The planar hub location problem: a probabilistic clustering approach

Given the demand between each origin-destination pair on a network, the planar hub location problem is to locate the multiple hubs anywhere on the plane and to assign the traffic to them so as to minimize the total travelling cost. The trips between any two points can be nonstop (no hubs used) or started by visiting any of the hubs. The travel cost between hubs is discounted with a factor. It is assumed that each point can be served by multiple hubs. We propose a probabilistic clustering method for the planar hub-location problem which is analogous to the method of Iyigun and Ben-Israel (in Operations Research Letters 38, 207–214, 2010; Computational Optmization and Applications, 2013) for the solution of the multi-facility location problem. The proposed method is an iterative probabilistic approach assuming that all trips can be taken with probabilities that depend on the travel costs based on the hub locations. Each hub location is the convex combination of all data points and other hubs. The probabilities are updated at each iteration together with the hub locations. Computations stop when the hub locations stop moving. Fermat-Weber problem and multi-facility location problem are the special cases of the proposed approach.     

A new probabilistic fuzzy model: Fuzzification–Maximization (FM) approach

Over the past few decades, fuzzy logic systems have been used for nonlinear modeling and approximation in many fields ranging from engineering to science. In this paper, a new fuzzy model is developed from the probabilistic and statistical point of view. The proposed model decomposes the input–output characteristics into noise-free part and probabilistic noise part and identifies them simultaneously. The noise-free model recovers the nominal input–output characteristics of the target system and the noise model gives approximation to the probabilistic nature of the added noise. To identify the two submodels simultaneously, we propose the Fuzzification–Maximization (FM). Finally, some simulations are conducted and the effectiveness of the proposed method is demonstrated through the comparison with the previous methods.     

On a new naturally indexed quick clustering method with a global objective function

A new clustering method is presented which proposes a class of objective functions and an algorithm which sub-optimizes the objective functions over the whole space of partitions. The objective functions have a global nature, encompassing both the cluster contents and the cluster number. However, the accompanying suboptimization algorithm works according to a simple progressive merger scheme. The algorithmic scheme produces in a quite natural way an indexed hierarchy. The hierarchy index is not just tacked on to the method—see Diday and Moreau¹—on the contrary, the algorithm refers directly to its values which measure, depending upon the particular formulation, either the relative affinity or the relative difference of the two clusters merged at a given level of hierarchy. In this way, the scale of hierarchy and hierarchy-wise validity of clusters can easily be established, which is of great importance in analysing unstructured data sets whose generating process is unknown and can only be hypothesized after an initial structure had been established, e.g. owing to clustering, as is the case in pattern recognition—see Kaminuma².     

A new learning strategy for stereo matching derived from a fuzzy clustering method

This paper presents an approach to the local stereo correspondence problem. The primitives or features used are groups of collinear connected edge points called segments. Each segment has several associated attributes or properties. We have verified that the differences of the attributes for the true matches cluster in a cloud around a center. Then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center. The correspondence is established in the basis of the minimum distance criterion (similarity constraint). We have designed an image understanding system to learn the best representative cluster center. For such purpose a new learning method is derived from the Fuzzy c-Means (FcM) algorithm where the dispersion of the true samples in the cluster is taken into account through the Mahalanobis distance. This is the main contribution of this paper. A better performance of the proposed local stereo-matching learning method is illustrated with a comparative analysis between classical local methods without learning.     

Locating a minisum annulus: a new partial coverage distance model

The problem is to find the best location in the plane of a minisum annulus with fixed width using a partial coverage distance model. Using the concept of partial coverage distance, those demand points within the area of the annulus are served at no cost, while for ‘uncovered’ demand points there will be additional costs proportional to their distances to the annulus. The objective of the problem is to locate the annulus such that the sum of distances from the uncovered demand points to the annulus (covering area) is minimized. The distance is measured by the Euclidean norm. We discuss the case where the radius of the inner circle of the annulus is variable, and prove that at least two demand points must be on the boundary of any optimal annulus. An algorithm to solve the problem is derived based on this result.     

The rectilinear distance Weber problem in the presence of a probabilistic line barrier

This paper considers the problem of locating a single facility in the presence of a line barrier that occurs randomly on a given horizontal route on the plane. The objective is to locate this new facility such that the sum of the expected rectilinear distances from the facility to the demand points in the presence of the probabilistic barrier is minimized. Some properties of the problem are reported, a solution algorithm is provided with an example problem, and some future extensions to the problem are discussed.     

Some properties for probabilistic and multinomial (probabilistic) values on cooperative games

We investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games.     

Fuzzy number linear programming: A probabilistic approach (3)

In the real world there are many linear programming problems where all decision parameters are fuzzy numbers. Several approaches exist which use different ranking functions for solving these problems. Unfortunately when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, these methods can not specify a clear approach for choosing a solution. In this paper we propose a method to remove the above shortcoming in solving fuzzy number linear programming problems using the concept of expectation and variance as ranking functions.     

On a new type of distance Fibonacci numbers

In this paper, we define a new kind of Fibonacci numbers generalized in the distance sense. This generalization is related to distance Fibonacci numbers and distance Lucas numbers, introduced quite recently. We also study distinct properties of these numbers for negative integers. Their representations and interpretations in graphs are also studied.     

Fusion (2D)PCALDA: A new method for face recognition

This paper proposes an efficient face representation and recognition method, which combines the both information between rows and those between columns from two-directional 2DPCA on fusion face image and the optimal discriminative information from column-directional 2DLDA. Experiment results on ORL and Yale face database demonstrate the effectiveness of the proposed method.     

求解Klein-Gordon-Schr(o)dinger方程组的一个新型守恒差分算法的收敛性分析

对复Schr(o)dinger场和实Klein-Gordon场相互作用下一类耦合方程组的初边值问题进行了数值研究,提出了一个高效差分格式,该格式非耦合且为半显格式,因此比隐格式具有更快的计算速度,而且便于并行计算;同时,该格式很好地模拟了初边值问题的守恒性质,保证了格式计算的可靠性,从而便于长时间计算.细致讨论了格式的守恒性质,并在先验估计的基础上运用能量方法分析了差分格式的收敛性.     

Implicational (semilinear) logics I: a new hierarchy

In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of logics expanding Leibniz hierarchy: the hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field.     

Euclidean distance matrices: new characterization and boundary properties

In this article we give a new characterization of Euclidean distance matrices using known necessary conditions. We also relate this characterization with the faces of the cone and give new properties for the boundary. Finally, a new characterization of spherical/non-spherical matrices is proposed.     

Adapted single-cell consensus clustering (adaSC3)

Advances in Data Analysis and Classification - The analysis of single-cell RNA sequencing data is of great importance in health research. It challenges data scientists, but has enormous potential...     

Mining categorical sequences from data using a hybrid clustering method

The identification of different dynamics in sequential data has become an every day need in scientific fields such as marketing, bioinformatics, finance, or social sciences. Contrary to cross-sectional or static data, this type of observations (also known as stream data, temporal data, longitudinal data or repeated measures) are more challenging as one has to incorporate data dependency in the clustering process. In this research we focus on clustering categorical sequences. The method proposed here combines model-based and heuristic clustering. In the first step, the categorical sequences are transformed by an extension of the hidden Markov model into a probabilistic space, where a symmetric Kullback–Leibler distance can operate. Then, in the second step, using hierarchical clustering on the matrix of distances, the sequences can be clustered. This paper illustrates the enormous potential of this type of hybrid approach using a synthetic data set as well as the well-known Microsoft dataset with website users search patterns and a survey on job career dynamics.     

Functional data clustering: a survey

Clustering techniques for functional data are reviewed. Four groups of clustering algorithms for functional data are proposed. The first group consists of methods working directly on the evaluation points of the curves. The second groups is defined by filtering methods which first approximate the curves into a finite basis of functions and second perform clustering using the basis expansion coefficients. The third groups is composed of methods which perform simultaneously dimensionality reduction of the curves and clustering, leading to functional representation of data depending on clusters. The last group consists of distance-based methods using clustering algorithms based on specific distances for functional data. A software review as well as an illustration of the application of these algorithms on real data are presented.     

The Guessing Secrets problem: a probabilistic approach

We introduce a probabilistic variant of the Guessing Secrets problem proposed by Chung et al. in [Electron. J. Combin. 8 (2001) R13]. In our variation, a player tries to discover the identity of a set S of n unknown secrets drawn by a second player, from a space Ω of N secrets. The first player tries to learn as much as possible about the elements of S by asking binary questions. For each question asked, the second player randomly chooses one of the n secrets of S that he uses in supplying the answer, which in any case must be truthful. We define a simple probabilistic guessing algorithm that allows us to guess all secrets of S with probability one. We show that the expected number of questions needed to guess all secrets is 2n²log₂N and the expected time complexity of the algorithm is . We also propose a generalization of this probabilistic guessing secrets problem, and provide some similar results for this generalization.     

(2, 1)-Separating systems beyond the probabilistic bound

Building on previous results of Xing, we give new lower bounds on the rate of linear intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry (although nothing beyond the basic theory of linear systems on curves). Then, using these new bounds within a concatenation argument, we construct binary (2,1)-separating systems of asymptotic rate exceeding the one given by the probabilistic method, which was the best lower bound available up to now. This answers (negatively) the question of whether this probabilistic bound was exact, which has remained open for more than 30 years.