Dynamic Grouped Mixture Models for Intermittent Multivariate Sensor Data

For secure and efficient operation of engineering systems, it is of great importance to watch daily logs generated by them, which mainly consist of multivariate time-series obtained with many sensors. This work focuses on challenges in practical analyses of those sensor data: temporal unevenness and sparseness. To handle the unevenly and sparsely spaced multivariate time-series, this work presents a novel method, which roughly models temporal information that still remains in the data. The proposed model is a mixture model with dynamic hierarchical structure that considers dependency between temporally close batches of observations, instead of every single observation. We conducted experiments with synthetic and real dataset, and confirmed validity of the proposed model quantitatively and qualitatively.

[1]  Thomas S. Huang,et al.  Regularized Maximum Likelihood for Intrinsic Dimension Estimation , 2010, UAI.

[2]  Neil D. Lawrence,et al.  Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models , 2005, J. Mach. Learn. Res..

[3]  Grant Foster,et al.  Wavelets for period analysis of unevenly sampled time series , 1996 .

[4]  J. Kurths,et al.  Comparison of correlation analysis techniques for irregularly sampled time series , 2011 .

[5]  Sebastian Thrun,et al.  Text Classification from Labeled and Unlabeled Documents using EM , 2000, Machine Learning.

[6]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[7]  Bernhard Schölkopf,et al.  Estimating the Support of a High-Dimensional Distribution , 2001, Neural Computation.

[8]  J. Scargle.  Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data , 1982 .

[9]  John D. Lafferty,et al.  Dynamic topic models , 2006, ICML.

[10]  Naomi Murakami,et al.  Small Demonstration Satellite-4 (SDS-4): Development, Flight Results, and Lessons Learned in JAXA’s Microsatellite Project , 2013 .

[11]  Ulrich A. Müller,et al.  Operators on Inhomogeneous Time Series , 2000 .

[12]  Geoffrey E. Hinton,et al.  The EM algorithm for mixtures of factor analyzers , 1996 .

[13]  Thomas F. Edgar,et al.  Identification of faulty sensors using principal component analysis , 1996 .

[14]  Peter J. Brockwell,et al.  Lévy–Driven Continuous–Time ARMA Processes , 2009 .

[15]  J. Scargle.  Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data , 1989 .

[16]  Richard H. Jones.  5 Time series analysis with unequally spaced data , 1985 .

[17]  Oliver Tomic,et al.  Independent component analysis applied on gas sensor array measurement data , 2003 .

[18]  Christopher M. Bishop,et al.  Mixtures of Probabilistic Principal Component Analyzers , 1999, Neural Computation.

[19]  R. Engle,et al.  Alternative Algorithms for the Estimation of Dynamic Factor , 1983 .

[20]  Sheng Ma,et al.  Statictical Models for Unequally Spaced Time Series , 2005, SDM.

[21]  Mark J. F. Gales,et al.  Factor analysed hidden Markov models for speech recognition , 2004, Comput. Speech Lang..

[22]  Michael I. Jordan,et al.  Factorial Hidden Markov Models , 1995, Machine Learning.

[23]  N. Yoshida,et al.  On covariance estimation of non-synchronously observed diffusion processes , 2005 .

[24]  P. Brockwell.  Continuous-time ARMA processes , 2001 .