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Swayam Prabha

Course Title

Multivariate Data Mining- Methods and Applications

Lecture 18

Latent Variable Model for Blind Source Separation

By

Anoop Chaturvedi

Department of Statistics, University of Allahabad

Prayagraj (India)

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Slides can be downloaded from https://sites.google.com/view/anoopchaturvedi/swayam-prabha

Latent Variable Model for Blind Source Separation�Latent variable ⇒ Used to give a formal representation of ideas or concepts that cannot be well defined or measured directly. �Examples: Fuzzy concepts such as ‘general intelligence’, ‘verbal ability’, ‘ambition’, ‘socio economic status’, ‘quality of life’ and ‘happiness’.���

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• A casual relationship may exist between latent variables and observable variables.
• Unobservable concepts are constructed from certain observed variables.
• Latent variables are usually formed as linear combination of some observable variables.
• Observed variables are proxies for unobserved concepts.
• Latent variables play important role in Blind source separation problems.�

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Blind Source Separation (BSS)

• Both the sources and the mixing methodology are unknown.
• Mixture signals are available for further separation process.
• Data consist of multiple time series of mixed signals.
• Objective is to recover all individual sources from the mixed signal, or to separate a particular source.
• Involves decomposition of unknown mixture of non-Gaussian signals into its independent component signals.�

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More Applications

Biomedical Signal Processing:

EEG: Separating brainwave signals from different regions of the brain for analysis of neural activity.

• To separate EEG, ERP, MEG recording into individual source signals.
• ICA can be used to separate the signals so that an accurate representation of brain activity may be observed.

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EEG → relate certain types of behaviour to changes in the electrical activity of the cerebral cortex.

ERP → Event-related potential is fine tuned EEG’s resulting from simulation of visual, auditory or sensory systems.

MEG → strength of magnetic fields generated by cortical activity.

f MRI (functional magnetic resonance) → experiments used to study human brain.

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Removing noise on the ECG:

ICA can be used for removing artifacts from the ECG

To access health condition of the fetus using ECG of mother.

(ECG: mixture of fetus and maternal heart rate)

Separation of musical signals:

ICA provides a fairly accurate separation, although some accidental/unwanted signals remain.

Agricultural remote sensing images

Web image & classification ⇒ Classify web image into mountains, agriculture land, sea forest area etc.

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Astronomy: In Celestial sources a pixel value can be considered as a mixture of different sources. BSS can be used to display interesting features and helps astronomers to improve description of celestial sources.

Audio Signal Processing:

Music Source Separation: Decomposing mixed music tracks into individual instruments or vocal tracks.

Surveillance: Separating sounds of interest (e.g., footsteps, conversations) from background noise in surveillance recordings.

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Classification of microarray gene profiles

Gene expression data is considered a linear combination of independent components having specific biological interpretations.

Biomedical scientists can use ICA to explore gene expression features and discover underlying biological information from large microarray data sets.

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Telecommunications:

Wireless Communication: Separating signals transmitted over a shared channel in wireless communication systems.

Radio Frequency Identification (RFID): Separating signals from different RFID tags in a crowded environment.

Speech Enhancement and Acoustic Monitoring:

• Separating speech signals from background noise to enhance speech quality in communication systems.
• Separating sounds of interest (e.g., animal calls, environmental sounds) from background noise

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Image Processing:

Image Decomposition: Separating mixed images captured by sensors (e.g., satellite images) into constituent components (e.g., vegetation, buildings, water bodies).

Medical Imaging:

Separating different tissue types in medical images for diagnostic purposes.

Financial Signal Processing:

Separating different market factors contributing to stock price movements for analysis and prediction.

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Portfolio Management:

Separating signals related to different financial assets to optimize portfolio allocation.

Seismic Signal Processing: Separating seismic signals from different sources (e.g., earthquakes, human activities) for monitoring seismic activity.

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Independent Component Analysis (ICA)

Seeks to uncover hidden variables in high dimensional data.

Three Assumptions of ICA models

1. Each measured signal is a linear combination of the sources.
2. The source signals (Hidden variables) are statistically independent of each other.
3. The values in each source signal have non-Gaussian distribution.

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• The number of inputs and outputs are the same.
• Linear mixture of an unknown number of unknown variables where mixing coefficient are also unknown.
• Since outputs are mutually independent, we can not drop components as in Principal Component Analysis.

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