Search results for: Sequential block clustering.

Authors: R. Vishnu Priya, A. Vadivel

Abstract:

Sequential pattern mining is a challenging task in data mining area with large applications. One among those applications is mining patterns from weblog. Recent times, weblog is highly dynamic and some of them may become absolute over time. In addition, users may frequently change the threshold value during the data mining process until acquiring required output or mining interesting rules. Some of the recently proposed algorithms for mining weblog, build the tree with two scans and always consume large time and space. In this paper, we build Revised PLWAP with Non-frequent Items (RePLNI-tree) with single scan for all items. While mining sequential patterns, the links related to the nonfrequent items are not considered. Hence, it is not required to delete or maintain the information of nodes while revising the tree for mining updated transactions. The algorithm supports both incremental and interactive mining. It is not required to re-compute the patterns each time, while weblog is updated or minimum support changed. The performance of the proposed tree is better, even the size of incremental database is more than 50% of existing one. For evaluation purpose, we have used the benchmark weblog dataset and found that the performance of proposed tree is encouraging compared to some of the recently proposed approaches.

Keywords: Sequential pattern mining, weblog, frequent and non-frequent items, incremental and interactive mining.

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Authors: G.B. Nurlikhina, G.N. Azhimetova, R. M. Ashimova

Abstract:

Currently, one of the main directions is developing of development based on the clustering of economic operations of Kazakhstan, providing for the organization and concentration of production capacity in one region or the most optimal system. In the modern economic literature clustering is regarded as one of the most effective tools to ensure competitive businesses, and improve their business itself.

Keywords: A cluster, food market, innovation cluster.

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Authors: Boregowda S.B., Hemanth Kumar A.R. Babu N.V, Puttamadappa C., And H.S Mruthyunjaya

Abstract:

In the past few years, the use of wireless sensor networks (WSNs) potentially increased in applications such as intrusion detection, forest fire detection, disaster management and battle field. Sensor nodes are generally battery operated low cost devices. The key challenge in the design and operation of WSNs is to prolong the network life time by reducing the energy consumption among sensor nodes. Node clustering is one of the most promising techniques for energy conservation. This paper presents a novel clustering algorithm which maximizes the network lifetime by reducing the number of communication among sensor nodes. This approach also includes new distributed cluster formation technique that enables self-organization of large number of nodes, algorithm for maintaining constant number of clusters by prior selection of cluster head and rotating the role of cluster head to evenly distribute the energy load among all sensor nodes.

Keywords: Clustering algorithms, Cluster head, Energy consumption, Sensor nodes, and Wireless sensor networks.

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Authors: John Mark Lampos, Virgilio Sison

Abstract:

Two constructions of unit-memory binary convolutional codes from linear block codes over the finite semi-local ring F2r +vF2r , where v2 = v, are presented. In both cases, if the linear block code is systematic, then the resulting convolutional encoder is systematic, minimal, basic and non-catastrophic. The Hamming free distance of the convolutional code is bounded below by the minimum Hamming distance of the block code. New examples of binary convolutional codes that meet the Heller upper bound for systematic codes are given.

Keywords: Convolutional codes, semi-local ring, free distance, Heller bound.

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Authors: D. I. De Souza, G. P. Azevedo, R. Rocha

Abstract:

In this paper we will develop a sequential life test approach applied to a modified low alloy-high strength steel part used in highway overpasses in Brazil.We will consider two possible underlying sampling distributions: the Normal and theInverse Weibull models. The minimum life will be considered equal to zero. We will use the two underlying models to analyze a fatigue life test situation, comparing the results obtained from both.Since a major chemical component of this low alloy-high strength steel part has been changed, there is little information available about the possible values that the parameters of the corresponding Normal and Inverse Weibull underlying sampling distributions could have. To estimate the shape and the scale parameters of these two sampling models we will use a maximum likelihood approach for censored failure data. We will also develop a truncation mechanism for the Inverse Weibull and Normal models. We will provide rules to truncate a sequential life testing situation making one of the two possible decisions at the moment of truncation; that is, accept or reject the null hypothesis H0. An example will develop the proposed truncated sequential life testing approach for the Inverse Weibull and Normal models.

Keywords: Sequential life testing, normal and inverse Weibull models, maximum likelihood approach, truncation mechanism.

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Authors: Norashikin Ahmad, Damminda Alahakoon

Abstract:

Self-organizing map (SOM) provides both clustering and visualization capabilities in mining data. Dynamic self-organizing maps such as Growing Self-organizing Map (GSOM) has been developed to overcome the problem of fixed structure in SOM to enable better representation of the discovered patterns. However, in mining large datasets or historical data the hierarchical structure of the data is also useful to view the cluster formation at different levels of abstraction. In this paper, we present a technique to generate concept trees from the GSOM. The formation of tree from different spread factor values of GSOM is also investigated and the quality of the trees analyzed. The results show that concept trees can be generated from GSOM, thus, eliminating the need for re-clustering of the data from scratch to obtain a hierarchical view of the data under study.

Keywords: dynamic self-organizing map, concept formation, clustering.

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Authors: H. Mehdi, Kh. S. Karimov, A. A. Kavokin

Abstract:

Methods of clustering which were developed in the data mining theory can be successfully applied to the investigation of different kinds of dependencies between the conditions of environment and human activities. It is known, that environmental parameters such as temperature, relative humidity, atmospheric pressure and illumination have significant effects on the human mental performance. To investigate these parameters effect, data mining technique of clustering using entropy and Information Gain Ratio (IGR) K(Y/X) = (H(X)–H(Y/X))/H(Y) is used, where H(Y)=-ΣPi ln(Pi). This technique allows adjusting the boundaries of clusters. It is shown that the information gain ratio (IGR) grows monotonically and simultaneously with degree of connectivity between two variables. This approach has some preferences if compared, for example, with correlation analysis due to relatively smaller sensitivity to shape of functional dependencies. Variant of an algorithm to implement the proposed method with some analysis of above problem of environmental effects is also presented. It was shown that proposed method converges with finite number of steps.

Keywords: Clustering, Correlation analysis, EnvironmentalParameters, Information Gain Ratio, Mental Performance.

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Authors: Dhany Saputra, Dayang R. A. Rambli, Oi Mean Foong

Abstract:

In this paper, we propose an improvement of pattern growth-based PrefixSpan algorithm, called I-PrefixSpan. The general idea of I-PrefixSpan is to use sufficient data structure for Seq-Tree framework and separator database to reduce the execution time and memory usage. Thus, with I-PrefixSpan there is no in-memory database stored after index set is constructed. The experimental result shows that using Java 2, this method improves the speed of PrefixSpan up to almost two orders of magnitude as well as the memory usage to more than one order of magnitude.

Keywords: ArrayList, ArrayIntList, minimum support, sequence database, sequential patterns.

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Authors: Shu-Xin Miao

Abstract:

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.

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Authors: Seung Hwan Park, Cheng-Sool Park, Jun Seok Kim, Youngji Yoo, Daewoong An, Jun-Geol Baek

Abstract:

Depending on the big data analysis becomes important, yield prediction using data from the semiconductor process is essential. In general, yield prediction and analysis of the causes of the failure are closely related. The purpose of this study is to analyze pattern affects the final test results using a die map based clustering. Many researches have been conducted using die data from the semiconductor test process. However, analysis has limitation as the test data is less directly related to the final test results. Therefore, this study proposes a framework for analysis through clustering using more detailed data than existing die data. This study consists of three phases. In the first phase, die map is created through fail bit data in each sub-area of die. In the second phase, clustering using map data is performed. And the third stage is to find patterns that affect final test result. Finally, the proposed three steps are applied to actual industrial data and experimental results showed the potential field application.

Keywords: Die-Map Clustering, Feature Extraction, Pattern Recognition, Semiconductor Manufacturing Process.

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Authors: A. M. Fahim, G. Saake, A. M. Salem, F. A. Torkey, M. A. Ramadan

Abstract:

Data clustering is an important data exploration technique with many applications in data mining. The k-means algorithm is well known for its efficiency in clustering large data sets. However, this algorithm is suitable for spherical shaped clusters of similar sizes and densities. The quality of the resulting clusters decreases when the data set contains spherical shaped with large variance in sizes. In this paper, we introduce a competent procedure to overcome this problem. The proposed method is based on shifting the center of the large cluster toward the small cluster, and recomputing the membership of small cluster points, the experimental results reveal that the proposed algorithm produces satisfactory results.

Keywords: K-Means, Data Clustering, Cluster Analysis.

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Authors: Z. Zainuddin, W. K. Lye

Abstract:

In this paper, a clustering algorithm named KHarmonic means (KHM) was employed in the training of Radial Basis Function Networks (RBFNs). KHM organized the data in clusters and determined the centres of the basis function. The popular clustering algorithms, namely K-means (KM) and Fuzzy c-means (FCM), are highly dependent on the initial identification of elements that represent the cluster well. In KHM, the problem can be avoided. This leads to improvement in the classification performance when compared to other clustering algorithms. A comparison of the classification accuracy was performed between KM, FCM and KHM. The classification performance is based on the benchmark data sets: Iris Plant, Diabetes and Breast Cancer. RBFN training with the KHM algorithm shows better accuracy in classification problem.

Keywords: Neural networks, Radial basis functions, Clusteringmethod, K-harmonic means.

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Authors: Ajay Shekhar Pandey, D. Singh, S. K. Sinha

Abstract:

A clustering based technique has been developed and implemented for Short Term Load Forecasting, in this article. Formulation has been done using Mean Absolute Percentage Error (MAPE) as an objective function. Data Matrix and cluster size are optimization variables. Model designed, uses two temperature variables. This is compared with six input Radial Basis Function Neural Network (RBFNN) and Fuzzy Inference Neural Network (FINN) for the data of the same system, for same time period. The fuzzy inference system has the network structure and the training procedure of a neural network which initially creates a rule base from existing historical load data. It is observed that the proposed clustering based model is giving better forecasting accuracy as compared to the other two methods. Test results also indicate that the RBFNN can forecast future loads with accuracy comparable to that of proposed method, where as the training time required in the case of FINN is much less.

Keywords: Load forecasting, clustering, fuzzy inference.

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Authors: Mahmoud Zarrini, Sanaz Torkaman

Abstract:

In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

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Authors: Chen Wu, Jingyu Yang

Abstract:

Using maximal consistent blocks of tolerance relation on the universe in incomplete decision table, the concepts of join block and meet block are introduced and studied. Including tolerance class, other blocks such as tolerant kernel and compatible kernel of an object are also discussed at the same time. Upper and lower approximations based on those blocks are also defined. Default definite decision rules acquired from incomplete decision table are proposed in the paper. An incremental algorithm to update default definite decision rules is suggested for effective mining tasks from incomplete decision table into which data is appended. Through an example, we demonstrate how default definite decision rules based on maximal consistent blocks, join blocks and meet blocks are acquired and how optimization is done in support of discernibility matrix and discernibility function in the incomplete decision table.

Keywords: rough set, incomplete decision table, maximalconsistent block, default definite decision rule, join and meet block.

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Authors: Mohamed A. Mahfouz, M. A. Ismail

Abstract:

This paper introduces new algorithms (Fuzzy relative of the CLARANS algorithm FCLARANS and Fuzzy c Medoids based on randomized search FCMRANS) for fuzzy clustering of relational data. Unlike existing fuzzy c-medoids algorithm (FCMdd) in which the within cluster dissimilarity of each cluster is minimized in each iteration by recomputing new medoids given current memberships, FCLARANS minimizes the same objective function minimized by FCMdd by changing current medoids in such away that that the sum of the within cluster dissimilarities is minimized. Computing new medoids may be effected by noise because outliers may join the computation of medoids while the choice of medoids in FCLARANS is dictated by the location of a predominant fraction of points inside a cluster and, therefore, it is less sensitive to the presence of outliers. In FCMRANS the step of computing new medoids in FCMdd is modified to be based on randomized search. Furthermore, a new initialization procedure is developed that add randomness to the initialization procedure used with FCMdd. Both FCLARANS and FCMRANS are compared with the robust and linearized version of fuzzy c-medoids (RFCMdd). Experimental results with different samples of the Reuter-21578, Newsgroups (20NG) and generated datasets with noise show that FCLARANS is more robust than both RFCMdd and FCMRANS. Finally, both FCMRANS and FCLARANS are more efficient and their outputs are almost the same as that of RFCMdd in terms of classification rate.

Keywords: Data Mining, Fuzzy Clustering, Relational Clustering, Medoid-Based Clustering, Cluster Analysis, Unsupervised Learning.

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Authors: Filiz Ersoz, Taner Ersoz, Tugrul Bayraktar

Abstract:

Renewable energy is referred to as "clean energy" and common popular support for the use of renewable energy (RE) is to provide electricity with zero carbon dioxide emissions. This study provides useful insight into the European Union (EU) RE, especially, into electricity generation obtained from renewables, and their targets. The objective of this study is to identify groups of European countries, using multivariate statistical analysis and selected indicators. The hierarchical clustering method is used to decide the number of clusters for EU countries. The conducted statistical hierarchical cluster analysis is based on the Ward’s clustering method and squared Euclidean distances. Hierarchical cluster analysis identified eight distinct clusters of European countries. Then, non-hierarchical clustering (k-means) method was applied. Discriminant analysis was used to determine the validity of the results with data normalized by Z score transformation. To explore the relationship between the selected indicators, correlation coefficients were computed. The results of the study reveal the current situation of RE in European Union Member States.

Keywords: Share of electricity generation, CO2 emission, targets, multivariate methods, hierarchical clustering, K-means clustering, discriminant analyzed, correlation, EU member countries.

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Authors: Ying-Wen Bai, Ju-Maw Chen

Abstract:

To successfully provide a fast FIR filter with FTT algorithms, overlapped-save algorithms can be used to lower the computational complexity and achieve the desired real-time processing. As the length of the input block increases in order to improve the efficiency, a larger volume of zero padding will greatly increase the computation length of the FFT. In this paper, we use the overlapped block digital filtering to construct a parallel structure. As long as the down-sampling (or up-sampling) factor is an exact multiple lengths of the impulse response of a FIR filter, we can process the input block by using a parallel structure and thus achieve a low-complex fast FIR filter with overlapped-save algorithms. With a long filter length, the performance and the throughput of the digital filtering system will also be greatly enhanced.

Keywords: FIR Filter, Overlapped-save Algorithm, ParallelStructure

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Authors: U. Idachaba, F. Z. Wang, A. Qi, N. Helian

Abstract:

Artificial Bee Colony (ABC) algorithm is a relatively new swarm intelligence technique for clustering. It produces higher quality clusters compared to other population-based algorithms but with poor energy efficiency, cluster quality consistency and typically slower in convergence speed. Inspired by energy saving foraging behavior of natural honey bees this paper presents a Quality and Quantity Aware Artificial Bee Colony (Q2ABC) algorithm to improve quality of cluster identification, energy efficiency and convergence speed of the original ABC. To evaluate the performance of Q2ABC algorithm, experiments were conducted on a suite of ten benchmark UCI datasets. The results demonstrate Q2ABC outperformed ABC and K-means algorithm in the quality of clusters delivered.

Keywords: Artificial bee colony algorithm, clustering.

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

Abstract:

In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: Balanced truncation, Clustering, Dominant pole, Hankel norm, Model reduction.

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Authors: Soon-Hyun Park, Takami Matsuo

Abstract:

This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: Samir Brahim Belhaouari

Abstract:

By taking advantage of both k-NN which is highly accurate and K-means cluster which is able to reduce the time of classification, we can introduce Cluster-k-Nearest Neighbor as "variable k"-NN dealing with the centroid or mean point of all subclasses generated by clustering algorithm. In general the algorithm of K-means cluster is not stable, in term of accuracy, for that reason we develop another algorithm for clustering our space which gives a higher accuracy than K-means cluster, less subclass number, stability and bounded time of classification with respect to the variable data size. We find between 96% and 99.7 % of accuracy in the lassification of 6 different types of Time series by using K-means cluster algorithm and we find 99.7% by using the new clustering algorithm.

Keywords: Pattern recognition, Time series, k-Nearest Neighbor, k-means cluster, Gaussian Mixture Model, Classification

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Authors: Miika Toivanen, Jouko Lampinen

Abstract:

This paper presents an online method that learns the corresponding points of an object from un-annotated grayscale images containing instances of the object. In the first image being processed, an ensemble of node points is automatically selected which is matched in the subsequent images. A Bayesian posterior distribution for the locations of the nodes in the images is formed. The likelihood is formed from Gabor responses and the prior assumes the mean shape of the node ensemble to be similar in a translation and scale free space. An association model is applied for separating the object nodes and background nodes. The posterior distribution is sampled with Sequential Monte Carlo method. The matched object nodes are inferred to be the corresponding points of the object instances. The results show that our system matches the object nodes as accurately as other methods that train the model with annotated training images.

Keywords: Bayesian modeling, Gabor filters, Online learning, Sequential Monte Carlo.

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Authors: D. I. De Souza, D. R. Fonseca, G. P. Azevedo

Abstract:

Sometimes the amount of time available for testing could be considerably less than the expected lifetime of the component. To overcome such a problem, there is the accelerated life-testing alternative aimed at forcing components to fail by testing them at much higher-than-intended application conditions. These models are known as acceleration models. One possible way to translate test results obtained under accelerated conditions to normal using conditions could be through the application of the “Maxwell Distribution Law.” In this paper we will apply a combined approach of a sequential life testing and an accelerated life testing to a low alloy high-strength steel component used in the construction of overpasses in Brazil. The underlying sampling distribution will be three-parameter Inverse Weibull model. To estimate the three parameters of the Inverse Weibull model we will use a maximum likelihood approach for censored failure data. We will be assuming a linear acceleration condition. To evaluate the accuracy (significance) of the parameter values obtained under normal conditions for the underlying Inverse Weibull model we will apply to the expected normal failure times a sequential life testing using a truncation mechanism. An example will illustrate the application of this procedure.

Keywords: Sequential Life Testing, Accelerated Life Testing, Underlying Three-Parameter Weibull Model, Maximum Likelihood Approach, Hypothesis Testing.

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Authors: K. M. Faraoun, A. Boukelif

Abstract:

In the present work, we propose a new technique to enhance the learning capabilities and reduce the computation intensity of a competitive learning multi-layered neural network using the K-means clustering algorithm. The proposed model use multi-layered network architecture with a back propagation learning mechanism. The K-means algorithm is first applied to the training dataset to reduce the amount of samples to be presented to the neural network, by automatically selecting an optimal set of samples. The obtained results demonstrate that the proposed technique performs exceptionally in terms of both accuracy and computation time when applied to the KDD99 dataset compared to a standard learning schema that use the full dataset.

Keywords: Neural networks, Intrusion detection, learningenhancement, K-means clustering

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Authors: Muhanned Alfarras

Abstract:

The recent growth of using multimedia transmission over wireless communication systems, have challenges to protect the data from lost due to wireless channel effect. Images are corrupted due to the noise and fading when transmitted over wireless channel, in wireless channel the image is transmitted block by block, Due to severe fading, entire image blocks can be damaged. The aim of this paper comes out from need to enhance the digital images at the wireless receiver side. Proposed Boundary Interpolation (BI) Algorithm using wavelet, have been adapted here used to reconstruction the lost block in the image at the receiver depend on the correlation between the lost block and its neighbors. New Proposed technique by using Boundary Interpolation (BI) Algorithm using wavelet with Pixel interleaver has been implemented. Pixel interleaver work on distribute the pixel to new pixel position of original image before transmitting the image. The block lost through wireless channel is only effects individual pixel. The lost pixels at the receiver side can be recovered by using Boundary Interpolation (BI) Algorithm using wavelet. The results showed that the New proposed algorithm boundary interpolation (BI) using wavelet with pixel interleaver is better in term of MSE and PSNR.

Keywords: Image Transmission, Wavelet, Pixel Interleaver, Boundary Interpolation Algorithm

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Authors: A. Habibizad Navin, A. Sadighi, M. Naghian Fesharaki, M. Mirnia, M. Teshnelab, R. Keshmiri

Abstract:

This paper presents a new data oriented model of image. Then a representation of it, ADBT, is introduced. The ability of ADBT is clustering, segmentation, measuring similarity of images etc, with desired precision and corresponding speed.

Keywords: Data oriented modelling, image, clustering, segmentation, classification, ADBT and image processing.

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: Luciana Abednego, Cecilia Nugraheni

Abstract:

There are many approaches proposed for solving Sudoku puzzles. One of them is by modelling the puzzles as block world problems. There have been three model for Sudoku solvers based on this approach. Each model expresses Sudoku solver as a parameterized multi agent systems. In this work, we propose a new model which is an improvement over the existing models. This paper presents the development of a Sudoku solver that implements all the proposed models. Some experiments have been conducted to determine the performance of each model.

Keywords: Sudoku puzzle, Sudoku solver, block world problem, parameterized multi agent systems.

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Authors: Lubna Eljabu, Mohammad Etemad, Stan Matwin

Abstract:

The automatic extraction of shipping routes is advantageous for intelligent traffic management systems to identify events and support decision-making in maritime surveillance. At present, there is a high demand for the extraction of maritime traffic networks that resemble the real traffic of vessels accurately, which is valuable for further analytical processing tasks for vessels trajectories (e.g., naval routing and voyage planning, anomaly detection, destination prediction, time of arrival estimation). With the help of big data and processing huge amounts of vessels’ trajectory data, it is possible to learn these shipping routes from the navigation history of past behaviour of other, similar ships that were travelling in a given area. In this paper, we propose a spatial clustering model of vessels’ trajectories (SPTCLUST) to extract spatial representations of sailing routes from historical Automatic Identification System (AIS) data. The whole model consists of three main parts: data preprocessing, path finding, and route extraction, which consists of clustering and representative trajectory extraction. The proposed clustering method provides techniques to overcome the problems of: (i) optimal input parameters selection; (ii) the high complexity of processing a huge volume of multidimensional data; (iii) and the spatial representation of complete representative trajectory detection in the context of trajectory clustering algorithms. The experimental evaluation showed the effectiveness of the proposed model by using a real-world AIS dataset from the Port of Halifax. The results contribute to further understanding of shipping route patterns. This could aid surveillance authorities in stable and sustainable vessel traffic management.

Keywords: Vessel trajectory clustering, trajectory mining, Spatial Clustering, marine intelligent navigation, maritime traffic network extraction, sdailing routes extraction.

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