Chebyshev Distance Research Articles

A Comparative Study of Three Heuristic Functions Used to Solve the 8-Puzzle

This paper introduces a new heuristic function with high efficiency for an optimum solving of the 8 - puzzle, this one being the double of the Chebyshev distance. The comparative study is realized among this new heuristic (Chebyshev heuristic), the Hamming h euristic and the Manhattan heuristic using A* algorithm implemented in Java. The Chebyshev heuristic function is more informed than Hamming and Manhattan heuristics. This paper also presents the necessary stages in object oriented development of an interactive software dedicated to simulate the A* search algorithm for 8 -puzzle. The modeling of the software is achieved through specific UML diagrams representing the phases of analysis, design and implementation, the system thus being described in a clear and practical manner. In order to confirm the obtained theoretical results which show that Chebyshev heuristic is more efficient, two performance criteria were used: space complexity and time complexity. The space complexity was measured by the number of generated nodes from the search tree, by the number of the expanded nodes and by the effective branching factor. The time complexity was measured by the running time. From the experimental results obtained by using the Chebyshev heuristic, improvements were obs erved regarding space and time complexity of A* algorithm versus Hamming and Manhattan heuristics.

The HPLC Fingerprint Analysis of SelectedCirsiumSpecies with Aid of Chemometrics

Twelve Cirsium sp. methanolic extracts were analyzed using high-performance liquid chromatography gradient elution method with run time of 45 min. Four Kinetex (150 × 4.6 mm) chromatographic columns (C18 5 µm, C18 2.6 µm, pentafluorophenyl 5 µm, phenyl-hexyl 5 µm) and mobile phase consisting of methanol/water/formic acid 1% were used. Eight standards (naringin, vanilic acid, chlorogenic acid, caffeic acid, rutin, luteolin, apigenin, p-coumaric acid) were analyzed in the same conditions to confirm their presence in all of Cirsium methanolic extracts. The obtained chromatograms were compared and the similarity between them was evaluated using the similarity indices (Pearson's correlation coefficient, determination coefficient and congruence coefficient), distance indices (Euclidean, Manhattan and Chebyshev distance) and multi-scale structural similarity (MS-SSIM). Obtained results were confirmed using the principal component analysis (PCA). The attempt of identification of two unknown Cirsium species was performed using the similarity, distance indices and PCA analysis.

Compression in the Space of Permutations

We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion characteristic for the permutation space under the uniform distribution, and the minimum achievable rate of compression that allows a bounded distortion after recovery. Our analysis is with respect to different practical and useful distortion measures, including Kendall-tau distance, Spearman's footrule, Chebyshev distance and inversion-$\ell_1$ distance. We establish equivalence of source code designs under certain distortions and show simple explicit code designs that incur low encoding/decoding complexities and are asymptotically optimal. Finally, we show that for the Mallows model, a popular nonuniform ranking model on the permutation space, both the entropy and the maximum distortion at zero rate are much lower than the uniform counterparts, which motivates the future design of efficient compression schemes for this model.

Image Understanding Applications of Lattice Autoassociative Memories.

Multivariate mathematical morphology (MMM) aims to extend the mathematical morphology from gray scale images to images whose pixels are high-dimensional vectors, such as remote sensing hyperspectral images and functional magnetic resonance images (fMRIs). Defining an ordering over the multidimensional image data space is a fundamental issue MMM, to ensure that ensuing morphological operators and filters are mathematically consistent. Recent approaches use the outputs of two-class classifiers to build such reduced orderings. This paper presents the applications of MMM built on reduced supervised orderings based on lattice autoassociative memories (LAAMs) recall error measured by the Chebyshev distance. Foreground supervised orderings use one set of training data from a foreground class, whereas background/foreground supervised orderings use two training data sets, one for each relevant class. The first case study refers to the realization of the thematic segmentation of the hyperspectral images using spatial-spectral information. Spectral classification is enhanced by a spatial processing consisting in the spatial correction guided by a watershed segmentation computed by the LAAM-based morphological operators. The approach improves the state-of-the-art hyperspectral spatial-spectral thematic map building approaches. The second case study is the analysis of resting state fMRI data, working on a data set of healthy controls, schizophrenia patients with and without auditory hallucinations. We perform two experiments: 1) the localization of differences in brain functional networks on population-dependent templates and 2) the classification of subjects into each possible pair of cases. In this data set, we find that the LAAM-based morphological features improve over the conventional correlation-based graph measure features often employed in fMRI data classification.

A fast and efficient adaptive parallel ray tracing based model for thermally coupled surface radiation in casting and heat treatment processes

A new algorithm for heat exchange between thermally coupled diffusely radiating interfaces is presented, which can be applied for closed and half open transparent radiating cavities. Interfaces between opaque and transparent materials are automatically detected and subdivided into elementary radiation surfaces named tiles. Contrary to the classical view factor method, the fixed unit sphere area subdivision oriented along the normal tile direction is projected onto the surrounding radiation mesh and not vice versa. Then, the total incident radiating flux of the receiver is approximated as a direct sum of radiation intensities of representative “senders” with the same weight factor. A hierarchical scheme for the space angle subdivision is selected in order to minimize the total memory and the computational demands during thermal calculations. Direct visibility is tested by means of a voxel-based ray tracing method accelerated by means of the anisotropic Chebyshev distance method, which reuses the computational grid as a Chebyshev one. The ray tracing algorithm is fully parallelized using MPI and takes advantage of the balanced distribution of all available tiles among all CPU's. This approach allows tracing of each particular ray without any communication. The algorithm has been implemented in a commercial casting process simulation software. The accuracy and computational performance of the new radiation model for heat treatment, investment and ingot casting applications is illustrated using industrial examples.

Sustainable and renewable implementation multi-criteria energy model (SRIME)—case study: Sri Lanka

Sustainable and renewable are certainly very appreciated terms nowadays. These words may summarize a whole new attitude towards our world and the people who live in it. This paper’s goal is to define an original multi-criteria energy model, named SRIME, specially designed for developing countries. First, an extensive research will be carried out on: energy demand; potential renewable energy, its current know-how and potential future development; potential avoided emissions (CO2, NOX, SO2); and the possible international support versus the in-country possibilities. The precedence constraints will be applied to establish in which degree renewable energy may be substituting for the fossil fuel: the purely economic approach will give way to a sustainable, renewable, development focused energy planning. It must be noted that an innovative function has been specifically included in the SRIME, which evaluates, applying the precedence constraints, the influence renewable energy may have on developing countries rural health and education. Six functions have been established: replaceable amount of fossil energy; CO2, NOX and SO2 avoidable emissions; rural health and education development maximization; and the cost function. These functions will be optimized through the Chebyshev distance (L ∞) compromise programming minimization, so that the Pareto optimal solution may be obtained.

Determining the best vector distance measure for use in location fingerprinting

Location fingerprinting is a technique that records vectors of received signal strength (RSS) from several transmitters at some reference points (RPs) into a database, and later matches these recorded vectors to a new measurement to position the user. In this work we deal with deterministic fingerprinting algorithms based on the nearest neighbor algorithm (NN). Distance measures between the recorded RSS values and the new measurements are then necessary, which can be calculated using Minkowski distance. The most popular cases of Minkowski distance, Manhattan, Euclidean and Chebyshev, are widely used in various studies in location fingerprinting. However, their positioning performance has not been analytically discussed yet. This causes unknown performance degradation when these signal distances are utilized, which can affect the positioning procedure. In this paper, the positioning performance using Manhattan, Euclidean and Chebyshev distance in terms of the probability of error (POE) are compared analytically and then the results are confirmed by simulations and real experiments. The relationship between the POE and distance error is also analyzed. The results show that using the NN method and a RSS Gaussian distribution assumption, Euclidean distance is the optimum distance which provides the lowest POE and mean distance error (MDE) for indoor fingerprinting.

A bicriteria heuristic for an elective surgery scheduling problem

Resource rationalization and reduction of waiting lists for surgery are two main guidelines for hospital units outlined in the Portuguese National Health Plan. This work is dedicated to an elective surgery scheduling problem arising in a Lisbon public hospital. In order to increase the surgical suite's efficiency and to reduce the waiting lists for surgery, two objectives are considered: maximize surgical suite occupation and maximize the number of surgeries scheduled. This elective surgery scheduling problem consists of assigning an intervention date, an operating room and a starting time for elective surgeries selected from the hospital waiting list. Accordingly, a bicriteria surgery scheduling problem arising in the hospital under study is presented. To search for efficient solutions of the bicriteria optimization problem, the minimization of a weighted Chebyshev distance to a reference point is used. A constructive and improvement heuristic procedure specially designed to address the objectives of the problem is developed and results of computational experiments obtained with empirical data from the hospital are presented. This study shows that by using the bicriteria approach presented here it is possible to build surgical plans with very good performance levels. This method can be used within an interactive approach with the decision maker. It can also be easily adapted to other hospitals with similar scheduling conditions.

Similarities in Time-Series of Housing Prices on Local Markets in Poland

Abstract This study examined similarities between local real estate markets in Poland from 2006 - 2013 by analyzing changes in housing prices. The analyses covered five cities - all of which are major centers of their regions: Warsaw (Mazovia - the center of Poland), Bialystok (Podlasie - the east of Poland), Cracow (Malopolska - the south of Poland), Poznan (Wielkopolska - the west of Poland) and Gdansk (Pomerania - the north of Poland). The time period was chosen so that it covered an interval of rapid changes in real estate prices (a housing bubble) and their subsequent relaxation to the equilibrium state. Firstly, a multi-dimensional analysis which took into account the Chebyshev distance was employed. This helped to conduct an analysis of the correlation of price changes over time, which revealed their concurrence and, moreover, showed specific propagation delays to external stimuli, and hence could be a measure of the market’s inertia. The degree of integration of the local markets under study changed only slightly over time; therefore, a thesis can be put forth in regard to the interrelation of local real estate markets, imagined as a system of communicating vessels. In the second stage, the damped harmonic oscillator model was employed to describe the observed evolution of real estate prices. This study exhibited high inertia in real estate markets, manifested during rapid structural changes in the system’s state occurring in conditions far from equilibrium. In long-term evolution, the pace of change is slow enough for the systems to remain close to equilibrium

Distance Based Hybrid Approach for Cluster Analysis Using Variants of K-means and Evolutionary Algorithm

Clustering is a process of grouping same objects into a specified number of clusters. K-means and K-medoids algorithms are the most popular partitional clustering techniques for large data sets. However, they are sensitive to random selection of initial centroids and are fall into local optimal solution. K-means++ algorithm has good convergence rate than other algorithms. Distance metric is used to find the dissimilarity between objects. Euclidean distance metric is commonly used by number of researchers in most algorithms. In recent years, Evolutionary algorithms are the global optimization techniques for solving clustering problems. In this study, we present hybrid K-means++ with PSO technique (K++_PSO) clustering algorithm based on different distance metrics like City Block and Chebyshev. The algorithms are tested on four popular benchmark data sets from UCI machine learning repository and an artificial data set. The clustering results are evaluated through the fitness function values. We have made a comparative study of proposed algorithm with other algorithms. It has been found that K++_PSO algorithm using Chebyshev distance metric produces good clustering results as compared to other approaches.

Automatic spinal canal detection in lumbar MR images in the sagittal view using dynamic programming

As there is an increasing need for the computer-aided effective management of pathology in lumbar spine, we have developed a computer-aided diagnosis and characterization framework using lumbar spine MRI that provides radiologists a second opinion. In this paper, we propose a left spinal canal boundary extraction method, based on dynamic programming in lumbar spine MRI. Our method fuses the absolute intensity difference of T1-weighted and T2-weighted sagittal images and the inverted gradient of the difference image into a dynamic programming scheme and works in a fully automatic fashion. The boundaries generated by our method are compared against reference boundaries in terms of the Euclidean distance and the Chebyshev distance. The experimental results from 85 clinical data show that our methods find the boundary with a mean Euclidean distance of 3mm, achieving a speedup factor of 167 compared with manual landmark extraction. The proposed method successfully extracts landmarks automatically and fits well with our framework for computer-aided diagnosis in lumbar spine.

CBIR Evaluation using Different Distances and DWT

In this paper, evaluation is made on the result of CBIR system based on haar wavelet transform with different distances for similarity matching to calculate the deviation from query image. So, different distances used are Chessboard distance, Cityblock distance and Euclidean distance. In this paper discrete wavelet transform is used to decompose the image. The image is decomposed till sixth level and last level approximate component is saved as feature vector. Comparison is made between different distances to see the best suited distance for CBIR. The wavelet used is “Haar”. Haar has compact support and it is the simplest orthogonal wavelet. It is very fast also. General Terms Average Precision, Average Recall, Query Image, Database, Similarity Measurement.

Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images

This paper presents a methodology for glaucoma detection based on measuring displacements of blood vessels within the optic disc (vascular bundle) in human retinal images. The method consists of segmenting the region of the vascular bundle in an optic disc to set a reference point in the temporal side of the cup, determining the position of the centroids of the superior, inferior, and nasal vascular bundle segmented zones located within the segmented region, and calculating the displacement from normal position using the chessboard distance metric. The method was successful in 62 images out of 67, achieving 93.02% sensitivity, 91.66% specificity, and 91.34% global accuracy in pre-diagnosis.

Grid Resource Discovery Algorithm Based on Distance

Resource discovery in a Grid environment is a critical problem and also a fundamental task which provides searching and locating necessary resources for given processes. Based on the domain and resource routing nodes, a grid resource discovery model of multilayer overlay network is given in this paper. And on this basis, using a linear combination of the block distance and chessboard distance instead of Euclidean distance, grid resource discovery algorithm based on distance is proposed. Experiment shows that the algorithm has low cost, fast response and can obtain better success rate of lookup, as well as the effectiveness of the resource discovery algorithm.

Grid Resource Discovery Algorithm of the Multi-Layer Overlay Network Model Based on Distance

The resource discovery mechanism is a hot topic issue in grid environments and It has great impact on the efficiency of the resource sharing and cooperative computing. Based on the domain and resource routing nodes, a grid resource discovery model of multilayer overlay network was given in this paper. And on this basis, using a linear combination of the block distance and chessboard distance instead of Euclidean distance, grid resource discovery algorithm based on distance was proposed. Experiment shows that the algorithm has low cost, fast response and can obtain better success rate of lookup, as well as the effectiveness of the resource discovery algorithm.

C-LAS Relief-An Improved Feature Selection Technique in Data Mining

selection or Feature subset selection is a process of reducing the attribute space in the feature set. It is also stated that feature selection is a technique of identifying a subset of features. These subsets of features are selected by removing irrelevant or redundant features in the feature set. A good feature set is said to be that it contains highly correlated features with the class. Such feature set improves the efficiency of the classification algorithms and also the classification accuracy. The Chebyshev distance with median variance in the weight estimation of attributes in the Relief imparts the consistency and good accuracy. In this paper a novel algorithm called C LAS-Relief is used to improve the reliability and accuracy of classification. Here C LAS-Relief stands for Chebyshev distance LAS-Relief. The efficiency and effectiveness of proposed method is experimented using agriculture soil data sets, Soybean and Ozone data sets. Similarly the new approach is compared with LAS-Relief approach using Naive bayes and J48 classifiers. The classification accuracy of C-LAS-Relief is superior over LAS- Relief. C LAS-Relief algorithm increases the accuracy of classification compared to LAS-Relief algorithm.

Postoptimal analysis of bicriteria boolean problems of selecting investment projects with Wald’s and Savage’s criteria

Lower and upper feasible bounds on the stability radius of the Pareto-optimal portfolio in the bicriteria Boolean investment problem with the Wald maximin efficiency criterion and the Savage minimax risk criterion are obtained in the case when the Chebyshev metric is defined in the space of varying parameters.

Improvement of ASIFT for Object Matching Based on Optimized Random Sampling

This paper proposes an efficient matching algorithm based on ASIFT (Affine Scale-Invariant Feature Transform) which is fully invariant to affine transformation. In our approach, we proposed a method of reducing similar measure matching cost and the number of outliers. First, we combined the Manhattan and Chessboard metrics replacing the Euclidean metric by a linear combination for measuring the similarity of keypoints. These two metrics are simple but really efficient. Using our method the computation time for matching step was saved and also the number of correct matches was increased. By applying an Optimized Random Sampling Algorithm (ORSA), we can remove most of the outlier matches to make the result meaningful. This method was experimented on various combinations of affine transform. The experimental result shows that our method is superior to SIFT and ASIFT.

Inverse multi-objective combinatorial optimization

Inverse multi-objective combinatorial optimization consists of finding a minimal adjustment of the objective functions coefficients such that a given set of feasible solutions becomes efficient. An algorithm is proposed for rendering a given feasible solution into an efficient one. This is a simplified version of the inverse problem when the cardinality of the set is equal to one. The adjustment is measured by the Chebyshev distance. It is shown how to build an optimal adjustment in linear time based on this distance, and why it is right to perform a binary search for determining the optimal distance. These results led us to develop an approach based on the resolution of mixed-integer linear programs. A second approach based on a branch-and-bound is proposed to handle any distance function that can be linearized. Finally, the initial inverse problem is solved by a cutting plane algorithm.

ANO Detection with K-Nearest Neighbor Using Minkowski Distance

Full unloading of the left ventricle in patients implanted with ventricular assist devices over a long period of time has been reported to cause aortic valve fusion and thrombosis. Therefore, it is vital to detect the occurrence of aortic valve non-opening (ANO) in these patients. In the present study, measurements were obtained from four greyhounds under a wide range of operating conditions, which covered varying levels of blood volume, vascular resistances, contractilities and pumping speeds. K nearest neighbor classifier was implemented on two features, i.e. root mean square and standard deviation of pump speed amplitude. Classification performance using different Minkowski distance metrics (Manhattan distance, Euclidean distance, Minkowski distance with a power of 3 and Chebyshev distance) and k parameter (odd numbers ranging from 1 to 29) were evaluated. Results showed that the compared metrics achieved similar performance (accuracy of 93%) and concurred unanimously with regards to the optimal numbers of k parameters (k=9) for the data tested. 