Neighborhood Sequences Research Articles

Biometric identity recognition based on contrastive positive-unlabeled learning

With the development of neural networks, identity recognition techniques utilizing human physiological signals have found applications in healthcare systems. However, many current physiological signal datasets have to spend a lot of resources in the pre-labeling phase, which leads to longer training times. To reduce the cost of labeling, we propose a self-supervised time-series representation learning framework based on contrastive positive-unlabeled learning (TS − CPUL), to learn the representations of temporal neighborhood sequences. To obtain the representations, the unit root test divides the unlabeled time series into neighborhood samples and unlabeled samples. Secondly, we use neighborhood sample representations and unlabeled sample representations to do self-supervised contrastive learning and positive-unlabeled learning with a negative sample selector. Both approaches can deepen the model’s understanding of the sample representation. Lastly, to enhance the model’s capability in discriminating between ambiguous sample pairs, we design the distance-polarized matrix. The proposed TS-CPUL is evaluated through experiments on three physiological signal datasets. The results demonstrate its effectiveness in understanding time-series representations and performing well in classification. For the identity recognition task, we achieve accuracy comparable to the supervised model by fine-tuning the model with only 10% of the labeled data.

Grundy Total Hop Dominating Sequences in Graphs

Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) \Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy total hop domination number of a graph G is between the total hop domination number and twice the Grundy hop domination number of G. Moreover, determine values or bounds of the Grundy total hop domination number of some graphs.

Distribution of number of observations required to obtain a cover for the support of a uniform distribution

For a given positive number ‘δ′, we consider a sequence of δ − neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U ( 0 , 1 ) distribution, and “stop as soon as their union contains the interval ( 0 , 1 ) . ” We call such a union “a cover.” To find the distributions of N ( δ ) , the stopping time random variable, we need the joint distribution of order statistics from a U ( 0 , 1 ) distribution. For each δ > 0 and n = 1 , 2 , … , we obtain a general expression for P ( N ( δ ) ≤ n ) , and for a fixed value of δ , it is the distribution function of N ( δ ) . For a given n, let Δ ( n ) be the minimum value of δ , so that the union of the n δ − neighborhoods of the first n observations contains the interval ( 0 , 1 ) . Because N ( δ ) ≤ n if and only if Δ ( n ) ≤ δ , the distributions of Δ ( n ) can be obtained by fixing n in the general expression for P ( N ( δ ) ≤ n ) . To describe the impact of δ on the distribution of N ( δ ) and that of n on Δ ( n ) , we sketch the graphs of distribution functions and the empirical distribution functions.

Equivalence, Partial Order and Lattice of Neighborhood Sequences on the Triangular Grid

In (digital) grids, neighbor relation is a crucial concept; digital distances are based on paths through neighbor points. Digital distances are significant, e.g., in digital image processing for giving an approximation of the Euclidean distance and allowing incremental algorithms on images. Neighborhood sequences (i.e., infinite sequences of the possible types of neighbors) are defining digital distances with a lower rotational dependency than the distances based only on a sole neighborhood. They allow one to change the used neighborhood condition in every step along a path. They are defined in various grids, and they can be periodic. Generalized neighborhood sequences do not need to be periodic. In this paper, the triangular grid is studied. An equivalence and two partial order relations on the set of generalized and periodic neighborhood sequences are shown on this grid. The first partial order, the “faster” relation, is based on distances defined by neighborhood sequences, and it does not provide a lattice but gives a relatively complex relation for neighborhood sequences with a short period. The other partial order, the relation “componentwise dominate”, defines a complete distributive lattice on the set of generalized neighborhood sequences. Finally, a relation of the above-mentioned relations is established. Important differences regarding the cases of the square and triangular grids are also highlighted.

Grundy Hop Domination in Graphs

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. Let S = (v1, v2, · · · , vk) be a sequence of distinct vertices of G and let Sˆ = {v1, v2, . . . , vk}. Then S is a legal closed hop neighborhood sequence of G if N2 G[vi]\∪i−1j=1N 2 G[vj ] ̸= ∅ for each i ∈ {2, · · · , k}. If, in addition, Sˆ is a hop dominating set of G, then S is called a Grundy hop dominating sequence.The maximum length of a Grundy hop dominating sequence in a graph G, denoted by γ hgr(G), is called the Grundy hop domination number of G. In this paper, we determine some (extreme) values for the Grundy hop domination number. It is pointed out that the Grundy hop domination number is at least equal to the hop domination. Bounds for the Grundy hop domination numbersof some graphs resulting from some binary operations of two graphs are also obtained.

A Multiobjective Variable Neighborhood Search with Learning and Swarm for Permutation Flowshop Scheduling with Sequence-Dependent Setup Times

In recent years, the permutation flowshop scheduling problem (PFSP) with sequence-dependent setup times has been widely investigated in the literature, most focusing on the single-objective optimization problem. However, in a practical production environment, schedulers usually need to handle several conflicting objectives simultaneously, which makes the multiobjective PFSP with sequence-dependent setup times (MOPFSP-SDST) more difficult and time consuming to be solved. Therefore, this paper proposes a learning and swarm based multiobjective variable neighborhood search (LS-MOVNS) for this problem to minimize makespan and total flowtime. The main characteristic of the proposed LS-MOVNS is that it can achieve the balance between exploration and exploitation by integrating swarm-based search with VNS in the multiobjective environment through machine learning technique. For example, the learning-based selection of solutions for multiobjective local search and the adaptive determination of neighborhood sequence to perform the local search are presented based on clustering and statistics to improve the search efficiency. Experimental results on benchmark problems illustrate that the proposed LS-MOVNS algorithm is very effective and competitive to solve MOPFSP-SDST.

Learning to Search in Local Branching

Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce improving solutions and has been highly influential for the development of local search methods in MILP. The algorithm iteratively explores a sequence of solution neighborhoods defined by the so-called local branching constraint, namely, a linear inequality limiting the distance from a reference solution. For a LB algorithm, the choice of the neighborhood size is critical to performance. Although it was initialized by a conservative value in the original LB scheme, our new observation is that the "best" size is strongly dependent on the particular MILP instance. In this work, we investigate the relation between the size of the search neighborhood and the behavior of the underlying LB algorithm, and we devise a leaning-based framework for guiding the neighborhood search of the LB heuristic. The framework consists of a two-phase strategy. For the first phase, a scaled regression model is trained to predict the size of the LB neighborhood at the first iteration through a regression task. In the second phase, we leverage reinforcement learning and devise a reinforced neighborhood search strategy to dynamically adapt the size at the subsequent iterations. We computationally show that the neighborhood size can indeed be learned, leading to improved performances and that the overall algorithm generalizes well both with respect to the instance size and, remarkably, across instances.

Graph Substructure Assembling Network with Soft Sequence and Context Attention

There has been a surge of researchers' interest in building predictive models over graphs. However, the overwhelming complexity of graph space often makes it challenging to extract interpretable and discriminative structural features for graph classification. In this work, we propose a new graph neural network model called Substructure Assembling Network (SAN) to learn graph representations for classification. The key innovation is a unified Substructure Assembling Unit (SAU), which is a variant of Recurrent Neural Network (RNN) designed to hierarchically assemble useful pieces of graph components so as to fabricate discriminative substructures. A key challenge is that SAUs need to process the neighbors of a node sequentially while no natural order is defined therein. SAN tries to make the model insensitive to neighborhood orders by randomly shuffling neighborhood sequences in training. However, this could suffer high variance, especially when the neighborhood size is large. Hence, we further propose to equip SAN with a novel module named Soft Sequence with Context Attention (SSCA). SAN-SSCA employs the proposed context attention technique to learn the best "soft" permutation of the neighbors w.r.t. classification. It helps the model achieve higher accuracy as well as lower variance. Experiments confirm the effectiveness of SAN-SSCA.

A method for finding least‐cost corridors in three‐dimensional raster space

AbstractOptimal routing of a path with a constant width in a two‐dimensional grid of cost‐weighted square cells or pixels is a recent extension of the least‐cost path problem, and models and solutions are available and ready to be integrated into raster‐based geographic information systems. In this article we consider yet another variation of this problem in a three‐dimensional grid of cost‐weighted cubic cells or voxels, which is to find a tubular region of voxels with a constant width, referred to here as “corridor,” connecting two termini while accumulating the least amount of cost. We model a corridor as a sequence of sets of voxels, called “neighborhoods,” that are arranged in a 26‐hedral form, design a heuristic method to find a sequence of such neighborhoods that sweeps the minimum cost‐weighted volume, and test its performance with computer‐generated random data. Results show that the method finds a low‐cost, if not least‐cost, corridor with a specified width in a three‐dimensional cost grid and has a reasonable efficiency as its complexity is O(n2), where n is the number of voxels in the input cost grid and is independent of corridor width. A major drawback is that the corridor found may self‐intersect, which often not only is an undesirable quality but also makes the estimation of its cost‐weighted volume inaccurate.

Uniform Length Dominating Sequence Graphs

A sequence of vertices $(v_1,\, \dots , \,v_k)$ of a graph $G$ is called a {\it dominating closed neighborhood sequence} if $\{v_1,\, \dots , \,v_k\}$ is a dominating set of $G$ and $N[v_i]\nsubseteq \cup _{j=1}^{i-1} N[v_j]$ for every $i$. A graph $G$ is said to be {\it $k-$uniform} if all dominating closed neighborhood sequences have equal length $k$. Bre{\v s}ar et al. (2014) characterized $k$-uniform graphs with $k\leq 3$. In this article we extend their work by giving a complete characterization of all $k$-uniform graphs with $k\geq 4$.

Sensitivity of sequence methods in the study of neighborhood change in the United States

There is a recent surge in research focused on urban transformations in the United States via empirical analysis of neighborhood sequences. The alignment-based sequence analysis methods have seen many applications in urban neighborhood change research. However, it is unclear to what extent these methods are robust in terms of producing consistent and converging neighborhood sequence typologies. This article sheds light on this issue by applying four sequence analysis methods to the same data set – 50 largest Metropolitan Statistical Areas (MSAs) of the United States from 1970 to 2010, and finds that these methods do not provide converging neighborhood sequence typologies, and their behavior varies across MSAs, thus prohibiting meaningful comparisons of similar studies. MSAs with higher average household income in 1970 tend to be less sensitive to the choice of the SA methods. In other words, when investigating neighborhood change in these MSAs, different SA methods tend to produce a more converging neighborhood sequence typology. Comparatively, for MSAs hosting neighborhoods which have experienced frequent changes during the period 1970–2010, they are less likely to produce similar typologies with different SA methods. In addition, there is a big difference in the neighborhood sequence typology between applying the classic SA methods with varying costs and using the SA variant focusing on the second-order sequence property. After comparing the behavior of these methods, we highlight one method (“OMecenter”) which leverages the socioeconomic similarities of neighborhoods and suggest researchers consider it as the building block towards designing a meaningful sequence analysis method for neighborhood change research.

Efficient distance transformation for path-based metrics

In many applications, separable algorithms have demonstrated their efficiency to perform high performance volumetric processing of shape, such as distance transformation or medial axis extraction. In the literature, several authors have discussed about conditions on the metric to be considered in a separable approach. In this article, we present generic separable algorithms to efficiently compute Voronoi maps and distance transformations for a large class of metrics. Focusing on path-based norms (chamfer masks, neighborhood sequences), we propose efficient algorithms to compute such volumetric transformation in dimension n. We describe a new O(n⋅Nn⋅logN⋅(n+logf)) algorithm for shapes in a Nn domain for chamfer norms with a rational ball of f facets (compared to O(f⌊n2⌋⋅Nn) with previous approaches). Last we further investigate a more elaborate algorithm with the same worst-case complexity, but reaching a complexity of O(n⋅Nn⋅logf⋅(n+logf)) experimentally, under assumption of regularity distribution of the mask vectors.

On the number of shortest paths by neighborhood sequences on the square grid

On the number of shortest paths by neighborhood sequences on the square grid

Generalised distances of sequences II: B-distances with weight sequences

In this paper, we investigate the weighted B-distances of infinite sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Zn), and the theory was recently extended for application to sequences. By assigning various weights to the elements of the sequences the concept is further generalized. An algorithm is presented which provides a shortest path between two sequences. Formula is also provided to calculate the weighted B-distance of any two sequences with a neighbourhood sequence B and a weight sequence. There are several neighbourhood sequences, which do not generate metrics. We prove a necessary and sufficient condition for a B-distance to define a generalized metric space above the sequences. Moreover, our results can be applied if the elements of the sequences used with various weights. In case of weight functions used B-distances we present also the metric conditions.

A Heterogeneous Graph Embedding Framework for Location-Based Social Network Analysis in Smart Cities

In recent years, with the advancement of wireless communication and location acquisition technology in the context of modern smart cities, and the increasing popularity of mobile devices with location capabilities based on Social Internet of Things, we can now easily introduce location services into traditional social networks. How to effectively use these massive data to provide decision support for smart cities is an emerging task. It is necessary to find an efficient way to effectively extract and represent useful information from location-based social networks (LBSNs) by dealing with the data heterogeneity. Against this background, this article proposes a heterogeneous graph embedding framework for LBSN analysis named location based social network embedding (LBSNE). LBSNE framework first constructs the heterogeneous neighborhood of a node by formalizing a metapath-based random walk on LBSNs. Then, it leverages the learned heterogeneous neighborhood sequence to do network embedding by employing a heterogeneous skip-gram model. The effectiveness of the proposed model is evaluated on the tasks of location recommendation and visitor predict on two LBSN datasets.

Distance Functions Based on Multiple Types of Weighted Steps Combined with Neighborhood Sequences

In this paper, we present a general framework for digital distance functions, defined as minimal cost paths, on the square grid. Each path is a sequence of pixels, where any two consecutive pixels are adjacent and associated with a weight. The allowed weights between any two adjacent pixels along a path are given by a weight sequence, which can hold an arbitrary number of weights. We build on our previous results, where only two or three unique weights are considered, and present a framework that allows any number of weights. We show that the rotational dependency can be very low when as few as three or four unique weights are used. Moreover, by using n weights, the Euclidean distance can be perfectly obtained on the perimeter of a square with side length 2n. A sufficient condition for weight sequences to provide metrics is proven.

Grundy dominating sequences and zero forcing sets

If G is a graph, then a sequence v1,…,vm of vertices is a closed neighborhood sequence if for all 2≤i≤m we have N[vi]⁄⊆∪j=1i−1N[vj], and it is an open neighborhood sequence if for all 2≤i≤m we have N(vi)⁄⊆∪j=1i−1N(vj). The length of a longest closed (open) neighborhood sequence is the Grundy (Grundy total) domination number of G. In this paper we introduce two similar concepts in which the requirement on the neighborhoods is changed to N(vi)⁄⊆∪j=1i−1N[vj] or N[vi]⁄⊆∪j=1i−1N(vj). In the former case we establish a strong connection to the zero forcing number of a graph, while we determine the complexity of the decision problem in the latter case. We also study the relationships among the four concepts, and discuss their computational complexities.

Memetic algorithm based on sequential variable neighborhood descent for the minmax multiple traveling salesman problem

In this paper, we consider the multiple traveling salesman problem (MTSP) with the minmax objective, which includes more than one salesman to serve a set of cities while minimizing the maximum distance traveled by any salesman. For this problem, we have proposed a novel memetic algorithm, which integrates with a sequential variable neighborhood descent that is a powerful local search procedure to exhaustively search the areas near the high-quality solutions. However, there are some inefficient neighborhoods in the existing sequential variable neighborhood descent for the minmax MTSP, which could restrict the search performance. Therefore, we have redefined a new neighborhood sequence where only the neighborhoods that move cities from one tour to another unidirectionally are considered. Computational experiments on a wide range of benchmark problems within an acceptable time limit show that compared with six existing algorithms, the proposed algorithm is better than the other algorithms in terms of three aspects, including the precision, the robustness and the convergence speed. Meanwhile, we have also investigated the total distance traveled by all the salesmen when optimizing the minmax objective, and the results show that in comparison with the six existing algorithms, the proposed algorithm has a better or at least competitive capacity to maintain the total distance as short as possible. Furthermore, two kinds of statistical tests are utilized to examine the significance of the presented results, indicating the superiority of the proposed algorithm over the other algorithms on the minmax objective.

Error analysis of octagonal distances defined by periodic neighborhood sequences for approximating Euclidean metrics in arbitrary dimension

In this paper, we consider approximation of Euclidean metrics by octagonal distances defined by periodic neighborhood sequences in arbitrary dimension. We derive an expression for maximum relative error (MRE) of an octagonal distance approximated by a weighted t-cost distance (WtD) function, with respect to the Euclidean metric in n-dimensional space. For this, we have used a general expression of MRE reported previously for a class of distances, in the form of a linear combination of weighted t-cost (WtD) and weighted (or chamfering) distances (CWD) and derived the expressions for specific cases of WtDs and CWDs. Further, this has also been applied to obtain theoretical expressions of MRE for m-neighbor distances (mND) in arbitrary dimension, and it improves the previously reported results regarding optimum value of m in an n-dimensional space. We also considered the adjustment of MRE values choosing an optimum scale factor. Computing theoretical values of scale adjusted MRE, we have reported good octagonal distances for approximating Euclidean metrics in different dimensional spaces. Previously, only a few such distances were reported for 2-D and 3-D spaces.

Heuristic Search Algorithm for the Single-row Machine Layout in an Automated Manufacturing System

Machine lay out is one of the important factors that affects material handling time, manufacturing time and cost. In this work, design of manufacturing facilities is made with the consideration of repeat operations at the same manufacturing facility, in sequence moments. There are six flow-line analysis methods reported in the literature. Among these six methods, two best methods are considered in this paper. They are Flow Line Analysis (FLA)-5 for bidirectional flow lines and Flow Line Analysis-6 for unidirectional flow lines. A random insertion perturbation scheme is used to find out neighborhood sequences from a seed sequence. The seed sequences are found from the FLA 5 and 6 methods. A hybrid search algorithm is proposed by combining FLA-5 and 6 with Simulated Annealing algorithm to find out optimum machine layout with less material handling time. Twenty five sets of data are created and tested with the proposed algorithm.