Transcript Blind Signal Separation using Principal Components Analysis

Blind Signal Separation
using Principal Components
Analysis
Alok Ahuja
Problem Formulation
Motivation
► Methods
based on Higher Order Statistics
Computational burden
Require large amount of data
► PCA utilizes Second Order Statistics
Alleviates the computational cost
Both differ in underlying assumptions
Principal Components Analysis
► Reduction
of feature dimension of data
space
► Redundant feature removal e.g. Linear
combination of features
► Eigen Analysis : Expansion of data vector in
terms of its Eigen vectors
 This application : Algorithm used to find ALL
of the Eigen vectors
Adaptive Principal Components
Extraction (APEX) Algorithm
► Train
the network one neuron at a time
► Feedback from each neuron to all neurons
that follow it
► Neurons are assumed to be linear
► Weight updates based on modified Hebbian
learning rules