A regression model based on the nearest centroid neighborhood

The renowned k-nearest neighbor decision rule is widely used for classification tasks, where the label of any new sample is estimated based on a similarity criterion defined by an appropriate distance function. It has also been used successfully for regression problems where the purpose is to predict a continuous numeric label. However, some alternative neighborhood definitions, such as the surrounding neighborhood, have considered that the neighbors should fulfill not only the proximity property, but also a spatial location criterion. In this paper, we explore the use of the k-nearest centroid neighbor rule, which is based on the concept of surrounding neighborhood, for regression problems. Two support vector regression models were executed as reference. Experimentation over a wide collection of real-world data sets and using fifteen odd different values of k demonstrates that the regression algorithm based on the surrounding neighborhood significantly outperforms the traditional k-nearest neighborhood method and also a support vector regression model with a RBF kernel.     

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.     

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.     

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.     

Estimation of the influence of information class coverage on generalized ability of the <Emphasis Type="Italic">k</Emphasis>-nearest-neighbors classifier

In this paper an approach that provides an estimate of the influence of decreasing sizes of database classes on a recognition rate when the k-nearest-neighbors classifiers are in use is proposed. The approach also ensures the feasibility of identifying an optimal number k of the nearest neighbors on a given set.     

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.     

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.     

Participant selection for <Emphasis Type="Italic">t</Emphasis>-sweep <Emphasis Type="Italic">k</Emphasis>-coverage crowd sensing tasks

With the popularization of wireless networks and mobile intelligent terminals, mobile crowd sensing is becoming a promising sensing paradigm. Tasks are assigned to users with mobile devices, which then collect and submit ambient information to the server. The composition of participants greatly determines the quality and cost of the collected information. This paper aims to select fewest participants to achieve the quality required by a sensing task. The requirement namely “t-sweep k-coverage” means for a target location, every t time interval should at least k participants sense. The participant selection problem for “t-sweep k-coverage” crowd sensing tasks is NP-hard. Through delicate matrix stacking, linear programming can be adopted to solve the problem when it is in small size. We further propose a participant selection method based on greedy strategy. The two methods are evaluated through simulated experiments using users’ call detail records. The results show that for small problems, both the two methods can find a participant set meeting the requirement. The number of participants picked by the greedy based method is roughly twice of the linear programming based method. However, when problems become larger, the linear programming based method performs unstably, while the greedy based method can still output a reasonable solution.     

Mutually independent Hamiltonian cycles in dual-cubes

The hypercube family Q _n is one of the most well-known interconnection networks in parallel computers. With Q _n , dual-cube networks, denoted by DC _n , was introduced and shown to be a (n+1)-regular, vertex symmetric graph with some fault-tolerant Hamiltonian properties. In addition, DC _n ’s are shown to be superior to Q _n ’s in many aspects. In this article, we will prove that the n-dimensional dual-cube DC _n contains n+1 mutually independent Hamiltonian cycles for n≥2. More specifically, let v _i ∈V(DC _n ) for 0≤i≤|V(DC _n )|?1 and let \(\langle v_{0},v_{1},\ldots ,v_{|V(\mathit{DC}_{n})|-1},v_{0}\rangle\) be a Hamiltonian cycle of DC _n . We prove that DC _n contains n+1 Hamiltonian cycles of the form \(\langle v_{0},v_{1}^{k},\ldots,v_{|V(\mathit{DC}_{n})|-1}^{k},v_{0}\rangle\) for 0≤k≤n, in which v _i ^k ≠v _i ^k′ whenever k≠k′. The result is optimal since each vertex of DC _n has only n+1 neighbors.     

Diversified top-<Emphasis Type="Italic">k</Emphasis> clique search

Maximal clique enumeration is a fundamental problem in graph theory and has been extensively studied. However, maximal clique enumeration is time-consuming in large graphs and always returns enormous cliques with large overlaps. Motivated by this, in this paper, we study the diversified top-k clique search problem which is to find top-k cliques that can cover most number of nodes in the graph. Diversified top-k clique search can be widely used in a lot of applications including community search, motif discovery, and anomaly detection in large graphs. A naive solution for diversified top-k clique search is to keep all maximal cliques in memory and then find k of them that cover most nodes in the graph by using the approximate greedy max k-cover algorithm. However, such a solution is impractical when the graph is large. In this paper, instead of keeping all maximal cliques in memory, we devise an algorithm to maintain k candidates in the process of maximal clique enumeration. Our algorithm has limited memory footprint and can achieve a guaranteed approximation ratio. We also introduce a novel light-weight \(\mathsf {PNP}\)-\(\mathsf {Index}\), based on which we design an optimal maximal clique maintenance algorithm. We further explore three optimization strategies to avoid enumerating all maximal cliques and thus largely reduce the computational cost. Besides, for the massive input graph, we develop an I/O efficient algorithm to tackle the problem when the input graph cannot fit in main memory. We conduct extensive performance studies on real graphs and synthetic graphs. One of the real graphs contains 1.02 billion edges. The results demonstrate the high efficiency and effectiveness of our approach.     

Making Doubling Metrics Geodesic

The starting point of our research is the following problem: given a doubling metric ?=(V,d), can one (efficiently) find an unweighted graph G′=(V′,E′) with V?V′ whose shortest-path metric d′ is still doubling, and which agrees with d on V×V? While it is simple to show that the answer to the above question is negative if distances must be preserved exactly. However, allowing a (1+ε) distortion between d and d′ enables us bypass this hurdle, and obtain an unweighted graph G′ with doubling dimension at most a factor O(log?ε ^?1) times the doubling dimension of G.More generally, this paper gives algorithms that construct graphs G′ whose convex (or geodesic) closure has doubling dimension close to that of ?, and the shortest-path distances in G′ closely approximate those of ? when restricted to V×V. Similar results are shown when the metric ? is an additive (tree) metric and the graph G′ is restricted to be a tree.     

On the <Emphasis Type="Italic">k</Emphasis>-accessibility of cores of <Emphasis Type="Italic">TU</Emphasis>-cooperative games

This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α _v ) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x₀, x₁,..., such that x₀ = x, lim x _r ∈ C(α _v ) and x_r?m is dominated by any successive imputation x _r with m ∈ [1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ? G(N) of dominated imputations that contains all the α _G -monotonic sequential improvement trajectories originating at any point x ∈ B.     

Bionic knowledge and information reuse methodology for uncertainty minimization in product design

Given two spatial point sets R and B in the plane, with cardinalities m and n, respectively, and stored in two separate R-trees, we propose an efficient algorithm to verify whether R and B are linearly separable. The sets R and B are linearly separable if there exists a line that splits the plane into to halfplanes, one containing all R and the other one containing all B. This is the first algorithm that answers the separability question in the context of the spatial data bases. That is, it considers as input big spatial data stored in secondary storage data structures (e.g., the R-tree) which are not allowed to be completely stored in the main memory of the computer to run a classic algorithm. The algorithms designed in this context aim to minimize as much as possible the number of blocks read from the secondary storage data structures to the main memory. Studied problems in this setting are the k-nearest neighbor problem and the spatial range query problem. Our algorithm explicitly exploits the geometric and spatial properties of the R-trees to access only the nodes relevant to decide the linear separability of the given sets. Our experimental results show the efficiency of the algorithm, since it accesses between the 0.34 and 2.79% of the nodes of the R-trees. We also analyze the asymptotic running time of the algorithm, showing that it runs in \(O(m\log m + n\log n)\) time in the worst case.     

Bounded Unpopularity Matchings

We investigate the following problem: given a set of jobs and a set of people with preferences over the jobs, what is the optimal way of matching people to jobs? Here we consider the notion of popularity. A matching M is popular if there is no matching M′ such that more people prefer M′ to M than the other way around. Determining whether a given instance admits a popular matching and, if so, finding one, was studied by Abraham et al. (SIAM J. Comput. 37(4):1030–1045, 2007). If there is no popular matching, a reasonable substitute is a matching whose unpopularity is bounded. We consider two measures of unpopularity—unpopularity factor denoted by u(M) and unpopularity margin denoted by g(M). McCutchen recently showed that computing a matching M with the minimum value of u(M) or g(M) is NP-hard, and that if G does not admit a popular matching, then we have u(M)≥2 for all matchings M in G.Here we show that a matching M that achieves u(M)=2 can be computed in \(O(m\sqrt{n})\) time (where m is the number of edges in G and n is the number of nodes) provided a certain graph H admits a matching that matches all people. We also describe a sequence of graphs: H=H ₂,H ₃,…,H _k such that if H _k admits a matching that matches all people, then we can compute in \(O(km\sqrt{n})\) time a matching M such that u(M)≤k?1 and \(g(M)\le n(1-\frac{2}{k})\). Simulation results suggest that our algorithm finds a matching with low unpopularity in random instances.     

Pseudo-Randomness of Certain Sequences of <Emphasis Type="Italic">k</Emphasis> Symbols with Length <Emphasis Type="Italic">pq</Emphasis>

The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sárközy and later extended to sequences of k symbols (or k-ary sequences). Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.     

Monochromatic and bichromatic ranked reverse boolean spatial keyword nearest neighbors search

Recently, Reverse k Nearest Neighbors (RkNN) queries, returning every answer for which the query is one of its k nearest neighbors, have been extensively studied on the database research community. But the RkNN query cannot retrieve spatio-textual objects which are described by their spatial location and a set of keywords. Therefore, researchers proposed a RSTkNN query to find these objects, taking both spatial and textual similarity into consideration. However, the RSTkNN query cannot control the size of answer set and to be sorted according to the degree of influence on the query. In this paper, we propose a new problem Ranked Reverse Boolean Spatial Keyword Nearest Neighbors query called Ranked-RBSKNN query, which considers both spatial similarity and textual relevance, and returns t answers with most degree of influence. We propose a separate index and a hybrid index to process such queries efficiently. Experimental results on different real-world and synthetic datasets show that our approaches achieve better performance.     

On transitive partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into codes

We present methods to construct transitive partitions of the set E ⁿ of all binary vectors of length n into codes. In particular, we show that for all n = 2 ^k ? 1, k ≥ 3, there exist transitive partitions of E ⁿ into perfect transitive codes of length n.     

Cost-Based Target Selection Techniques Towards Full Space Exploration and Coverage for USAR Applications in a Priori Unknown Environments

Full coverage and exploration of an environment is essential in robot rescue operations where victim identification is required. Three methods of target selection towards full exploration and coverage of an unknown space oriented for Urban Search and Rescue (USAR) applications have been developed. These are the Selection of the closest topological node, the Selection of the minimum cost topological node and the Selection of the minimum cost sub-graph. All methods employ a topological graph extracted from the Generalized Voronoi Diagram (GVD), in order to select the next best target during exploration. The first method utilizes a distance metric for determining the next best target whereas the Selection of the minimum cost topological node method assigns four different weights on the graph’s nodes, based on certain environmental attributes. The Selection of the minimum cost sub-graph uses a similar technique, but instead of single nodes, sets of graph nodes are examined. In addition, a modification of A* algorithm for biased path creation towards uncovered areas, aiming at a faster spatial coverage, is introduced. The proposed methods’ performance is verified by experiments conducted in two heterogeneous simulated environments. Finally, the results are compared with two common exploration methods.     

The Number of Tree Stars Is <Emphasis Type="Italic">O</Emphasis><Superscript>*</Superscript>(1.357<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>)

Every rectilinear Steiner tree problem admits an optimal tree T ^* which is composed of tree stars. Moreover, the currently fastest algorithms for the rectilinear Steiner tree problem proceed by composing an optimum tree T ^* from tree star components in the cheapest way. The efficiency of such algorithms depends heavily on the number of tree stars (candidate components). Fößmeier and Kaufmann (Algorithmica 26, 68–99, 2000) showed that any problem instance with k terminals has a number of tree stars in between 1.32 ^k and 1.38 ^k (modulo polynomial factors) in the worst case. We determine the exact bound O ^*(ρ ^k ) where ρ≈1.357 and mention some consequences of this result.