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.     

Speeding up dynamic time warping distance for sparse time series data

Dynamic time warping (DTW) distance has been effectively used in mining time series data in a multitude of domains. However, in its original formulation DTW is extremely inefficient in comparing long sparse time series, containing mostly zeros and some unevenly spaced nonzero observations. Original DTW distance does not take advantage of this sparsity, leading to redundant calculations and a prohibitively large computational cost for long time series. We derive a new time warping similarity measure (AWarp) for sparse time series that works on the run-length encoded representation of sparse time series. The complexity of AWarp is quadratic on the number of observations as opposed to the range of time of the time series. Therefore, AWarp can be several orders of magnitude faster than DTW on sparse time series. AWarp is exact for binary-valued time series and a close approximation of the original DTW distance for any-valued series. We discuss useful variants of AWarp: bounded (both upper and lower), constrained, and multidimensional. We show applications of AWarp to three data mining tasks including clustering, classification, and outlier detection, which are otherwise not feasible using classic DTW, while producing equivalent results. Potential areas of application include bot detection, human activity classification, search trend analysis, seismic analysis, and unusual review pattern mining.     

Recognizing multiple emotion from ambiguous facial expressions on mobile platforms

Extracting and understanding of emotion is of high importance for the interaction between human and machine communication systems. The most expressive way to display the human’s emotion is through facial expression analysis. This paper proposes a multiple emotion recognition system that can recognize combinations of up to a maximum of three different emotions using an active appearance model (AAM), the proposed classification standard, and a k-nearest neighbor (k-NN) classifier in mobile environments. AAM can take the expression of variations that are calculated by the proposed classification standard according to changes in human expressions in real time. The proposed k-NN can classify basic emotions (normal, happy, sad, angry, surprise) as well as more ambiguous emotions by combining the basic emotions in real time, and each recognized emotion that can be subdivided has strength. Whereas most previous methods of emotion recognition recognize various kind of a single emotion, this paper recognizes various emotions with a combination of the five basic emotions. To be easily understood, the recognized result is presented in three ways on a mobile camera screen. The result of the experiment was an average 85 % recognition rate and a 40 % performance showed optimized emotions. The implemented system can be represented by one of the example for augmented reality on displaying combination of real face video and virtual animation with user’s avatar.     

Diverse nearest neighbors queries using linear skylines

k-nearest neighbor (k-NN) queries are well-known and widely used in a plethora of applications. However, in the original definition of k-NN queries there is no concern regarding diversity of the answer set with respect to the user’s interests. For instance, travelers may be looking for touristic sites that are close to where they are, but that would also lead them to see different parts of the city. Likewise, if one is looking for restaurants close by, it may be more interesting to learn about restaurants of different categories or ethnicities which are nonetheless relatively close. The interesting novel aspect of this type of query is that there are two competing criteria to be optimized: closeness and diversity. We propose two approaches that leverage the notion of linear skyline queries in order to find the k diverse nearest neighbors within a radius r from a given query point, or (k, r)-DNNs for short. Our proposed approaches return a relatively small set containing all optimal solutions for any linear combination of the weights a user could give to the two competing criteria, and we consider three different notions of diversity: spatial, categorical and angular. Our experiments, varying a number of parameters and exploring synthetic and real datasets, in both Euclidean space and road networks, respectively, show that our approaches are several orders of magnitude faster than a straightforward approach.     

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.     

Linear Time Algorithms for Generalizations of the Longest Common Substring Problem

In its simplest form, the longest common substring problem is to find a longest substring common to two or multiple strings. Using (generalized) suffix trees, this problem can be solved in linear time and space. A first generalization is the k -common substring problem: Given m strings of total length n, for all k with 2≤k≤m simultaneously find a longest substring common to at least k of the strings. It is known that the k-common substring problem can also be solved in O(n) time (Hui in Proc. 3rd Annual Symposium on Combinatorial Pattern Matching, volume 644 of Lecture Notes in Computer Science, pp. 230–243, Springer, Berlin, 1992). A further generalization is the k -common repeated substring problem: Given m strings T ⁽¹⁾,T ⁽²⁾,…,T ^(m) of total length n and m positive integers x ₁,…,x _m , for all k with 1≤k≤m simultaneously find a longest string ω for which there are at least k strings \(T^{(i_{1})},T^{(i_{2})},\ldots,T^{(i_{k})}\) (1≤i ₁<i ₂<???<i _k ≤m) such that ω occurs at least \(x_{i_{j}}\) times in \(T^{(i_{j})}\) for each j with 1≤j≤k. (For x ₁=???=x _m =1, we have the k-common substring problem.) In this paper, we present the first O(n) time algorithm for the k-common repeated substring problem. Our solution is based on a new linear time algorithm for the k-common substring problem.     

Multiple <Emphasis Type="Italic">k</Emphasis> nearest neighbor search

The problem of kNN (k Nearest Neighbor) queries has received considerable attention in the database and information retrieval communities. Given a dataset D and a kNN query q, the k nearest neighbor algorithm finds the closest k data points to q. The applications of kNN queries are board, not only in spatio-temporal databases but also in many areas. For example, they can be used in multimedia databases, data mining, scientific databases and video retrieval. The past studies of kNN query processing did not consider the case that the server may receive multiple kNN queries at one time. Their algorithms process queries independently. Thus, the server will be busy with continuously reaccessing the database to obtain the data that have already been acquired. This results in wasting I/O costs and degrading the performance of the whole system. In this paper, we focus on this problem and propose an algorithm named COrrelated kNN query Evaluation (COKE). The main idea of COKE is an “information sharing” strategy whereby the server reuses the query results of previously executed queries for efficiently processing subsequent queries. We conduct a comprehensive set of experiments to analyze the performance of COKE and compare it with the Best-First Search (BFS) algorithm. Empirical studies indicate that COKE outperforms BFS, and achieves lower I/O costs and less running time.     

<Emphasis Type="Italic">k</Emphasis>-Nearest neighbors tracking in wireless sensor networks with coverage holes

Target tracking is one of the important applications of wireless sensor networks (WSNs). Most of the existing approaches assume that the nodes are dense enough and ignore the coverage holes which are very common in WSNs because of random deployment of the sensor nodes, block of obstacles, etc. Besides, predicting the target’s location of the next time instance is unwise because of the quite a lot random factors. In this paper, we propose a novel target tracking approach without any predicting, called k-nearest neighbors tracking (k-NNT), to tackle the problems of energy efficiency, continuity and coverage holes. In k-NNT, only the k-nearest neighbors keep active and track the target when more than k nodes can sense the target; the k′-nearest neighbors work when there are only k′ nodes (k′ < k) can sense the target. A sophisticated rotation mechanism is designed to improve the continuity of the tracking process. In the worst case, none of the nodes can sense the target, i.e., the target enters into the coverage holes, and then k-NNT recovers by the Round Up mode (RU mode). The nodes on the perimeter of the coverage hole always keep active for a time threshold t and sense the around environment to find the target in time. Once a node finds the target, the RU mode is over and the irrelevant nodes turn into inactive mode. A series of simulation show that k-NNT performs superiorly compared with several existing approaches in terms of tracking accuracy, continuity and energy efficiency.     

Protecting query privacy with differentially private <Emphasis Type="Italic">k</Emphasis>-anonymity in location-based services

Nowadays, location-based services (LBS) are facilitating people in daily life through answering LBS queries. However, privacy issues including location privacy and query privacy arise at the same time. Existing works for protecting query privacy either work on trusted servers or fail to provide sufficient privacy guarantee. This paper combines the concepts of differential privacy and k-anonymity to propose the notion of differentially private k-anonymity (DPkA) for query privacy in LBS. We recognize the sufficient and necessary condition for the availability of 0-DPkA and present how to achieve it. For cases where 0-DPkA is not achievable, we propose an algorithm to achieve ??-DPkA with minimized ??. Extensive simulations are conducted to validate the proposed mechanisms based on real-life datasets and synthetic data distributions.     

An all-pair quantum SVM approach for big data multiclass classification

In this paper, we discuss a quantum approach for the all-pair multiclass classification problem. In an all-pair approach, there is one binary classification problem for each pair of classes, and so there are k(k???1)/2 classifiers for a k-class classification problem. As compared to the classical multiclass support vector machine that can be implemented with polynomial run time complexity, our approach exhibits exponential speedup due to quantum computing. The quantum all-pair algorithm can also be used with other classification algorithms, and a speedup gain can be achieved as compared to their classical counterparts.     

Learning safe multi-label prediction for weakly labeled data

In this paper we study multi-label learning with weakly labeled data, i.e., labels of training examples are incomplete, which commonly occurs in real applications, e.g., image classification, document categorization. This setting includes, e.g., (i) semi-supervised multi-label learning where completely labeled examples are partially known; (ii) weak label learning where relevant labels of examples are partially known; (iii) extended weak label learning where relevant and irrelevant labels of examples are partially known. Previous studies often expect that the learning method with the use of weakly labeled data will improve the performance, as more data are employed. This, however, is not always the cases in reality, i.e., weakly labeled data may sometimes degenerate the learning performance. It is desirable to learn safe multi-label prediction that will not hurt performance when weakly labeled data is involved in the learning procedure. In this work we optimize multi-label evaluation metrics (\(\hbox {F}_1\) score and Top-k precision) given that the ground-truth label assignment is realized by a convex combination of base multi-label learners. To cope with the infinite number of possible ground-truth label assignments, cutting-plane strategy is adopted to iteratively generate the most helpful label assignments. The whole optimization is cast as a series of simple linear programs in an efficient manner. Extensive experiments on three weakly labeled learning tasks, namely, (i) semi-supervised multi-label learning; (ii) weak label learning and (iii) extended weak label learning, clearly show that our proposal improves the safeness of using weakly labeled data compared with many state-of-the-art methods.     

Answering subgraph queries over massive disk resident graphs

Due to its wide applications, subgraph query has attracted lots of attentions in database community. In this paper, we focus on subgraph query over a single large graph G, i.e., finding all embeddings of query Q in G. Different from existing feature-based approaches, we map all edges into a two-dimensional space R ² and propose a bitmap structure to index R ². At run time, we find a set of adjacent edge pairs (AEP) or star-style patterns (SSP) to cover Q. We develop edge join (EJ) algorithms to address both AEP and SSP subqueries. Based on the bitmap index, our method can optimize I/O and CPU cost. More importantly, our index has the linear space complexity instead of exponential complexity in feature-based approaches, which indicates that our index can scale well with respect to large data size. Furthermore, our index has light maintenance overhead, which has not been considered in most of existing work. Extensive experiments show that our method significantly outperforms existing ones in both online and offline processing with respect to query response time, index building time, index size and index maintenance overhead.     

Improved Approximation Algorithm for k-level Uncapacitated Facility Location Problem (with Penalties)

We study the k-level uncapacitated facility location problem (k-level UFL) in which clients need to be connected with paths crossing open facilities of k types (levels). In this paper we first propose an approximation algorithm that for any constant k, in polynomial time, delivers solutions of cost at most α _k times OPT, where α _k is an increasing function of k, with \(\lim _{k\to \infty } \alpha _{k} = 3\). Our algorithm rounds a fractional solution to an extended LP formulation of the problem. The rounding builds upon the technique of iteratively rounding fractional solutions on trees (Garg, Konjevod, and Ravi SODA’98) originally used for the group Steiner tree problem. We improve the approximation ratio for k-level UFL for all k ≥ 3, in particular we obtain the ratio equal 2.02, 2.14, and 2.24 for k = 3,4, and 5.     

Sparse Support Vector Machine with <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Penalty for Feature Selection

We study the strategies in feature selection with sparse support vector machine (SVM). Recently, the socalled L _p -SVM (0 < p < 1) has attracted much attention because it can encourage better sparsity than the widely used L ₁-SVM. However, L _p -SVM is a non-convex and non-Lipschitz optimization problem. Solving this problem numerically is challenging. In this paper, we reformulate the L _p -SVM into an optimization model with linear objective function and smooth constraints (LOSC-SVM) so that it can be solved by numerical methods for smooth constrained optimization. Our numerical experiments on artificial datasets show that LOSC-SVM (0 < p < 1) can improve the classification performance in both feature selection and classification by choosing a suitable parameter p. We also apply it to some real-life datasets and experimental results show that it is superior to L ₁-SVM.     

Asymptotic assessments of CRC error probabilities in some telecommunication protocols

We study the value distributions for the control cyclic redundancy check (CRC) of length k, drawn at the data section of volume n. The behavior of CRC value distribution is examined at large n and fixed values of k (k = const, n → ∞). With the application of the character theory, we find the conditions of asymptomatic uniformity of the CRC distribution. The asymptomatic results can be applied during the assessment of errors of a series of protocols such as USB, X.25, HDLC, Bluetooth, Ethernet, etc.     

Remark on balanced incomplete block designs,near-resolvable block designs,and <Emphasis Type="Italic">q</Emphasis>-ary constant-weight codes

We prove that any balanced incomplete block design B(v, k, 1) generates a nearresolvable balanced incomplete block design NRB(v, k ? 1, k ? 2). We establish a one-to-one correspondence between near-resolvable block designs NRB(v, k ?1, k ?2) and the subclass of nonbinary (optimal, equidistant) constant-weight codes meeting the generalized Johnson bound.     

A novel weighting scheme for random k-SAT关于随机 k-SAT 的新加权方法

Consider a random k-conjunctive normal form F_k(n, rn) with n variables and rn clauses. We prove that if the probability that the formula F_k(n, rn) is satisfiable tends to 0 as n→∞, then r ? 2.83, 8.09, 18.91, 40.81, and 84.87, for k = 3, 4, 5, 6, and 7, respectively.     

On Fixed Cost k-Flow Problems

In the Fixed Cost k-Flow problem, we are given a graph G = (V, E) with edge-capacities {u _e ∣e ∈ E} and edge-costs {c _e ∣e ∈ E}, source-sink pair s, t ∈ V, and an integer k. The goal is to find a minimum cost subgraph H of G such that the minimum capacity of an st-cut in H is at least k. By an approximation-preserving reduction from Group Steiner Tree problem to Fixed Cost k-Flow, we obtain the first polylogarithmic lower bound for the problem; this also implies the first non-constant lower bounds for the Capacitated Steiner Network and Capacitated Multicommodity Flow problems. We then consider two special cases of Fixed Cost k-Flow. In the Bipartite Fixed-Cost k-Flow problem, we are given a bipartite graph G = (A ∪ B, E) and an integer k > 0. The goal is to find a node subset S ? A ∪ B of minimum size |S| such G has k pairwise edge-disjoint paths between S ∩ A and S ∩ B. We give an \(O(\sqrt {k\log k})\) approximation for this problem. We also show that we can compute a solution of optimum size with Ω(k/polylog(n)) paths, where n = |A| + |B|. In the Generalized-P2P problem we are given an undirected graph G = (V, E) with edge-costs and integer charges {b _v : v ∈ V}. The goal is to find a minimum-cost spanning subgraph H of G such that every connected component of H has non-negative charge. This problem originated in a practical project for shift design [11]. Besides that, it generalizes many problems such as Steiner Forest, k-Steiner Tree, and Point to Point Connection. We give a logarithmic approximation algorithm for this problem. Finally, we consider a related problem called Connected Rent or Buy Multicommodity Flow and give a log^3+?? n approximation scheme for it using Group Steiner Tree techniques.     

Efficient distance-based representative skyline computation in 2D space

Representative skyline computation is a fundamental issue in database area, which has attracted much attention in recent years. A notable definition of representative skyline is the distance-based representative skyline (DBRS). Given an integer k, a DBRS includes k representative skyline points that aims at minimizing the maximal distance between a non-representative skyline point and its nearest representative. In the 2D space, the state-of-the-art algorithm to compute the DBRS is based on dynamic programming (DP) which takes O(k m ²) time complexity, where m is the number of skyline points. Clearly, such a DP-based algorithm cannot be used for handling large scale datasets due to the quadratic time cost. To overcome this problem, in this paper, we propose a new approximate algorithm called ARS, and a new exact algorithm named PSRS, based on a carefully-designed parametric search technique. We show that the ARS algorithm can guarantee a solution that is at most ?? larger than the optimal solution. The proposed ARS and PSRS algorithms run in O(klog2mlog(T/??)) and O(k ² log3m) time respectively, where T is no more than the maximal distance between any two skyline points. We also propose an improved exact algorithm, called PSRS+, based on an effective lower and upper bounding technique. We conduct extensive experimental studies over both synthetic and real-world datasets, and the results demonstrate the efficiency and effectiveness of the proposed algorithms.