Lower Dimensional Space

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M R Oliveira - One of the best experts on this subject based on the ideXlab platform.

  • algorithms for projection pursuit robust principal component analysis
    Chemometrics and Intelligent Laboratory Systems, 2007
    Co-Authors: Christophe Croux, Peter Filzmoser, M R Oliveira
    Abstract:

    Principal Component Analysis (PCA) is very sensitive in presence of outliers. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a Lower-Dimensional Space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real datasets.

Hendri Murfi - One of the best experts on this subject based on the ideXlab platform.

  • monitoring trending topics of real world events on indonesian tweets using fuzzy c means in Lower Dimensional Space
    Proceedings of the 2019 3rd International Conference on Advances in Artificial Intelligence, 2019
    Co-Authors: Hendri Murfi
    Abstract:

    Topic detection is an automatic method to extract topics in textual data, i.e., trending topic in social media. One of the recent topic detection methods is EigenSpace-based Fuzzy C-Means, which is a soft clustering-based topic detection method. In this method, the textual data are transformed into a Lower-Dimensional EigenSpace using truncated singular value decomposition. Fuzzy C-Means is performed on the EigenSpace to identify the memberships of each textual data to each cluster. Using these memberships, we extract the topics from textual data on the original Space. In this paper, we use another approach to extract the topics by transforming back the centroids of the clusters into the positive subSpace of the original Space. Our simulations show that this new approach improves the old one regarding the topic interpretability in term of the coherence score. Moreover, this EigenSpace-based Fuzzy C-Means becomes better than both standard methods, i.e., nonnegative matrix factorization and latent Dirichlet allocation.

  • fuzzy c means in Lower Dimensional Space for topics detection on indonesian online news
    International Conference on Data Mining, 2019
    Co-Authors: Praditya Nugraha, Muhammad Rifky Yusdiansyah, Hendri Murfi
    Abstract:

    One of the automated methods for textual data analysis is topic detection. Fuzzy C-Means is a soft clustering-based method for topic detection. Textual data usually has a high Dimensional data, which make Fuzzy C-Means fails for topic detection. An approach to overcome the problem is transforming the textual data into Lower Dimensional Space to identify the memberships of the textual data in clusters and use these memberships to generate topics from the high Dimensional textual data in the original Space. In this paper, we apply the Fuzzy C-Means in Lower Dimensional Space for topic detection on Indonesian online news. Our simulations show that the Fuzzy C-Means gives comparable accuracies than nonnegative matrix factorization and better accuracies than latent Dirichlet allocation regarding topic interpretation in the form of coherence values.

  • DMBD - Fuzzy C-means in Lower Dimensional Space for topics detection on indonesian online news
    Data Mining and Big Data, 2019
    Co-Authors: Praditya Nugraha, Muhammad Rifky Yusdiansyah, Hendri Murfi
    Abstract:

    One of the automated methods for textual data analysis is topic detection. Fuzzy C-Means is a soft clustering-based method for topic detection. Textual data usually has a high Dimensional data, which make Fuzzy C-Means fails for topic detection. An approach to overcome the problem is transforming the textual data into Lower Dimensional Space to identify the memberships of the textual data in clusters and use these memberships to generate topics from the high Dimensional textual data in the original Space. In this paper, we apply the Fuzzy C-Means in Lower Dimensional Space for topic detection on Indonesian online news. Our simulations show that the Fuzzy C-Means gives comparable accuracies than nonnegative matrix factorization and better accuracies than latent Dirichlet allocation regarding topic interpretation in the form of coherence values.

  • the accuracy of fuzzy c means in Lower Dimensional Space for topic detection
    3rd International Conference on Smart Computing and Communications SmartCom 2018, 2018
    Co-Authors: Hendri Murfi
    Abstract:

    Topic detection is an automatic method to discover topics in textual data. The standard methods of the topic detection are nonnegative matrix factorization (NMF) and latent Dirichlet allocation (LDA). Another alternative method is a clustering approach such as a k-means and fuzzy c-means (FCM). FCM extend the k-means method in the sense that the textual data may have more than one topic. However, FCM works well for low-Dimensional textual data and fails for high-Dimensional textual data. An approach to overcome the problem is transforming the textual data into Lower Dimensional Space, i.e., EigenSpace, and called EigenSpace-based FCM (EFCM). Firstly, the textual data are transformed into an EigenSpace using truncated singular value decomposition. FCM is performed on the eigenSpace data to identify the memberships of the textual data in clusters. Using these memberships, we generate topics from the high Dimensional textual data in the original Space. In this paper, we examine the accuracy of EFCM for topic detection. Our simulations show that EFCM results in the accuracies between the accuracies of LDA and NMF regarding both topic interpretation and topic recall.

  • SmartCom - The Accuracy of Fuzzy C-Means in Lower-Dimensional Space for Topic Detection
    Lecture Notes in Computer Science, 2018
    Co-Authors: Hendri Murfi
    Abstract:

    Topic detection is an automatic method to discover topics in textual data. The standard methods of the topic detection are nonnegative matrix factorization (NMF) and latent Dirichlet allocation (LDA). Another alternative method is a clustering approach such as a k-means and fuzzy c-means (FCM). FCM extend the k-means method in the sense that the textual data may have more than one topic. However, FCM works well for low-Dimensional textual data and fails for high-Dimensional textual data. An approach to overcome the problem is transforming the textual data into Lower Dimensional Space, i.e., EigenSpace, and called EigenSpace-based FCM (EFCM). Firstly, the textual data are transformed into an EigenSpace using truncated singular value decomposition. FCM is performed on the eigenSpace data to identify the memberships of the textual data in clusters. Using these memberships, we generate topics from the high Dimensional textual data in the original Space. In this paper, we examine the accuracy of EFCM for topic detection. Our simulations show that EFCM results in the accuracies between the accuracies of LDA and NMF regarding both topic interpretation and topic recall.

Christophe Croux - One of the best experts on this subject based on the ideXlab platform.

  • algorithms for projection pursuit robust principal component analysis
    Chemometrics and Intelligent Laboratory Systems, 2007
    Co-Authors: Christophe Croux, Peter Filzmoser, M R Oliveira
    Abstract:

    Principal Component Analysis (PCA) is very sensitive in presence of outliers. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a Lower-Dimensional Space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real datasets.

  • GfKl - Robust Multivariate Methods: The Projection Pursuit Approach
    From Data and Information Analysis to Knowledge Engineering, 2006
    Co-Authors: Peter Filzmoser, Christophe Croux, Sven Serneels, Pierre J. Van Espen
    Abstract:

    Projection pursuit was originally introduced to identify structures in multivariate data clouds (Huber, 1985). The idea of projecting data to a low-Dimensional subSpace can also be applied to multivariate statistical methods. The robustness of the methods can be achieved by applying robust estimators to the Lower-Dimensional Space. Robust estimation in high dimensions can thus be avoided which usually results in a faster computation. Moreover, flat data sets where the number of variables is much higher than the number of observations can be easier analyzed in a robust way.

Junyi Shen - One of the best experts on this subject based on the ideXlab platform.

  • Classification of multivariate time series using locality preserving projections
    Knowledge-Based Systems, 2008
    Co-Authors: Xiaoqing Weng, Junyi Shen
    Abstract:

    Multivariate time series (MTS) are used in very broad areas such as multimedia, medicine, finance and speech recognition. A new approach for MTS classification using locality preserving projections (LPP) is proposed. By using LPP, the MTS samples can be projected into a Lower-Dimensional Space in which the MTS samples related to the same class are close to each other, the MTS samples in testing set can be identified by one-nearest-neighbor classifier in the Lower-Dimensional Space. Experimental results performed on five real-world datasets demonstrate the effectiveness of our proposed approach for MTS classification.

  • Time Series Classification Using Locality Preserving Projections
    2007 IEEE International Conference on Automation and Logistics, 2007
    Co-Authors: Xiaoqing Weng, Junyi Shen
    Abstract:

    The time series is generally of high Dimensionality and classifying in such a high Dimensional Space is often infeasible due to the curse of Dimensionality. We propose a new time series classifying method, which aims to classify the time series into different classes. By using locality preserving projections (LPP), the time series can be projected into a Lower-Dimensional Space in which the time series related to the same class are close to each other, the time series in testing set can be identified by one-nearest-neighbor classifier in the Lower-Dimensional Space. Extensive experimental evaluations are performed on 20 time series datasets, which come from diverse fields, including medicine, biometrics, astronomy and industry. The experiment results demonstrate the effectiveness of our approach.

George J. Pappas - One of the best experts on this subject based on the ideXlab platform.

  • Approximate reduction of dynamical systems
    arXiv: Optimization and Control, 2007
    Co-Authors: Paulo Tabuada, Aaron D. Ames, A. Agung Julius, George J. Pappas
    Abstract:

    The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a Lower Dimensional Space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a Lower Dimensional Space. These concepts are illustrated on a series of examples.

  • CDC - Approximate Reduction of Dynamical Systems
    Proceedings of the 45th IEEE Conference on Decision and Control, 2006
    Co-Authors: Paulo Tabuada, Aaron D. Ames, A. Agung Julius, George J. Pappas
    Abstract:

    The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction is typically performed in an "exact" manner - as is the case with mechanical systems with symmetry - which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a Lower Dimensional Space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a Lower Dimensional Space. These concepts are illustrated on a series of examples