On kernel difference-weighted k-nearest neighbor classification

Nearest neighbor (NN) rule is one of the simplest and the most important methods in pattern recognition. In this paper, we propose a kernel difference-weighted k-nearest neighbor (KDF-KNN) method for pattern classification. The proposed method defines the weighted KNN rule as a constrained optimization problem, and we then propose an efficient solution to compute the weights of different nearest neighbors. Unlike traditional distance-weighted KNN which assigns different weights to the nearest neighbors according to the distance to the unclassified sample, difference-weighted KNN weighs the nearest neighbors by using both the correlation of the differences between the unclassified sample and its nearest neighbors. To take into account the effective nonlinear structure information, we further extend difference-weighted KNN to its kernel version KDF-KNN. Our experimental results indicate that KDF-WKNN is much better than the original KNN and the distance-weighted KNN methods, and is comparable to or better than several state-of-the-art methods in terms of classification accuracy.     

Image classification using local linear regression

In the past several decades, classifier design has attracted much attention. Inspired by the locality preserving idea of manifold learning, here we give a local linear regression (LLR) classifier. The proposed classifier consists of three steps: first, search k nearest neighbors of a pointed sample from each special class, respectively; second, reconstruct the pointed sample using the k nearest neighbors from each special class, respectively; and third, classify the test sample according to the minimum reconstruction error. The experimental results on the ETH80 database, the CENPAMI handwritten number database and the FERET face image database demonstrate that LLR works well, leading to promising image classification performance.     

K Nearest Neighbor Equality: Giving equal chance to all existing classes

The nearest neighbor classification method assigns an unclassified point to the class of the nearest case of a set of previously classified points. This rule is independent of the underlying joint distribution of the sample points and their classifications. An extension to this approach is the k-NN method, in which the classification of the unclassified point is made by following a voting criteria within the k nearest points.The method we present here extends the k-NN idea, searching in each class for the k nearest points to the unclassified point, and classifying it in the class which minimizes the mean distance between the unclassified point and the k nearest points within each class. As all classes can take part in the final selection process, we have called the new approach k Nearest Neighbor Equality (k-NNE).Experimental results we obtained empirically show the suitability of the k-NNE algorithm, and its effectiveness suggests that it could be added to the current list of distance based classifiers.     

The direction-constrained <Emphasis Type="Italic">k</Emphasis> nearest neighbor query

Finding k nearest neighbor objects in spatial databases is a fundamental problem in many geospatial systems and the direction is one of the key features of a spatial object. Moreover, the recent tremendous growth of sensor technologies in mobile devices produces an enormous amount of spatio-directional (i.e., spatially and directionally encoded) objects such as photos. Therefore, an efficient and proper utilization of the direction feature is a new challenge. Inspired by this issue and the traditional k nearest neighbor search problem, we devise a new type of query, called the direction-constrained k nearest neighbor (DCkNN) query. The DCkNN query finds k nearest neighbors from the location of the query such that the direction of each neighbor is in a certain range from the direction of the query. We develop a new index structure called MULTI, to efficiently answer the DCkNN query with two novel index access algorithms based on the cost analysis. Furthermore, our problem and solution can be generalized to deal with spatio-circulant dimensional (such as a direction and circulant periods of time such as an hour, a day, and a week) objects. Experimental results show that our proposed index structure and access algorithms outperform two adapted algorithms from existing kNN algorithms.     

Fast and versatile algorithm for nearest neighbor search based on a lower bound tree

In this paper, we present a fast and versatile algorithm which can rapidly perform a variety of nearest neighbor searches. Efficiency improvement is achieved by utilizing the distance lower bound to avoid the calculation of the distance itself if the lower bound is already larger than the global minimum distance. At the preprocessing stage, the proposed algorithm constructs a lower bound tree (LB-tree) by agglomeratively clustering all the sample points to be searched. Given a query point, the lower bound of its distance to each sample point can be calculated by using the internal node of the LB-tree. To reduce the amount of lower bounds actually calculated, the winner-update search strategy is used for traversing the tree. For further efficiency improvement, data transformation can be applied to the sample and the query points. In addition to finding the nearest neighbor, the proposed algorithm can also (i) provide the k-nearest neighbors progressively; (ii) find the nearest neighbors within a specified distance threshold; and (iii) identify neighbors whose distances to the query are sufficiently close to the minimum distance of the nearest neighbor. Our experiments have shown that the proposed algorithm can save substantial computation, particularly when the distance of the query point to its nearest neighbor is relatively small compared with its distance to most other samples (which is the case for many object recognition problems).     

Improving nearest neighbor classification with cam weighted distance

Nearest neighbor (NN) classification assumes locally constant class conditional probabilities, and suffers from bias in high dimensions with a small sample set. In this paper, we propose a novel cam weighted distance to ameliorate the curse of dimensionality. Different from the existing neighborhood-based methods which only analyze a small space emanating from the query sample, the proposed nearest neighbor classification using the cam weighted distance (CamNN) optimizes the distance measure based on the analysis of inter-prototype relationship. Our motivation comes from the observation that the prototypes are not isolated. Prototypes with different surroundings should have different effects in the classification. The proposed cam weighted distance is orientation and scale adaptive to take advantage of the relevant information of inter-prototype relationship, so that a better classification performance can be achieved. Experiments show that CamNN significantly outperforms one nearest neighbor classification (1-NN) and k-nearest neighbor classification (k-NN) in most benchmarks, while its computational complexity is comparable with that of 1-NN classification.     

基于相对密度和流形上k近邻的聚类算法

针对传统的基于欧氏距离的相似性度量不能完全反映复杂结构的数据分布特性的问题,提出了一种基于相对密度和流形上k近邻的聚类算法。基于能描述全局一致性信息的流形距离,及可体现局部相似性和紧密度的k近邻概念,通过流形上k近邻相似度度量数据对象间的相似性,采用k近邻的相对紧密度发现不同密度下的类簇,设计近邻点对约束规则搜寻k近邻点对构成的近邻链,归类数据对象及识别离群点。与标准k-means算法、流形距离改进的k-means算法进行了性能比较,在人工数据集和UCI数据集上的仿真实验结果均表明,该算法能有效地处理复杂结构的数据聚类问题,且聚类效果更好。     

基于双向选择的伪近邻算法

针对伪近邻分类算法（LMPNN）对异常点和噪声点仍然敏感的问题,提出了一种基于双向选择的伪近邻算法（BS-PNN）。利用邻近性度量选取[k]个最近邻,让测试样本和近邻样本通过互近邻定义进行双向选择;通过计算每类中互近邻的个数及其局部均值的加权距离,从而得到测试样本到伪近邻的欧氏距离;利用改进的类可信度作为投票度量方式,对测试样本进行分类。BS-PNN算法在处理复杂的分类任务时,具有能够准确识别噪声点,降低近邻个数[k]的敏感性,提高分类精度等优势。在UCI和KEEL的15个实际数据集上进行仿真实验,并与KNN、WKNN、LMKNN、PNN、LMPNN、DNN算法以及P-KNN算法进行比较,实验结果表明,基于双向选择的伪近邻算法的分类性能明显优于其他几种近邻分类算法。     

基于局部均值与类均值的近邻分类

k-近邻分类是一种流行且成功的非参数分类方法.但其分类性能由于离群点的存在而受到损害.为克服离群点对分类性能的不利影响,提出了一个k-近邻分类的变形和一个基于局部均值向量与类均值向量的近邻分类方法.该方法利用了未分类样本在每个训练类中k个近邻的局部均值的信息和整体均值的知识,不仅能够克服离群点对分类性能的影响,而且取得了比传统的k-近邻分类一致好的分类性能.     

Classification by nearness in complementary subspaces

This study introduces a classifier founded on k-nearest neighbours in the complementary subspaces (NCS). The global space, spanned by all training samples, can be decomposed into the direct sum of two subspaces in terms of one class: the projection vectors of this class into one subspace are nonzero, and that into another subspace are zero. A query sample is projected into the two subspaces for each class, respectively. In each subspace, the distance from the projection vector to the mean of its k-nearest neighbours can be calculated, and the final classification rules are designed in terms of the two distances calculated in the two complementary subspaces, respectively. Allowing for the geometric meaning of Gram determinant and kernel trick, the classifier is naturally implemented in the kernel space. The experimental results on 1 synthetic, 13 IDA binary class, and five UCI multi-class data sets show that NCS compares favourably to the comparing classifiers, which is founded on the k-nearest neighbours or the nearest subspace, on almost all the data sets. The classifier can straightforwardly solve multi-classification problems, and the performance is promising.     

Locally adaptive <Emphasis Type="Italic">k</Emphasis> parameter selection for nearest neighbor classifier: one nearest cluster

The k nearest neighbors (k-NN) classification technique has a worldly wide fame due to its simplicity, effectiveness, and robustness. As a lazy learner, k-NN is a versatile algorithm and is used in many fields. In this classifier, the k parameter is generally chosen by the user, and the optimal k value is found by experiments. The chosen constant k value is used during the whole classification phase. The same k value used for each test sample can decrease the overall prediction performance. The optimal k value for each test sample should vary from others in order to have more accurate predictions. In this study, a dynamic k value selection method for each instance is proposed. This improved classification method employs a simple clustering procedure. In the experiments, more accurate results are found. The reasons of success have also been understood and presented.     

Instance variant nearest neighbor using particle swarm optimization for function approximation

In this paper, a new approach called ‘instance variant nearest neighbor’ approximates a regression surface of a function using the concept of k nearest neighbor. Instead of fixed k neighbors for the entire dataset, our assumption is that there are optimal k neighbors for each data instance that best approximates the original function by fitting the local regions. This approach can be beneficial to noisy datasets where local regions form data characteristics that are different from the major data clusters. We formulate the problem of finding such k neighbors for each data instance as a combinatorial optimization problem, which is solved by a particle swarm optimization. The particle swarm optimization is extended with a rounding scheme that rounds up or down continuous-valued candidate solutions to integers, a number of k neighbors. We apply our new approach to five real-world regression datasets and compare its prediction performance with other function approximation algorithms, including the standard k nearest neighbor, multi-layer perceptron, and support vector regression. We observed that the instance variant nearest neighbor outperforms these algorithms in several datasets. In addition, our new approach provides consistent outputs with five datasets where other algorithms perform poorly.     

Efficient moving <Emphasis Type="Italic">k</Emphasis> nearest neighbor queries over line segment objects

The growing need for location based services motivates the moving k nearest neighbor query (MkNN), which requires to find the k nearest neighbors of a moving query point continuously. In most existing solutions, data objects are abstracted as points. However, lots of real-world data objects, such as roads, rivers or pipelines, should be reasonably modeled as line segments or polyline segments. In this paper, we present LV*-Diagram to handle MkNN queries over line segment data objects. LV*-Diagram dynamically constructs a safe region. The query results remain unchanged if the query point is in the safe region, and hence, the computation cost of the server is greatly reduced. Experimental results show that our approach significantly outperforms the baseline method w.r.t. CPU load, I/O, and communication costs.     

DART+: Direction-aware bichromatic reverse k nearest neighbor query processing in spatial databases

This article presents a novel type of queries in spatial databases, called the direction-aware bichromatic reverse k nearest neighbor(DBRkNN) queries, which extend the bichromatic reverse nearest neighbor queries. Given two disjoint sets, P and S, of spatial objects, and a query object q in S, the DBRkNN query returns a subset P′ of P such that k nearest neighbors of each object in P′ include q and each object in P′ has a direction toward q within a pre-defined distance. We formally define the DBRkNN query, and then propose an efficient algorithm, called DART, for processing the DBRkNN query. Our method utilizes a grid-based index to cluster the spatial objects, and the B⁺-tree to index the direction angle. We adopt a filter-refinement framework that is widely used in many algorithms for reverse nearest neighbor queries. In the filtering step, DART eliminates all the objects that are away from the query object more than a pre-defined distance, or have an invalid direction angle. In the refinement step, remaining objects are verified whether the query object is actually one of the k nearest neighbors of them. As a major extension of DART, we also present an improved algorithm, called DART+, for DBRkNN queries. From extensive experiments with several datasets, we show that DART outperforms an R-tree-based naive algorithm in both indexing time and query processing time. In addition, our extension algorithm, DART+, also shows significantly better performance than DART.     

Noisy data elimination using mutual k-nearest neighbor for classification mining

k nearest neighbor (kNN) is an effective and powerful lazy learning algorithm, notwithstanding its easy-to-implement. However, its performance heavily relies on the quality of training data. Due to many complex real-applications, noises coming from various possible sources are often prevalent in large scale databases. How to eliminate anomalies and improve the quality of data is still a challenge. To alleviate this problem, in this paper we propose a new anomaly removal and learning algorithm under the framework of kNN. The primary characteristic of our method is that the evidence of removing anomalies and predicting class labels of unseen instances is mutual nearest neighbors, rather than k nearest neighbors. The advantage is that pseudo nearest neighbors can be identified and will not be taken into account during the prediction process. Consequently, the final learning result is more creditable. An extensive comparative experimental analysis carried out on UCI datasets provided empirical evidence of the effectiveness of the proposed method for enhancing the performance of the k-NN rule.     

The nearest subclass classifier: a compromise between the nearest mean and nearest neighbor classifier

We present the Nearest Subclass Classifier (NSC), which is a classification algorithm that unifies the flexibility of the nearest neighbor classifier with the robustness of the nearest mean classifier. The algorithm is based on the Maximum Variance Cluster algorithm and, as such, it belongs to the class of prototype-based classifiers. The variance constraint parameter of the cluster algorithm serves to regularize the classifier, that is, to prevent overfitting. With a low variance constraint value, the classifier turns into the nearest neighbor classifier and, with a high variance parameter, it becomes the nearest mean classifier with the respective properties. In other words, the number of prototypes ranges from the whole training set to only one per class. In the experiments, we compared the NSC with regard to its performance and data set compression ratio to several other prototype-based methods. On several data sets, the NSC performed similarly to the k-nearest neighbor classifier, which is a well-established classifier in many domains. Also concerning storage requirements and classification speed, the NSC has favorable properties, so it gives a good compromise between classification performance and efficiency.     

Nearest and reverse nearest neighbor queries for moving objects

With the continued proliferation of wireless communications and advances in positioning technologies, algorithms for efficiently answering queries about large populations of moving objects are gaining interest. This paper proposes algorithms for k nearest and reverse k nearest neighbor queries on the current and anticipated future positions of points moving continuously in the plane. The former type of query returns k objects nearest to a query object for each time point during a time interval, while the latter returns the objects that have a specified query object as one of their k closest neighbors, again for each time point during a time interval. In addition, algorithms for so-called persistent and continuous variants of these queries are provided. The algorithms are based on the indexing of object positions represented as linear functions of time. The results of empirical performance experiments are reported.     

A fast prototype reduction method based on template reduction and visualization-induced self-organizing map for nearest neighbor algorithm

The k nearest neighbor is a lazy learning algorithm that is inefficient in the classification phase because it needs to compare the query sample with all training samples. A template reduction method is recently proposed that uses only samples near the decision boundary for classification and removes those far from the decision boundary. However, when class distributions overlap, more border samples are retrained and it leads to inefficient performance in the classification phase. Because the number of reduced samples are limited, using an appropriate feature reduction method seems a logical choice to improve classification time. This paper proposes a new prototype reduction method for the k nearest neighbor algorithm, and it is based on template reduction and ViSOM. The potential property of ViSOM is displaying the topology of data on a two-dimensional feature map, it provides an intuitive way for users to observe and analyze data. An efficient classification framework is then presented, which combines the feature reduction method and the prototype selection algorithm. It needs a very small data size for classification while keeping recognition rate. In the experiments, both of synthetic and real datasets are used to evaluate the performance. Experimental results demonstrate that the proposed method obtains above 70 % speedup ratio and 90 % compression ratio while maintaining similar performance to kNN.     

Active learning based on coupled KNN pseudo pruning

It is very expensive and time-consuming to annotate huge amounts of data. Active learning would be a suitable approach to minimize the effort of annotation. A novel active learning approach, coupled K nearest neighbor pseudo pruning (CKNNPP), is proposed in the paper, which is based on querying examples by KNNPP method. The KNNPP method applies k nearest neighbor technique to search for k neighbor samples from labeled samples of unlabeled samples. When k labeled samples are not belong to the same class, the corresponded unlabeled sample is queried and given its right label by supervisor, and then it is added to labeled training set. In contrast with the previous depiction, the unlabeled sample is not selected and pruned, that is the pseudo pruning. This definition is enlightened from the K nearest neighbor pruning preprocessing. These samples selected by KNNPP are considered to be near or on the optimal classification hyperplane that is crucial for active learning. Especially, in order to avoid the excursion of the optimal classification hyperplane after adding a queried sample, CKNNPP method is proposed finally that two samples with different class label (like a couple, annotated by supervisor) are queried by KNNPP and added in the training set simultaneously for updating training set in each iteration. The CKNNPP can provide a good performance, and especially it is simple, effective, and robust, and can solve the classification problem with unbalanced dataset compared with the existing methods. Then, the computational complexity of CKNNPP is analyzed. Additionally, a new stopping criterion is applied in the proposed method, and the classifier is implemented by Lagrangian Support Vector Machines in iterations of active learning. Finally, twelve UCI datasets, image datasets of aircrafts, and the dataset of radar high-resolution range profile are used to validate the feasibility and effectiveness of the proposed method. The results illuminate that CKNNPP gains superior performance compared with the other seven state-of-the-art active learning approaches.