🍸 Cocktail Party Problem — ICA-Based Speech Separation

This project demonstrates the Cocktail Party Problem — separating multiple mixed audio signals into their individual source signals using Independent Component Analysis (ICA) implemented from scratch in Python.

Given a set of mixed recordings (e.g., multiple people speaking simultaneously), ICA attempts to recover the original independent sources without knowing the mixing process.

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📌 Features

• Uses Laplace prior via the sign nonlinearity to update the unmixing matrix.
• Implements stochastic gradient ascent ICA without external ML libraries.
• Normalizes audio and saves both mixed and separated signals as .wav files.
• Simple and readable Python implementation.
• Demonstrates the classical blind source separation setup.

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📁 Project Structure

project/
│── mix.dat                # Input mixed audio signals (M samples × N channels)
│── code.py                # Main program (your code)
│── output/                # Folder where results are saved
│     ├── mixed_*.wav      # Audio files for each mixture channel
│     ├── split_*.wav      # Recovered separated sources
│     └── W.txt            # Learned unmixing matrix
│── README.md              # This file

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🎧 How It Works

1. Load & Normalize Audio

The file mix.dat contains mixed signals. They are normalized to the range [-1, 1] to prevent clipping.

2. Estimate Unmixing Matrix W

ICA is applied using the update rule:

[ W \leftarrow W + \eta\left( (W^T)^{-1} - \text{sign}(Wx)x^T \right) ]

• Uses a schedule of decreasing learning rates (anneal list).
• Updates one sample at a time (stochastic gradient ascent).
• Produces an unmixing matrix W.

3. Compute Separated Signals

Recovered sources are:

[ S = X W^T ]

These are normalized and saved as audio files.

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▶️ Running the Project

1. Install dependencies

pip install numpy scipy

2. Ensure your mix.dat file is present

This file should be shaped:

# rows = time samples
# columns = mixed audio channels

3. Run the program

python main.py

4. Check the output/ folder

You will find:

• mixed_0.wav, mixed_1.wav, …
• split_0.wav, split_1.wav, …
• W.txt — the learned unmixing matrix

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📊 Algorithm Details

This is a basic ICA implementation using:

• Laplace density → score function sign(y)
• Stochastic gradient updates
• Annealing learning rates
• No whitening stage (the update rule compensates for it)

This demonstrates core ICA behavior without relying on high-level libraries such as scikit-learn.

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🎤 Example Use Case: The Cocktail Party Problem

Imagine placing multiple microphones in a noisy room where several people are speaking simultaneously. Each microphone captures a mixture of all voices.

ICA attempts to recover the original voices individually.

This project showcases exactly that.

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🧠 References

• A. Hyvärinen & E. Oja — Independent Component Analysis: Algorithms and Applications
• The classic “cocktail party problem”

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