Introduction To Time Series Classification:

1. Introduction To Time Series Classification: An approach in reconstructed phase space for phoneme recognition Sanjay Patil Intelligent Electronics Systems Human and Systems Engineering Center for Advanced Vehicular Systems URL: www.cavs.msstate.edu/hse/ies/projects/nsf_nonlinear/doc/

2. Abstract • Present nonlinear classifiers: • use clustering and similarity measurement techniques, eg. NN, SVM. • Existing time-domain approaches: • Use a priori learned underlying pattern of template base. • Frequency-based techniques: • Use spectral patterns based on first and second order characteristics of the system. • Current work (as described in the paper): • Use modeling of signals in the reconstructed phase space.

3. Motivation (why did I read it?) An attempt to find an approach to model the speech signal using nonlinear modeling technique. • Takens and Sauer – new signal classification algorithm. • Time series of observations sampled from a single state variable of a system • Reconstructed space equivalent to the original system

4. The Approach • Two methods to tackle the issue: • Build global vector reconstructions and differentiate signals in a coefficient space. [Kadtke, 1995] • Build GMMs of signal trajectory densities in an RPS and differentiate between signals using Bayesian classifiers. [Authors, reference, 2004] • The steps (Algorithm): • Data Analysis – normalizing the signals, estimating the time lag and dimension of the RPS. • Learning GMMs for each signal class – deciding the number of Gaussian mixtures, parameters learning by Expectation-Maximization (EM) algorithm. • Classification – going through the above steps for the SUT (signal under test), using Bayesian maximum likelihood classifiers

5. Algorithm in details and Issues • Data Analysis – • normalizing the signals • Each signal is normalized to zero mean and unit standard deviation. • estimating the time lag  • Using first minimum of the automutual information function. • Overall time lag  is the mode of the histogram of the first minima for all signals. • estimating dimension d of the RPS • Using global false nearest-neighbor technique. • Overall RPS dimension is the mean plus two standard deviations of the distribution of individual signal RPS dimensions. • How do you normalize the signal to zero mean and unit standard deviation? • What is automutual information function? • How do you implement the global false nearest-neighbor technique?

6. Algorithm in details and Issues • 2. Gaussian Mixture Models – • Insert all the signals for a particular class into the RPS for a particular d and  selected in previous step, • GMM: • Where, M = # of mixtures, • N(x;, ) = normal distribution with mean  and covariance matrix  • W = mixture weight with the constraint • GMMs estimated using Expectation-Maximization (EM) algorithm. • How is EM algorithm implemented? • Classification accuracy depends on M, So how to determine the value of M? • What is value of M determined from the underlying distribution of the RPS density?

7. Algorithm in details and Issues • 3. Classification – • Maximum Likelihood estimates from previous step are: • Where, mean , covariance matrix , mixture weight W • Using Bayesian maximum likelihood classifiers: • Compute the conditional likelihoods of the signal under each learned model • Select the model with highest likelihood. • How are the conditional likelihoods computed?

8. Experiment details and Issues • TIMIT speech corpus: • 417 phonemes for speaker MJDE0. • 6 spoken only once, 47 classes in total (out of the standard 48 classes) • Sampling frequency 16KHz, Signal length – 227 to 5,201 samples • Phoneme boundaries and class labels determined by a group of experts • 25 iterations of EM algorithm are used. • Classification accuracy is around 50% (50% for 16GMMs, @48% for 32GMMs) [reason – due to insufficient training data] • Approach is compared with time delay NN with nonlinear one step predictor and minimum prediction error classifier. • Details on how the testing is done is missing. • How is insufficient training data causing reduction in accuracy for increase in GM mixtures?

9. References • R. Povinelli, M. Johnson, A. Lindgren, and J. Ye, “Time Series Classification using Gaussian Mixture Models of Reconstructed Phase Spaces,” IEEE Transactions on Knowledge and Data Engineering, Vol 16, no 6, June 2004, pp. 770-783.