Bayes Formula

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V P Kallimani - One of the best experts on this subject based on the ideXlab platform.

  • using the self organizing map for clustering of text documents
    Expert Systems With Applications, 2009
    Co-Authors: Dino Isa, V P Kallimani, Lam Hong Lee
    Abstract:

    An increasing number of computational and statistical approaches have been used for text classification, including nearest-neighbor classification, naive Bayes classification, support vector machines, decision tree induction, rule induction, and artificial neural networks. Among these approaches, naive Bayes classifiers have been widely used because of its simplicity. Due to the simplicity of the Bayes Formula, the naive Bayes classification algorithm requires a relatively small number of training data and shorter time in both the training and classification stages as compared to other classifiers. However, a major short coming of this technique is the fact that the classifier will pick the highest probability category as the one to which the document is annotated too. Doing this is tantamount to classifying using only one dimension of a multi-dimensional data set. The main aim of this work is to utilize the strengths of the self organizing map (SOM) to overcome the inadvertent dimensionality reduction resulting from using only the Bayes Formula to classify. Combining the hybrid system with new ranking techniques further improves the performance of the proposed document classification approach. This work describes the implementation of an enhanced hybrid classification approach which affords a better classification accuracy through the utilization of two familiar algorithms, the naive Bayes classification algorithm which is used to vectorize the document using a probability distribution and the self organizing map (SOM) clustering algorithm which is used as the multi-dimensional unsupervised classifier.

  • text document pre processing using the Bayes Formula for classification based on the vector space model
    Computer and Information Science, 2008
    Co-Authors: Dino Isa, V P Kallimani, Lee Lam Hong, Rajparthiban Kumar Rajkumar
    Abstract:

    This work utilizes the Bayes Formula to vectorize a document according to a probability distribution based on keywords reflecting the probable categories that the document may belong to. The Bayes Formula gives a range of probabilities to which the document can be assigned according to a pre determined set of topics (categories). Using this probability distribution as the vectors to represent the document, the text classification algorithms based on the vector space model, such as the Support Vector Machine (SVM) and Self-Organizing Map (SOM) can then be used to classify the documents on a multi-dimensional level, thus improving on the results obtained using only the highest probability to classify the document, such as that achieved by implementing the naive Bayes classifier by itself. The effects of an inadvertent dimensionality reduction can be overcome using these algorithms. We compare the performance of these classifiers for high dimensional data.

  • text document preprocessing with the Bayes Formula for classification using the support vector machine
    IEEE Transactions on Knowledge and Data Engineering, 2008
    Co-Authors: V P Kallimani, Rajprasad Kumar Rajkumar
    Abstract:

    This work implements an enhanced hybrid classification method through the utilization of the naive Bayes approach and the support vector machine (SVM). In this project, the Bayes Formula was used to vectorize (as opposed to classify) a document according to a probability distribution reflecting the probable categories that the document may belong to. The Bayes Formula gives a range of probabilities to which the document can be assigned according to a predetermined set of topics (categories) such as those found in the "20 Newsgroups" data set for instance. Using this probability distribution as the vectors to represent the document, the SVM can then be used to classify the documents on a multidimensional level. The effects of an inadvertent dimensionality reduction caused by classifying using only the highest probability using the naive Bayes classifier can be overcome using the SVM by employing all the probability values associated with every category for each document. This method can be used for any data set and shows a significant reduction in training time as compared to the Lsquare method and significant improvement in the classification accuracy when compared to pure naive Bayes systems and also the TF-IDF/SVM hybrids.

Wanying Yun - One of the best experts on this subject based on the ideXlab platform.

  • Efficient computational method based on AK-MCS and Bayes Formula for time-dependent failure probability function
    Structural and Multidisciplinary Optimization, 2019
    Co-Authors: Kaixuan Feng, Chunyan Ling, Wanying Yun
    Abstract:

    The time-dependent failure probability function (TDFPF) is defined as a function of the time-dependent failure probability (TDFP) varying with the design parameters and the service time, and it is useful in the reliability-based design optimization for the time-dependent problem. For the lack of method estimating TDFPF, the direct Monte Carlo simulation (DMCS) and an adaptive Kriging-MCS based on Bayes Formula (shorten as AK-MCS-Bay) are developed to estimate TDFPF. The DMCS is time-consuming, but its convergent solution can be used as reference to validate other methods. In the AK-MCS-Bay, the TDFPF is primarily transformed into the estimation of the augmented TDFP and the conditional probability density function (PDF) of design parameters on the time-dependent failure event. Then, a single AK model is constructed to efficiently identify the failure samples in the MCS sample pool at different service times. By using these identified failure samples, the TDFPs under different service times can be estimated by the double-loop MCS without any extra model evaluations, and the conditional PDF of design parameters can be also acquired by the kernel density estimation method. The numerical and engineering examples indicate the efficiency and accuracy of the proposed method.

Rajprasad Kumar Rajkumar - One of the best experts on this subject based on the ideXlab platform.

  • text document preprocessing with the Bayes Formula for classification using the support vector machine
    IEEE Transactions on Knowledge and Data Engineering, 2008
    Co-Authors: V P Kallimani, Rajprasad Kumar Rajkumar
    Abstract:

    This work implements an enhanced hybrid classification method through the utilization of the naive Bayes approach and the support vector machine (SVM). In this project, the Bayes Formula was used to vectorize (as opposed to classify) a document according to a probability distribution reflecting the probable categories that the document may belong to. The Bayes Formula gives a range of probabilities to which the document can be assigned according to a predetermined set of topics (categories) such as those found in the "20 Newsgroups" data set for instance. Using this probability distribution as the vectors to represent the document, the SVM can then be used to classify the documents on a multidimensional level. The effects of an inadvertent dimensionality reduction caused by classifying using only the highest probability using the naive Bayes classifier can be overcome using the SVM by employing all the probability values associated with every category for each document. This method can be used for any data set and shows a significant reduction in training time as compared to the Lsquare method and significant improvement in the classification accuracy when compared to pure naive Bayes systems and also the TF-IDF/SVM hybrids.

Jingyu Lei - One of the best experts on this subject based on the ideXlab platform.

  • the single loop kriging model combined with Bayes Formula for time dependent failure probability based global sensitivity
    Structures, 2021
    Co-Authors: Jingyu Lei
    Abstract:

    Abstract Time-dependent failure probability based global sensitivity (TDFP-GS) analysis quantifies the effect of input uncertainty on the failure probability for the time-dependent structure, which is usually time-consuming to be performed. For alleviating this issue, a method by combining the single-loop Kriging (SILK) model with BayesFormula is proposed in this work. After transformed by BayesFormula, the estimation of the conditional failure probability in the TDFP-GS expression is converted to that of conditional probability density function (PDF) of the input on the failure domain, which eliminates the dimensionality dependence in the calculation process. The SILK model is established to estimate the failure probability of the structure. When all the failure samples are accurately recognized by the converged SILK model, the conditional PDF can be estimated by the kernel density estimation (KDE), which doesn’t require any performance function evaluation. The TDFP-GS can be estimated by the difference between the original PDF and the conditional PDF of the input on the failure domain. Four examples are presented for validating the effectiveness and the efficiency of the proposed method.

Kaixuan Feng - One of the best experts on this subject based on the ideXlab platform.

  • Efficient computational method based on AK-MCS and Bayes Formula for time-dependent failure probability function
    Structural and Multidisciplinary Optimization, 2019
    Co-Authors: Kaixuan Feng, Chunyan Ling, Wanying Yun
    Abstract:

    The time-dependent failure probability function (TDFPF) is defined as a function of the time-dependent failure probability (TDFP) varying with the design parameters and the service time, and it is useful in the reliability-based design optimization for the time-dependent problem. For the lack of method estimating TDFPF, the direct Monte Carlo simulation (DMCS) and an adaptive Kriging-MCS based on Bayes Formula (shorten as AK-MCS-Bay) are developed to estimate TDFPF. The DMCS is time-consuming, but its convergent solution can be used as reference to validate other methods. In the AK-MCS-Bay, the TDFPF is primarily transformed into the estimation of the augmented TDFP and the conditional probability density function (PDF) of design parameters on the time-dependent failure event. Then, a single AK model is constructed to efficiently identify the failure samples in the MCS sample pool at different service times. By using these identified failure samples, the TDFPs under different service times can be estimated by the double-loop MCS without any extra model evaluations, and the conditional PDF of design parameters can be also acquired by the kernel density estimation method. The numerical and engineering examples indicate the efficiency and accuracy of the proposed method.