Speech Recognition
Analysis of Higher Order Statistical Techniques for Speech Signal Recognition
Chanchal #, Anuj Gupta
#Asst.Prof., *Lecturer, Electronics and Communication Department,
ABSTRACT
The present paper deals with the analysis of non linear system using higher order statistical techniques namely Independent component analysis (ICA). The Independent component analysis is a statistical technique for decomposing complex data set into independent sub-parts. PCA is also a higher order statistical technique to find the patterns in data of high dimension. ICA is a much more powerful technique, however, capable of finding the underlying factors or sources when the classic methods fail completely. In reality, the data often does not follow a Gaussian distribution and the situation is not as simple as those methods of factor analysis, projection pursuit or PCA assumes. Many real world data sets have super Gaussian Distributions. Hence the probability density of the data is peaked at zero and has many tails, when compared to a Gaussian density of the same variance. This is the starting point of ICA where we try to find statistically independent components in the general case where the data is non Gaussian .In this paper we provide the different estimation principles of ICA and their algorithms. The simulation results of ICA are carried out by MATLAB.
Keywords- Nonlinear system, PCA, ICA, Statistical independence, Non-Gaussianity
Introduction
Linearity is a specification of a field of activity, nonlinearity is a “non-specification” and its field is unbounded. In nature, nonlinearity is the rule rather than the exception, while linearity is a simplification adopted for analysis. Indeed, the complex structure of dynamic systems makes it almost impossible to use linear models to represent them accurately. Nonlinear models are designed to provide a better mathematical way to characterize the inherent nonlinearity in real dynamic systems,
In mathematics, a nonlinear system
Chanchal #, Anuj Gupta
#Asst.Prof., *Lecturer, Electronics and Communication Department,
ABSTRACT
The present paper deals with the analysis of non linear system using higher order statistical techniques namely Independent component analysis (ICA). The Independent component analysis is a statistical technique for decomposing complex data set into independent sub-parts. PCA is also a higher order statistical technique to find the patterns in data of high dimension. ICA is a much more powerful technique, however, capable of finding the underlying factors or sources when the classic methods fail completely. In reality, the data often does not follow a Gaussian distribution and the situation is not as simple as those methods of factor analysis, projection pursuit or PCA assumes. Many real world data sets have super Gaussian Distributions. Hence the probability density of the data is peaked at zero and has many tails, when compared to a Gaussian density of the same variance. This is the starting point of ICA where we try to find statistically independent components in the general case where the data is non Gaussian .In this paper we provide the different estimation principles of ICA and their algorithms. The simulation results of ICA are carried out by MATLAB.
Keywords- Nonlinear system, PCA, ICA, Statistical independence, Non-Gaussianity
Introduction
Linearity is a specification of a field of activity, nonlinearity is a “non-specification” and its field is unbounded. In nature, nonlinearity is the rule rather than the exception, while linearity is a simplification adopted for analysis. Indeed, the complex structure of dynamic systems makes it almost impossible to use linear models to represent them accurately. Nonlinear models are designed to provide a better mathematical way to characterize the inherent nonlinearity in real dynamic systems,
In mathematics, a nonlinear system
References: [1]Glen D. Brown, Satoshi Yamada and Terrence J. Sejnowski: “Independent component analysis at the neural cocktail party”. [2]Yiu-ming Cheung, Lei Xu: “Independent component ordering in ICA time series analysis”. [3]www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/node29.html [4]S.-I. Amari, Aapo Hyvarinen, Soo-Young Lee, Te-Won Lee and V. David Sanchez A. The Guest Editorial Team : “Blind signal separation and independent component analysis”. [5]“Dimension reduction of process dynamic trends using independent component analysis”. R.F. Li, X.Z. Wang.