# Week 2— Cocktail Party Problem

**Team Members:** Furkan Kaya, Girayhan Yıldırım, Ömer Faruk Yaşar, Yahya Koçak

This week we are going to mention about approaches on separating independent voice signals to each other.

In our problem we have two distinct independent voice source and linear combination of them as a record. As we mentioned last week our aim is separate voices from each other. But how to do it? Let’s look an efficient way of blindly separate signals BSS and an application of it ICA and their role in our problem.

# What Is Blind Source Separation?

Blind Signal Separation or Blind Source Separation is the separation of a set of signals from a set of mixed signals without the aid of information (or with very little information) about the signal source or the mixing process.

Blind source separation relies on the assumption that the source signals do not correlate with each other. For example, a set of signals may be statistically independent or decorrelated. Because of this independence, the set can be separated into another signal set, such that the regularity of each resulting signal is maximized, and the regularity between the different signals is minimized (i.e. statistical independence is maximized).

# BSS Methods

Typical methods for blind source separation include:

- Principal components analysis (PCA)
- Singular value decomposition (SVD)
- Independent component analysis (ICA)
- Dependent component analysis (DCA)
- Short-time Fourier transform (STFT)
- Degenerate unmixing estimation technique (DUET)
- W-disjoint orthogonality
- Joint approximate diagonalization eigen-matrices (JADE)
- Computational auditory scene analysis (CASA)
- Constant modulus algorithm (CMA)

# What is ICA and Why We Choose It?

“Independent component analysis (ICA) is a method for finding underlying factors or components from multivariate (multi-dimensional) statistical data. What distinguishes ICA from other methods is that it looks for components that are both

statistically independent, andnonGaussian.” A.Hyvarinen, A.Karhunen, E.Oja

We choose ICA among other approaches because the main idea of ICA focuses on ﬁnding the independent sources from mixed data rather than reducing the feature dimension toward maximum expression direction via PCA and extracting the Gaussian common factorsembedded in unknown data via FA which describes our problem in a exact way.

**X = AS**

where **X** is a random p-vector representing multivariate input measurements. **S **is a latent source p-vector whose components are independently distributed random variables. **A** is p × p mixing matrix. Given realizations x1,x2,…,xN of X, the goals of ICA are to estimate **A **estimate the source distributions **Sj ∼ fS, j = 1,…,p**

Principal components are uncorrelated linear combinations of X, chosen to successively maximize variance.

Independent components are also uncorrelated linear combinations of X, chosen to be as independent as possible.