Search results for: SVM classification

Authors: Laurent Letrilliart, Anne-Katty Bacis, François Mennerat, Cyrille Colin

Abstract:

The International Classification of Primary Care (ICPC), which belongs to the WHO Family of International Classifications (WHO-FIC), has a low granularity, which is convenient for describing general medical practice. However, its lack of specificity makes it useful to be used along with an interface terminology. An international survey has been performed, using a questionnaire sent by email to experts from 25 countries, in order to describe the terminologies interfacing with ICPC. Eleven interface terminologies have been identified, developed in Argentina, Australia, Belgium (2), Canada, Denmark, France, Germany, Norway, South Africa, and The Netherlands. Globally, these systems have been poorly assessed until now.

Keywords: Terminology, controlled vocabulary, thesaurus, classification, International Classification of Primary Care.

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Authors: Amr Mansour Mohsen, Hesham Ahmed Hassan, Amira M. Idrees

Abstract:

Emotions classification of text documents is applied to reveal if the document expresses a determined emotion from its writer. As different supervised methods are previously used for emotion documents’ classification, in this research we present a novel model that supports the classification algorithms for more accurate results by the support of TF-IDF measure. Different experiments have been applied to reveal the applicability of the proposed model, the model succeeds in raising the accuracy percentage according to the determined metrics (precision, recall, and f-measure) based on applying the refinement of the lexicon, integration of lexicons using different perspectives, and applying the TF-IDF weighting measure over the classifying features. The proposed model has also been compared with other research to prove its competence in raising the results’ accuracy.

Keywords: Emotion detection, TF-IDF, WEKA tool, classification algorithms.

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Authors: G. Dimauro, S. Impedovo, M.G. Lucchese, R. Modugno, G. Pirlo

Abstract:

This paper presents the analysis of similarity between local decisions, in the process of alphanumeric hand-prints classification. From the analysis of local characteristics of handprinted numerals and characters, extracted by a zoning method, the set of classification decisions is obtained and the similarity among them is investigated. For this purpose the Similarity Index is used, which is an estimator of similarity between classifiers, based on the analysis of agreements between their decisions. The experimental tests, carried out using numerals and characters from the CEDAR and ETL database, respectively, show to what extent different parts of the patterns provide similar classification decisions.

Keywords: Handwriting Recognition, Optical Character Recognition, Similarity Index, Zoning.

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Authors: Gregor A. Morrison, Dominic P. Searson, Mark J. Willis

Abstract:

The purpose of this paper is to demonstrate the ability of a genetic programming (GP) algorithm to evolve a team of data classification models. The GP algorithm used in this work is “multigene" in nature, i.e. there are multiple tree structures (genes) that are used to represent team members. Each team member assigns a data sample to one of a fixed set of output classes. A majority vote, determined using the mode (highest occurrence) of classes predicted by the individual genes, is used to determine the final class prediction. The algorithm is tested on a binary classification problem. For the case study investigated, compact classification models are obtained with comparable accuracy to alternative approaches.

Keywords: classification, genetic programming.

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Authors: Hema C. R., Paulraj M. P., S. Yaacob, A. H. Adom, R. Nagarajan

Abstract:

Motor imagery classification provides an important basis for designing Brain Machine Interfaces [BMI]. A BMI captures and decodes brain EEG signals and transforms human thought into actions. The ability of an individual to control his EEG through imaginary mental tasks enables him to control devices through the BMI. This paper presents a method to design a four state BMI using EEG signals recorded from the C3 and C4 locations. Principle features extracted through principle component analysis of the segmented EEG are analyzed using two novel classification algorithms using Elman recurrent neural network and functional link neural network. Performance of both classifiers is evaluated using a particle swarm optimization training algorithm; results are also compared with the conventional back propagation training algorithm. EEG motor imagery recorded from two subjects is used in the offline analysis. From overall classification performance it is observed that the BP algorithm has higher average classification of 93.5%, while the PSO algorithm has better training time and maximum classification. The proposed methods promises to provide a useful alternative general procedure for motor imagery classification

Keywords: Motor Imagery, Brain Machine Interfaces, Neural Networks, Particle Swarm Optimization, EEG signal processing.

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Authors: Thinh Ngo, Paul Rad, Brian Kelley

Abstract:

Noise estimation is essential in today wireless systems for power control, adaptive modulation, interference suppression and quality of service. Deep learning (DL) has already been applied in the physical layer for modulation and signal classifications. Unacceptably low accuracy of less than 50% is found to undermine traditional application of DL classification for SNR prediction. In this paper, we use divide-and-conquer algorithm and classifier fusion method to simplify SNR classification and therefore enhances DL learning and prediction. Specifically, multiple CNNs are used for classification rather than a single CNN. Each CNN performs a binary classification of a single SNR with two labels: less than, greater than or equal. Together, multiple CNNs are combined to effectively classify over a range of SNR values from −20 ≤ SNR ≤ 32 dB.We use pre-trained CNNs to predict SNR over a wide range of joint channel parameters including multiple Doppler shifts (0, 60, 120 Hz), power-delay profiles, and signal-modulation types (QPSK,16QAM,64-QAM). The approach achieves individual SNR prediction accuracy of 92%, composite accuracy of 70% and prediction convergence one order of magnitude faster than that of traditional estimation.

Keywords: Classification, classifier fusion, CNN, Deep Learning, prediction, SNR.

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Authors: Yueming Wang, Rendong Ying, Sumxin Jiang, Peilin Liu

Abstract:

Unified Speech Audio Coding (USAC), the latest MPEG standardization for unified speech and audio coding, uses a speech/audio classification algorithm to distinguish speech and audio segments of the input signal. The quality of the recovered audio can be increased by well-designed orchestra/percussion classification and subsequent processing. However, owing to the shortcoming of the system, introducing an orchestra/percussion classification and modifying subsequent processing can enormously increase the quality of the recovered audio. This paper proposes an orchestra/percussion classification algorithm for the USAC system which only extracts 3 scales of Mel-Frequency Cepstral Coefficients (MFCCs) rather than traditional 13 scales of MFCCs and use Iterative Dichotomiser 3 (ID3) Decision Tree rather than other complex learning method, thus the proposed algorithm has lower computing complexity than most existing algorithms. Considering that frequent changing of attributes may lead to quality loss of the recovered audio signal, this paper also design a modified subsequent process to help the whole classification system reach an accurate rate as high as 97% which is comparable to classical 99%.

Keywords: ID3 Decision Tree, MFCC, Orchestra/Percussion Classification, USAC

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Authors: Rui Antunes, Fernando V. Coito

Abstract:

This article presents the development of a neural network cognitive model for the classification and detection of different frequency signals. The basic structure of the implemented neural network was inspired on the perception process that humans generally make in order to visually distinguish between high and low frequency signals. It is based on the dynamic neural network concept, with delays. A special two-layer feedforward neural net structure was successfully implemented, trained and validated, to achieve minimum target error. Training confirmed that this neural net structure descents and converges to a human perception classification solution, even when far away from the target.

Keywords: Neural Networks, Signal Classification, Adaptative Filters, Cognitive Neuroscience

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Authors: R. K. Chaurasiya, N. D. Londhe, S. Ghosh

Abstract:

The study of the electrical signals produced by neural activities of human brain is called Electroencephalography. In this paper, we propose an automatic and efficient EEG signal classification approach. The proposed approach is used to classify the EEG signal into two classes: epileptic seizure or not. In the proposed approach, we start with extracting the features by applying Discrete Wavelet Transform (DWT) in order to decompose the EEG signals into sub-bands. These features, extracted from details and approximation coefficients of DWT sub-bands, are used as input to Principal Component Analysis (PCA). The classification is based on reducing the feature dimension using PCA and deriving the supportvectors using Support Vector Machine (SVM). The experimental are performed on real and standard dataset. A very high level of classification accuracy is obtained in the result of classification.

Keywords: Discrete Wavelet Transform, Electroencephalogram, Pattern Recognition, Principal Component Analysis, Support Vector Machine.

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Authors: Saleh Mesbah Elkaffas, Ahmed A. Toony

Abstract:

This paper details the application of a genetic programming framework for induction of useful classification rules from a database of income statements, balance sheets, and cash flow statements for North American public companies. Potentially interesting classification rules are discovered. Anomalies in the discovery process merit further investigation of the application of genetic programming to the dataset for the problem domain.

Keywords: Genetic programming, data mining classification rule.

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Authors: Darren Thompson, Philip Morrow, Bryan Scotney, John Winder

Abstract:

Patients with diabetes are susceptible to chronic foot wounds which may be difficult to manage and slow to heal. Diagnosis and treatment currently rely on the subjective judgement of experienced professionals. An objective method of tissue assessment is required. In this paper, a data fusion approach was taken to wound tissue classification. The supervised Maximum Likelihood and unsupervised Multi-Modal Expectation Maximisation algorithms were used to classify tissues within simulated wound models by weighting the contributions of both colour and 3D depth information. It was found that, at low weightings, depth information could show significant improvements in classification accuracy when compared to classification by colour alone, particularly when using the maximum likelihood method. However, larger weightings were found to have an entirely negative effect on accuracy.

Keywords: Classification, data fusion, diabetic foot, stereophotogrammetry, tissue colour.

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Authors: Vesile Evrim, Aliyu Awwal

Abstract:

Today, there is a large number of political transcripts available on the Web to be mined and used for statistical analysis, and product recommendations. As the online political resources are used for various purposes, automatically determining the political orientation on these transcripts becomes crucial. The methodologies used by machine learning algorithms to do an automatic classification are based on different features that are classified under categories such as Linguistic, Personality etc. Considering the ideological differences between Liberals and Conservatives, in this paper, the effect of Personality traits on political orientation classification is studied. The experiments in this study were based on the correlation between LIWC features and the BIG Five Personality traits. Several experiments were conducted using Convote U.S. Congressional- Speech dataset with seven benchmark classification algorithms. The different methodologies were applied on several LIWC feature sets that constituted by 8 to 64 varying number of features that are correlated to five personality traits. As results of experiments, Neuroticism trait was obtained to be the most differentiating personality trait for classification of political orientation. At the same time, it was observed that the personality trait based classification methodology gives better and comparable results with the related work.

Keywords: Politics, personality traits, LIWC, machine learning.

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Authors: Andrey V. Timofeev

Abstract:

This paper introduces an original method for guaranteed estimation of the accuracy for an ensemble of Lipschitz classifiers. The solution was obtained as a finite closed set of alternative hypotheses, which contains an object of classification with probability of not less than the specified value. Thus, the classification is represented by a set of hypothetical classes. In this case, the smaller the cardinality of the discrete set of hypothetical classes is, the higher is the classification accuracy. Experiments have shown that if cardinality of the classifiers ensemble is increased then the cardinality of this set of hypothetical classes is reduced. The problem of the guaranteed estimation of the accuracy for an ensemble of Lipschitz classifiers is relevant in multichannel classification of target events in C-OTDR monitoring systems. Results of suggested approach practical usage to accuracy control in C-OTDR monitoring systems are present.

Keywords: Lipschitz classifiers, confidence set, C-OTDR monitoring, classifiers accuracy, classifiers ensemble.

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Authors: Jia Xin Low, Keng Wah Choo

Abstract:

This paper presents an automatic normal and abnormal heart sound classification model developed based on deep learning algorithm. MITHSDB heart sounds datasets obtained from the 2016 PhysioNet/Computing in Cardiology Challenge database were used in this research with the assumption that the electrocardiograms (ECG) were recorded simultaneously with the heart sounds (phonocardiogram, PCG). The PCG time series are segmented per heart beat, and each sub-segment is converted to form a square intensity matrix, and classified using convolutional neural network (CNN) models. This approach removes the need to provide classification features for the supervised machine learning algorithm. Instead, the features are determined automatically through training, from the time series provided. The result proves that the prediction model is able to provide reasonable and comparable classification accuracy despite simple implementation. This approach can be used for real-time classification of heart sounds in Internet of Medical Things (IoMT), e.g. remote monitoring applications of PCG signal.

Keywords: Convolutional neural network, discrete wavelet transform, deep learning, heart sound classification.

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Authors: Hooman Hoodat, Hassan Rashidi

Abstract:

Despite various methods that exist in software risk management, software projects have a high rate of failure. When complexity and size of the projects are increased, managing software development becomes more difficult. In these projects the need for more analysis and risk assessment is vital. In this paper, a classification for software risks is specified. Then relations between these risks using risk tree structure are presented. Analysis and assessment of these risks are done using probabilistic calculations. This analysis helps qualitative and quantitative assessment of risk of failure. Moreover it can help software risk management process. This classification and risk tree structure can apply to some software tools.

Keywords: Risk analysis, risk assessment, risk classification, risk tree.

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Authors: Benjamin Y. M. Kwan, Jennifer Y. Y. Kwan, Hon Keung Kwan

Abstract:

In the paper, the relative performances on spectral classification of short exon and intron sequences of the human and eleven model organisms is studied. In the simulations, all combinations of sixteen one-sequence numerical representations, four threshold values, and four window lengths are considered. Sequences of 150-base length are chosen and for each organism, a total of 16,000 sequences are used for training and testing. Results indicate that an appropriate combination of one-sequence numerical representation, threshold value, and window length is essential for arriving at top spectral classification results. For fixed-length sequences, the precisions on exon and intron classification obtained for different organisms are not the same because of their genomic differences. In general, precision increases as sequence length increases.

Keywords: Exons and introns classification, Human genome, Model organism genome, Spectral analysis

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Authors: Mahesh Pal

Abstract:

This paper proposes to use ETM+ multispectral data and panchromatic band as well as texture features derived from the panchromatic band for land cover classification. Four texture features including one 'internal texture' and three GLCM based textures namely correlation, entropy, and inverse different moment were used in combination with ETM+ multispectral data. Two data sets involving combination of multispectral, panchromatic band and its texture were used and results were compared with those obtained by using multispectral data alone. A decision tree classifier with and without boosting were used to classify different datasets. Results from this study suggest that the dataset consisting of panchromatic band, four of its texture features and multispectral data was able to increase the classification accuracy by about 2%. In comparison, a boosted decision tree was able to increase the classification accuracy by about 3% with the same dataset.

Keywords: Internal texture; GLCM; decision tree; boosting; classification accuracy.

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Authors: Ehsan Amid, Sina Rezaei Aghdam

Abstract:

In this paper, a novel method for recognition of musical instruments in a polyphonic music is presented by using an embedded hidden Markov model (EHMM). EHMM is a doubly embedded HMM structure where each state of the external HMM is an independent HMM. The classification is accomplished for two different internal HMM structures where GMMs are used as likelihood estimators for the internal HMMs. The results are compared to those achieved by an artificial neural network with two hidden layers. Appropriate classification accuracies were achieved both for solo instrument performance and instrument combinations which demonstrates that the new approach outperforms the similar classification methods by means of the dynamic of the signal.

Keywords: hidden Markov model (HMM), embedded hidden Markov models (EHMM), MFCC, musical instrument.

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Authors: Walid Cherif

Abstract:

Data mining has, over recent years, seen big advances because of the spread of internet, which generates everyday a tremendous volume of data, and also the immense advances in technologies which facilitate the analysis of these data. In particular, classification techniques are a subdomain of Data Mining which determines in which group each data instance is related within a given dataset. It is used to classify data into different classes according to desired criteria. Generally, a classification technique is either statistical or machine learning. Each type of these techniques has its own limits. Nowadays, current data are becoming increasingly heterogeneous; consequently, current classification techniques are encountering many difficulties. This paper defines new measure functions to quantify the resemblance between instances and then combines them in a new approach which is different from actual algorithms by its reliability computations. Results of the proposed approach exceeded most common classification techniques with an f-measure exceeding 97% on the IRIS Dataset.

Keywords: Data mining, knowledge discovery, machine learning, similarity measurement, supervised classification.

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Authors: R. Mallika, V. Saravanan

Abstract:

This paper gives a novel method for improving classification performance for cancer classification with very few microarray Gene expression data. The method employs classification with individual gene ranking and gene subset ranking. For selection and classification, the proposed method uses the same classifier. The method is applied to three publicly available cancer gene expression datasets from Lymphoma, Liver and Leukaemia datasets. Three different classifiers namely Support vector machines-one against all (SVM-OAA), K nearest neighbour (KNN) and Linear Discriminant analysis (LDA) were tested and the results indicate the improvement in performance of SVM-OAA classifier with satisfactory results on all the three datasets when compared with the other two classifiers.

Keywords: Support vector machines-one against all, cancerclassification, Linear Discriminant analysis, K nearest neighbour, microarray gene expression, gene pair ranking.

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Authors: H. Khorashadi-Zadeh, M. R. Aghaebrahimi

Abstract:

A novel application of neural network approach to fault classification and fault location of Medium voltage cables is demonstrated in this paper. Different faults on a protected cable should be classified and located correctly. This paper presents the use of neural networks as a pattern classifier algorithm to perform these tasks. The proposed scheme is insensitive to variation of different parameters such as fault type, fault resistance, and fault inception angle. Studies show that the proposed technique is able to offer high accuracy in both of the fault classification and fault location tasks.

Keywords: Artificial neural networks, cable, fault location andfault classification.

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Authors: Jatinderkumar R. Saini, Apurva A. Desai

Abstract:

In recent times, the problem of Unsolicited Bulk Email (UBE) or commonly known as Spam Email, has increased at a tremendous growth rate. We present an analysis of survey based on classifications of UBE in various research works. There are many research instances for classification between spam and non-spam emails but very few research instances are available for classification of spam emails, per se. This paper does not intend to assert some UBE classification to be better than the others nor does it propose any new classification but it bemoans the lack of harmony on number and definition of categories proposed by different researchers. The paper also elaborates on factors like intent of spammer, content of UBE and ambiguity in different categories as proposed in related research works of classifications of UBE.

Keywords: E-mail, Scams, Spam Email, Unsolicited Bulk Email(UBE)

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Authors: Mahesh Pal

Abstract:

In recent years, a number of works proposing the combination of multiple classifiers to produce a single classification have been reported in remote sensing literature. The resulting classifier, referred to as an ensemble classifier, is generally found to be more accurate than any of the individual classifiers making up the ensemble. As accuracy is the primary concern, much of the research in the field of land cover classification is focused on improving classification accuracy. This study compares the performance of four ensemble approaches (boosting, bagging, DECORATE and random subspace) with a univariate decision tree as base classifier. Two training datasets, one without ant noise and other with 20 percent noise was used to judge the performance of different ensemble approaches. Results with noise free data set suggest an improvement of about 4% in classification accuracy with all ensemble approaches in comparison to the results provided by univariate decision tree classifier. Highest classification accuracy of 87.43% was achieved by boosted decision tree. A comparison of results with noisy data set suggests that bagging, DECORATE and random subspace approaches works well with this data whereas the performance of boosted decision tree degrades and a classification accuracy of 79.7% is achieved which is even lower than that is achieved (i.e. 80.02%) by using unboosted decision tree classifier.

Keywords: Ensemble learning, decision tree, remote sensingclassification.

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Authors: Omer Nebil Yaveroglu, Tolga Can

Abstract:

In this study, a high accuracy protein-protein interaction prediction method is developed. The importance of the proposed method is that it only uses sequence information of proteins while predicting interaction. The method extracts phylogenetic profiles of proteins by using their sequence information. Combining the phylogenetic profiles of two proteins by checking existence of homologs in different species and fitting this combined profile into a statistical model, it is possible to make predictions about the interaction status of two proteins. For this purpose, we apply a collection of pattern recognition techniques on the dataset of combined phylogenetic profiles of protein pairs. Support Vector Machines, Feature Extraction using ReliefF, Naive Bayes Classification, K-Nearest Neighborhood Classification, Decision Trees, and Random Forest Classification are the methods we applied for finding the classification method that best predicts the interaction status of protein pairs. Random Forest Classification outperformed all other methods with a prediction accuracy of 76.93%

Keywords: Protein Interaction Prediction, Phylogenetic Profile, SVM , ReliefF, Decision Trees, Random Forest Classification

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Authors: Samy Sadek, Ayoub Al-Hamadi, Bernd Michaelis, Usama Sayed

Abstract:

In this paper, we propose a supervised method for color image classification based on a multilevel sigmoidal neural network (MSNN) model. In this method, images are classified into five categories, i.e., “Car", “Building", “Mountain", “Farm" and “Coast". This classification is performed without any segmentation processes. To verify the learning capabilities of the proposed method, we compare our MSNN model with the traditional Sigmoidal Neural Network (SNN) model. Results of comparison have shown that the MSNN model performs better than the traditional SNN model in the context of training run time and classification rate. Both color moments and multi-level wavelets decomposition technique are used to extract features from images. The proposed method has been tested on a variety of real and synthetic images.

Keywords: Image classification, multi-level neural networks, feature extraction, wavelets decomposition.

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Authors: Bremananth R, Nithya B, Saipriya R

Abstract:

The proposed system identifies the species of the wood using the textural features present in its barks. Each species of a wood has its own unique patterns in its bark, which enabled the proposed system to identify it accurately. Automatic wood recognition system has not yet been well established mainly due to lack of research in this area and the difficulty in obtaining the wood database. In our work, a wood recognition system has been designed based on pre-processing techniques, feature extraction and by correlating the features of those wood species for their classification. Texture classification is a problem that has been studied and tested using different methods due to its valuable usage in various pattern recognition problems, such as wood recognition, rock classification. The most popular technique used for the textural classification is Gray-level Co-occurrence Matrices (GLCM). The features from the enhanced images are thus extracted using the GLCM is correlated, which determines the classification between the various wood species. The result thus obtained shows a high rate of recognition accuracy proving that the techniques used in suitable to be implemented for commercial purposes.

Keywords: Correlation, Grey Level Co-Occurrence Matrix, ProbabilityDensity Function, Wood Recognition.

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Authors: N. Deetae, S. Sukparungsee, Y. Areepong, K. Jampachaisri

Abstract:

This research is aimed to compare the percentages of correct classification of Empirical Bayes method (EB) to Classical method when data are constructed as near normal, short-tailed and long-tailed symmetric, short-tailed and long-tailed asymmetric. The study is performed using conjugate prior, normal distribution with known mean and unknown variance. The estimated hyper-parameters obtained from EB method are replaced in the posterior predictive probability and used to predict new observations. Data are generated, consisting of training set and test set with the sample sizes 100, 200 and 500 for the binary classification. The results showed that EB method exhibited an improved performance over Classical method in all situations under study.

Keywords: Classification, Empirical Bayes, Posterior predictive probability.

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Authors: A. Shukla, A. Tarsauliya, R. Tiwari, S. Sharma

Abstract:

Cancer classification to their corresponding cohorts has been key area of research in bioinformatics aiming better prognosis of the disease. High dimensionality of gene data has been makes it a complex task and requires significance data identification technique in order to reducing the dimensionality and identification of significant information. In this paper, we have proposed a novel approach for classification of oral cancer into metastasis positive and negative patients. We have used significance analysis of microarrays (SAM) for identifying significant genes which constitutes gene signature. 3 different gene signatures were identified using SAM from 3 different combination of training datasets and their classification accuracy was calculated on corresponding testing datasets using k-Nearest Neighbour (kNN), Fuzzy C-Means Clustering (FCM), Support Vector Machine (SVM) and Backpropagation Neural Network (BPNN). A final gene signature of only 9 genes was obtained from above 3 individual gene signatures. 9 gene signature-s classification capability was compared using same classifiers on same testing datasets. Results obtained from experimentation shows that 9 gene signature classified all samples in testing dataset accurately while individual genes could not classify all accurately.

Keywords: Cancer, Gene Signature, SAM, Classification.

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Authors: M. Nemissi, H. Seridi, H. Akdag

Abstract:

This paper presents and evaluates a new classification method that aims to improve classifiers performances and speed up their training process. The proposed approach, called labeled classification, seeks to improve convergence of the BP (Back propagation) algorithm through the addition of an extra feature (labels) to all training examples. To classify every new example, tests will be carried out each label. The simplicity of implementation is the main advantage of this approach because no modifications are required in the training algorithms. Therefore, it can be used with others techniques of acceleration and stabilization. In this work, two models of the labeled classification are proposed: the LMLP (Labeled Multi Layered Perceptron) and the LNFC (Labeled Neuro Fuzzy Classifier). These models are tested using Iris, wine, texture and human thigh databases to evaluate their performances.

Keywords: Artificial neural networks, Fusion of neural networkfuzzysystems, Learning theory, Pattern recognition.

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Authors: Yong-Quan Zhou, Deng-Xu He, Zheng Nong

Abstract:

In this paper two models using a functional network were employed to solving classification problem. Functional networks are generalized neural networks, which permit the specification of their initial topology using knowledge about the problem at hand. In this case, and after analyzing the available data and their relations, we systematically discuss a numerical analysis method used for functional network, and apply two functional network models to solving XOR problem. The XOR problem that cannot be solved with two-layered neural network can be solved by two-layered functional network, which reveals a potent computational power of functional networks, and the performance of the proposed model was validated using classification problems.

Keywords: Functional network, neural network, XOR problem, classification, numerical analysis method.

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