, image retrieval, and clustering. One difficulty of this problem is that submodular optimization algorithms require the calculation of pairwise benefits for all items in the dataset. This is infeasible for large problems, so recent work proposed to only calculate nearest neighbor benefits. One limitation is that several strong assumptions were invoked to obtain provable approximation guarantees. In this paper we establish that these extra assumptions are not necessary…
The indexing algorithms for the high-dimensional nearest neighbor search (NNS) with the best worst-case guarantees are based on the randomized Locality Sensitive Hashing (LSH), and its derivatives. In practice, many heuristic approaches exist to "learn" the best indexing method in order to speed-up NNS, crucially adapting to the structure of the given dataset. Oftentimes, these heuristics outperform the LSH-based algorithms on real datasets, but, almost always, come at the cost of losing the guarantees of either correctness or robust performance on adversarial queries, or apply to datasets wit…
Telecom Bretagne（布列塔尼电信学校）；University of Münster（明斯特大学）；Université de Bretagne Occidentale（布列塔尼西方大学）
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the dimension and the cardinal of the collection of vectors the search is performed in. Recently many works have focused on reducing the dimension of vectors using quantization techniques or hashing, while providing an approximate result. In this paper we focus instead on tackling the cardinal of the collection of vectors. Namely, we introduce a technique that partit…
In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering which computes arbitrarily shaped clusters as defined as the basins of attraction to the local modes created by the density gradient ascent paths. Despite its potential, the Mean Shift approach is a computationally expensive method for unsupervised learning. Thus, we introduce two …
The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original objective function. The solution of the simpler problem is used as the starting point to solve the original problem. We show a continuation method for discrete optimization problems. Ideally, we would like the evolved function to be hill-climbing friendly and to have the same global minima as the original function. We show that the proposed continuation method…
The era of Big Data has spawned unprecedented interests in developing hashing algorithms for efficient storage and fast nearest neighbor search. Most existing work learn hash functions that are numeric quantizations of feature values in projected feature space. In this work, we propose a novel hash learning framework that encodes feature's rank orders instead of numeric values in a number of optimal low-dimensional ranking subspaces. We formulate the ranking subspace learning problem as the optimization of a piece-wise linear convex-concave function and present two versions of our algorithm: o…
