Search results for: Least Squares Support Vector

Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

Abstract:

Predicting protein-protein interactions represent a key step in understanding proteins functions. This is due to the fact that proteins usually work in context of other proteins and rarely function alone. Machine learning techniques have been applied to predict protein-protein interactions. However, most of these techniques address this problem as a binary classification problem. Although it is easy to get a dataset of interacting proteins as positive examples, there are no experimentally confirmed non-interacting proteins to be considered as negative examples. Therefore, in this paper we solve this problem as a one-class classification problem using one-class support vector machines (SVM). Using only positive examples (interacting protein pairs) in training phase, the one-class SVM achieves accuracy of about 80%. These results imply that protein-protein interaction can be predicted using one-class classifier with comparable accuracy to the binary classifiers that use artificially constructed negative examples.

Keywords: Bioinformatics, Protein-protein interactions, One-Class Support Vector Machines

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Authors: Wei Zhang, Xin Zhao, Yi-Fan Zhu, Xin-Jian Zhang

Abstract:

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, Green function, support vectorregression

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Authors: Hossein Esbati, Jalil Shirazi

Abstract:

In this paper, in order to categorize ORL database face pictures, principle Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) methods by using Elman neural network and Support Vector Machine (SVM) categorization methods are used. Elman network as a recurrent neural network is proposed for modeling storage systems and also it is used for reviewing the effect of using PCA numbers on system categorization precision rate and database pictures categorization time. Categorization stages are conducted with various components numbers and the obtained results of both Elman neural network categorization and support vector machine are compared. In optimum manner 97.41% recognition accuracy is obtained.

Keywords: Face recognition, Principal Component Analysis, Kernel Principal Component Analysis, Neural network, Support Vector Machine.

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Authors: Monjed Ezzeddinne, Nicolas Lefebvre, Régis Lengellé

Abstract:

This paper presents a new version of the SVM mixture algorithm initially proposed by Kwok for classification and regression problems. For both cases, a slight modification of the mixture model leads to a standard SVM training problem, to the existence of an exact solution and allows the direct use of well known decomposition and working set selection algorithms. Only the regression case is considered in this paper but classification has been addressed in a very similar way. This method has been successfully applied to engine pollutants emission modeling.

Keywords: Identification, Learning systems, Mixture ofExperts, Support Vector Machines.

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Authors: Sorayya Malek, Mogeeb Mosleh, Sharifah M. Syed

Abstract:

In this study, Support Vector Machine (SVM) technique was applied to predict the dichotomized value of Dissolved oxygen (DO) from two freshwater lakes namely Chini and Bera Lake (Malaysia). Data sample contained 11 parameters for water quality features from year 2005 until 2009. All data parameters were used to predicate the dissolved oxygen concentration which was dichotomized into 3 different levels (High, Medium, and Low). The input parameters were ranked, and forward selection method was applied to determine the optimum parameters that yield the lowest errors, and highest accuracy. Initial results showed that pH, Water Temperature, and Conductivity are the most important parameters that significantly affect the predication of DO. Then, SVM model was applied using the Anova kernel with those parameters yielded 74% accuracy rate. We concluded that using SVM models to predicate the DO is feasible, and using dichotomized value of DO yields higher prediction accuracy than using precise DO value.

Keywords: Dissolved oxygen, Water quality, predication DO, Support Vector Machine.

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Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

Abstract:

The protein domain structure has been widely used as the most informative sequence feature to computationally predict protein-protein interactions. However, in a recent study, a research group has reported a very high accuracy of 94% using hydrophobicity feature. Therefore, in this study we compare and verify the usefulness of protein domain structure and hydrophobicity properties as the sequence features. Using the Support Vector Machines (SVM) as the learning system, our results indicate that both features achieved accuracy of nearly 80%. Furthermore, domains structure had receiver operating characteristic (ROC) score of 0.8480 with running time of 34 seconds, while hydrophobicity had ROC score of 0.8159 with running time of 20,571 seconds (5.7 hours). These results indicate that protein-protein interaction can be predicted from domain structure with reliable accuracy and acceptable running time.

Keywords: Bioinformatics, protein-protein interactions, support vector machines, protein features.

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Authors: Mona Soliman Habib

Abstract:

This paper explores the scalability issues associated with solving the Named Entity Recognition (NER) problem using Support Vector Machines (SVM) and high-dimensional features. The performance results of a set of experiments conducted using binary and multi-class SVM with increasing training data sizes are examined. The NER domain chosen for these experiments is the biomedical publications domain, especially selected due to its importance and inherent challenges. A simple machine learning approach is used that eliminates prior language knowledge such as part-of-speech or noun phrase tagging thereby allowing for its applicability across languages. No domain-specific knowledge is included. The accuracy measures achieved are comparable to those obtained using more complex approaches, which constitutes a motivation to investigate ways to improve the scalability of multiclass SVM in order to make the solution more practical and useable. Improving training time of multi-class SVM would make support vector machines a more viable and practical machine learning solution for real-world problems with large datasets. An initial prototype results in great improvement of the training time at the expense of memory requirements.

Keywords: Named entity recognition, support vector machines, language independence, bioinformatics.

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Authors: E. A. Mlybari, M. S. Elbisy, A. H. Alshahri, O. M. Albarakati

Abstract:

Sea level rise threatens to increase the impact of future  storms and hurricanes on coastal communities. Accurate sea level  change prediction and supplement is an important task in determining  constructions and human activities in coastal and oceanic areas. In  this study, support vector machines (SVM) is proposed to predict  daily tidal levels along the Jeddah Coast, Saudi Arabia. The optimal  parameter values of kernel function are determined using a genetic  algorithm. The SVM results are compared with the field data and  with back propagation (BP). Among the models, the SVM is superior  to BPNN and has better generalization performance.

 

Keywords: Tides, Prediction, Support Vector Machines, Genetic Algorithm, Back-Propagation Neural Network, Risk, Hazards.

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Authors: Usha Lokala, Srinivas Nowduri, Prabhakar K. Sharma

Abstract:

Useful information has been extracted from the road accident data in United Kingdom (UK), using data analytics method, for avoiding possible accidents in rural and urban areas. This analysis make use of several methodologies such as data integration, support vector machines (SVM), correlation machines and multinomial goodness. The entire datasets have been imported from the traffic department of UK with due permission. The information extracted from these huge datasets forms a basis for several predictions, which in turn avoid unnecessary memory lapses. Since data is expected to grow continuously over a period of time, this work primarily proposes a new framework model which can be trained and adapt itself to new data and make accurate predictions. This work also throws some light on use of SVM’s methodology for text classifiers from the obtained traffic data. Finally, it emphasizes the uniqueness and adaptability of SVMs methodology appropriate for this kind of research work.

Keywords: Road accident, machine learning, support vector machines.

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Authors: Yang Zhang, Yuncai Liu

Abstract:

Accurately predicting non-peak traffic is crucial to daily traffic for all forecasting models. In the paper, least squares support vector machines (LS-SVMs) are investigated to solve such a practical problem. It is the first time to apply the approach and analyze the forecast performance in the domain. For comparison purpose, two parametric and two non-parametric techniques are selected because of their effectiveness proved in past research. Having good generalization ability and guaranteeing global minima, LS-SVMs perform better than the others. Providing sufficient improvement in stability and robustness reveals that the approach is practically promising.

Keywords: Parametric and Nonparametric Techniques, Non-peak Traffic Forecasting

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Authors: M. Satya Sai Ram, P. Siddaiah, M. Madhavi Latha

Abstract:

Vector quantization is a powerful tool for speech coding applications. This paper deals with LPC Coding of speech signals which uses a new technique called Multi Switched Split Vector Quantization, This is a hybrid of two product code vector quantization techniques namely the Multi stage vector quantization technique, and Switched split vector quantization technique,. Multi Switched Split Vector Quantization technique quantizes the linear predictive coefficients in terms of line spectral frequencies. From results it is proved that Multi Switched Split Vector Quantization provides better trade off between bitrate and spectral distortion performance, computational complexity and memory requirements when compared to Switched Split Vector Quantization, Multi stage vector quantization, and Split Vector Quantization techniques. By employing the switching technique at each stage of the vector quantizer the spectral distortion, computational complexity and memory requirements were greatly reduced. Spectral distortion was measured in dB, Computational complexity was measured in floating point operations (flops), and memory requirements was measured in (floats).

Keywords: Unconstrained vector quantization, Linear predictiveCoding, Split vector quantization, Multi stage vector quantization, Switched Split vector quantization, Line Spectral Frequencies.

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Authors: Xiaohua Liu, Juan F. Beltran, Nishant Mohanchandra, Godfried T. Toussaint

Abstract:

Support vector machines (SVMs) are considered to be the best machine learning algorithms for minimizing the predictive probability of misclassification. However, their drawback is that for large data sets the computation of the optimal decision boundary is a time consuming function of the size of the training set. Hence several methods have been proposed to speed up the SVM algorithm. Here three methods used to speed up the computation of the SVM classifiers are compared experimentally using a musical genre classification problem. The simplest method pre-selects a random sample of the data before the application of the SVM algorithm. Two additional methods use proximity graphs to pre-select data that are near the decision boundary. One uses k-Nearest Neighbor graphs and the other Relative Neighborhood Graphs to accomplish the task.

Keywords: Machine learning, data mining, support vector machines, proximity graphs, relative-neighborhood graphs, k-nearestneighbor graphs, random sampling, training data condensation.

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Authors: Hajar Bouirouga, Sanaa El Fkihi , Abdeilah Jilbab, Driss Aboutajdine

Abstract:

In this paper we propose a method for recognition of adult video based on support vector machine (SVM). Different kernel features are proposed to classify adult videos. SVM has an advantage that it is insensitive to the relative number of training example in positive (adult video) and negative (non adult video) classes. This advantage is illustrated by comparing performance between different SVM kernels for the identification of adult video.

Keywords: Skin detection, Support vector machine, Pornographic videos, Feature extraction, Video filtering, Classification.

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Authors: Chih-Hung Wu, Chih-Chin Lai, Chun-Yen Chen, Yan-He Chen

Abstract:

Interpretation of aerial images is an important task in various applications. Image segmentation can be viewed as the essential step for extracting information from aerial images. Among many developed segmentation methods, the technique of clustering has been extensively investigated and used. However, determining the number of clusters in an image is inherently a difficult problem, especially when a priori information on the aerial image is unavailable. This study proposes a support vector machine approach for clustering aerial images. Three cluster validity indices, distance-based index, Davies-Bouldin index, and Xie-Beni index, are utilized as quantitative measures of the quality of clustering results. Comparisons on the effectiveness of these indices and various parameters settings on the proposed methods are conducted. Experimental results are provided to illustrate the feasibility of the proposed approach.

Keywords: Aerial imaging, image segmentation, machine learning, support vector machine, cluster validity index

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Authors: C. Slim

Abstract:

This paper presents an integrated model, which hybridized data envelopment analysis (DEA) and support vector machine (SVM) together, to class countries according to their efficiency and performance. This model takes into account aspects of multi-dimensional indicators, decision-making hierarchy and relativity of measurement. Starting from a set of indicators of performance as exhaustive as possible, a process of successive aggregations has been developed to attain an overall evaluation of a country’s competitiveness.

Keywords: Artificial neural networks, support vector machine, data envelopment analysis, aggregations, indicators of performance.

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Authors: Ehsan Amid, Sina Rezaei Aghdam, Hamidreza Amindavar

Abstract:

Steel surface defect detection is essentially one of pattern recognition problems. Support Vector Machines (SVMs) are known as one of the most proper classifiers in this application. In this paper, we introduce a more accurate classification method by using SVMs as our final classifier of the inspection system. In this scheme, multiclass classification task is performed based on the "one-againstone" method and different kernels are utilized for each pair of the classes in multiclass classification of the different defects. In the proposed system, a decision tree is employed in the first stage for two-class classification of the steel surfaces to "defect" and "non-defect", in order to decrease the time complexity. Based on the experimental results, generated from over one thousand images, the proposed multiclass classification scheme is more accurate than the conventional methods and the overall system yields a sufficient performance which can meet the requirements in steel manufacturing.

Keywords: Steel Surface Defect Detection, Support Vector Machines, Kernel Methods.

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Authors: Mohd A. Mezher, Maysam F. Abbod

Abstract:

Genetic Folding (GF) a new class of EA named as is introduced for the first time. It is based on chromosomes composed of floating genes structurally organized in a parent form and separated by dots. Although, the genotype/phenotype system of GF generates a kernel expression, which is the objective function of superior classifier. In this work the question of the satisfying mapping-s rules in evolving populations is addressed by analyzing populations undergoing either Mercer-s or none Mercer-s rule. The results presented here show that populations undergoing Mercer-s rules improve practically models selection of Support Vector Machine (SVM). The experiment is trained multi-classification problem and tested on nonlinear Ionosphere dataset. The target of this paper is to answer the question of evolving Mercer-s rule in SVM addressed using either genetic folding satisfied kernel-s rules or not applied to complicated domains and problems.

Keywords: Genetic Folding, GF, Evolutionary Algorithms, Support Vector Machine, Genetic Algorithm, Genetic Programming, Multi-Classification, Mercer's Rules

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Authors: Asma Mehan

Abstract:

Under the thrust of technological changes, population growth and vehicular traffic, Iranian historical squares have lost their significance and they are no longer the main social nodes of the society. This research focuses on how historical public squares can inspire designers to enhance social interactions among citizens in Iranian urban context. Moreover, the recent master plan of Tehran demonstrates the lack of public spaces designed for the purpose of people’s social gatherings. For filling this gap, first the current situation of 7 selected primary historical public squares in Tehran including Sabze Meydan, Arg, Topkhaneh, Baherstan, Mokhber-al-dole, Rah Ahan and Hassan Abad have been compared. Later, the influencing elements on social interactions of the public squares such as subjective factors (human relationships and memories) and objective factors (natural and built environment) have been investigated. As a conclusion, some strategies are proposed for improving social interactions in historical public squares like; holding cultural, national, athletic and religious events, defining different and new functions in public squares’ surrounding, increasing pedestrian routs, reviving the collective memory, demonstrating the historical importance of square, eliminating visual obstacles across the square, organization the natural elements of the square, appropriate pavement for social activities. Finally, it is argued that the combination of all influencing factors which are: human interactions, natural elements and built environment criteria will lead to enhance the historical public squares’ potential for social interaction.

Keywords: Historical Square, Iranian Public Square, Social Interaction, Tehran.

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Authors: Nnamdi I. Nwulu, Shola G. Oroja

Abstract:

It has become crucial over the years for nations to improve their credit scoring methods and techniques in light of the increasing volatility of the global economy. Statistical methods or tools have been the favoured means for this; however artificial intelligence or soft computing based techniques are becoming increasingly preferred due to their proficient and precise nature and relative simplicity. This work presents a comparison between Support Vector Machines and Artificial Neural Networks two popular soft computing models when applied to credit scoring. Amidst the different criteria-s that can be used for comparisons; accuracy, computational complexity and processing times are the selected criteria used to evaluate both models. Furthermore the German credit scoring dataset which is a real world dataset is used to train and test both developed models. Experimental results obtained from our study suggest that although both soft computing models could be used with a high degree of accuracy, Artificial Neural Networks deliver better results than Support Vector Machines.

Keywords: Artificial Neural Networks, Credit Scoring, SoftComputing Models, Support Vector Machines.

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Authors: Erna T. Herdiani, Maman A. Djauhari

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In recent years, the use of vector variance as a measure of multivariate variability has received much attention in wide range of statistics. This paper deals with a more economic measure of multivariate variability, defined as vector variance minus all duplication elements. For high dimensional data, this will increase the computational efficiency almost 50 % compared to the original vector variance. Its sampling distribution will be investigated to make its applications possible.

Keywords: Asymptotic distribution, covariance matrix, likelihood ratio test, vector variance.

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Authors: Bhupendra C. S. Chauhan, P. S. Bisht, O. P. S. Negi

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According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient, divergence and curl in seven dimension. It is shown that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We have tried to write all the vector inequalities and formulas in terms of seven dimensions and it is shown that same formulas loose their meaning in seven dimensions due to non-associativity of octonions. The vector formulas are retained only if we put certain restrictions on octonions and split octonions.

Keywords: Octonions, Vector Space and seven dimensions

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Authors: Hyunchul Ahn, William X. S. Wong

Abstract:

Corporate credit rating prediction is one of the most important topics, which has been studied by researchers in the last decade. Over the last decade, researchers are pushing the limit to enhance the exactness of the corporate credit rating prediction model by applying several data-driven tools including statistical and artificial intelligence methods. Among them, multiclass support vector machine (MSVM) has been widely applied due to its good predictability. However, heuristics, for example, parameters of a kernel function, appropriate feature and instance subset, has become the main reason for the critics on MSVM, as they have dictate the MSVM architectural variables. This study presents a hybrid MSVM model that is intended to optimize all the parameter such as feature selection, instance selection, and kernel parameter. Our model adopts genetic algorithm (GA) to simultaneously optimize multiple heterogeneous design factors of MSVM.

Keywords: Corporate credit rating prediction, feature selection, genetic algorithms, instance selection, multiclass support vector machines.

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Authors: Edward Guillén, Jeisson Sánchez, Carlos Omar Ramos

Abstract:

In recent years, a wide variety of applications are developed with Support Vector Machines -SVM- methods and Artificial Neural Networks -ANN-. In general, these methods depend on intrusion knowledge databases such as KDD99, ISCX, and CAIDA among others. New classes of detectors are generated by machine learning techniques, trained and tested over network databases. Thereafter, detectors are employed to detect anomalies in network communication scenarios according to user’s connections behavior. The first detector based on training dataset is deployed in different real-world networks with mobile and non-mobile devices to analyze the performance and accuracy over static detection. The vulnerabilities are based on previous work in telemedicine apps that were developed on the research group. This paper presents the differences on detections results between some network scenarios by applying traditional detectors deployed with artificial neural networks and support vector machines.

Keywords: Anomaly detection, back-propagation neural networks, network intrusion detection systems, support vector machines.

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Authors: Rajneesh Rani, Renu Dhir, G. S. Lehal

Abstract:

Script identification is one of the challenging steps in the development of optical character recognition system for bilingual or multilingual documents. In this paper an attempt is made for identification of English numerals at word level from Punjabi documents by using Gabor features. The support vector machine (SVM) classifier with five fold cross validation is used to classify the word images. The results obtained are quite encouraging. Average accuracy with RBF kernel, Polynomial and Linear Kernel functions comes out to be greater than 99%.

Keywords: Script identification, gabor features, support vector machines.

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Authors: Gehad S. Kaseb, Mona F. Ahmed

Abstract:

Arabic Sentiment Analysis (SA) is one of the most common research fields with many open areas. This paper proposes different pre-processing steps and a modified methodology to improve the accuracy using normal Support Vector Machine (SVM) classification. The paper works on two datasets, Arabic Sentiment Tweets Dataset (ASTD) and Extended Arabic Tweets Sentiment Dataset (Extended-ATSD), which are publicly available for academic use. The results show that the classification accuracy approaches 86%.

Keywords: Arabic, hybrid classification, sentiment analysis, tweets.

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Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu

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In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

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Authors: Hamdi Melih Saraoğlu, Muhlis Yıldırım, Abdurrahman Özbeyaz, Feyzullah Temurtas

Abstract:

In this research, the diabetes conditions of people (healthy, prediabete and diabete) were tried to be identified with noninvasive palm perspiration measurements. Data clusters gathered from 200 subjects were used (1.Individual Attributes Cluster and 2. Palm Perspiration Attributes Cluster). To decrase the dimensions of these data clusters, Principal Component Analysis Method was used. Data clusters, prepared in that way, were classified with Support Vector Machines. Classifications with highest success were 82% for Glucose parameters and 84% for HbA1c parametres.

Keywords: Palm perspiration, Diabetes, Support Vector Machine, Classification.

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Authors: Dileep Kumar Gupta, Rajendra Prasad, Pradeep Kumar, Varun Narayan Mishra, Ajeet Kumar Vishwakarma, Prashant Kumar Srivastava

Abstract:

An approach was evaluated for the retrieval of soil moisture of bare soil surface using bistatic scatterometer data in the angular range of 200 to 700 at VV- and HH- polarization. The microwave data was acquired by specially designed X-band (10 GHz) bistatic scatterometer. The linear regression analysis was done between scattering coefficients and soil moisture content to select the suitable incidence angle for retrieval of soil moisture content. The 250 incidence angle was found more suitable. The support vector regression analysis was used to approximate the function described by the input output relationship between the scattering coefficient and corresponding measured values of the soil moisture content. The performance of support vector regression algorithm was evaluated by comparing the observed and the estimated soil moisture content by statistical performance indices %Bias, root mean squared error (RMSE) and Nash-Sutcliffe Efficiency (NSE). The values of %Bias, root mean squared error (RMSE) and Nash-Sutcliffe Efficiency (NSE) were found 2.9451, 1.0986 and 0.9214 respectively at HHpolarization. At VV- polarization, the values of %Bias, root mean squared error (RMSE) and Nash-Sutcliffe Efficiency (NSE) were found 3.6186, 0.9373 and 0.9428 respectively.

Keywords: Bistatic scatterometer, soil moisture, support vector regression, RMSE, %Bias, NSE.

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Authors: Refaat M Mohamed, Ayman El-Baz, Aly A. Farag

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This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.

Keywords: Density Estimation, SVM, Learning Algorithms, Parameters Estimation.

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Authors: Muhammad Awais Shafique, Eiji Hato, Hideki Yaginuma

Abstract:

Recently GPS data is used in a lot of studies to automatically reconstruct travel patterns for trip survey. The aim is to minimize the use of questionnaire surveys and travel diaries so as to reduce their negative effects. In this paper data acquired from GPS and accelerometer embedded in smart phones is utilized to predict the mode of transportation used by the phone carrier. For prediction, Support Vector Machine (SVM) and Adaptive boosting (AdaBoost) are employed. Moreover a unique method to improve the prediction results from these algorithms is also proposed. Results suggest that the prediction accuracy of AdaBoost after improvement is relatively better than the rest.

Keywords: Accelerometer, AdaBoost, GPS, Mode Prediction, Support vector Machine.

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