independent-vector-analysis 0.1

Implementation of IVA-G and IVA-L-SOS

Independent Vector Analysis

This package contains the Python versions of IVA-G and IVA-L-SOS, converted from the MLSP-Lab MATLAB Codes.

• Website: http://mlsp.umbc.edu/jointBSS_introduction.html
• Source-code: https://github.com/SSTGroup/independent_vector_analysis

Installing independent_vector_analysis

The only pre-requisite is to have Python 3 installed. The iva package can be installed with

pip install independent_vector_analysis

Required third party packages will automatically be installed.

Quickstart

First, the imports:

import numpy as np
from independent_vector_analysis import iva_g, consistent_iva
from independent_vector_analysis.data_generation import generate_sources

Create a dataset with N=3 sources, which are correlated across K=4 datasets. Each source consists of T=10000 samples:

N = 3
K = 4
T = 10000
rho = 0.7

S = generate_sources(rho, N, T, K)
A = np.random.randn(N,N,K)
X = np.einsum('MNK, NTK -> MTK', A, S)

Apply IVA-G to reconstruct the sources. If the mixing matrix A is passed, the ISI is calculated. Let the demixing matrix W be initialized by joint diagonalization:

W, cost, Sigma_n, isi = iva_g(X, A=A, jdiag_initW=True)

W is the estimated demixing matrix. cost is the cost for each iteration. Sigma_n[:,:,n] contains the covariance matrix of the nth SCV. isi is the joint ISI for each iteration.

Find the most consistent result of 500 runs in IVA-L-SOS:

iva_results = consistent_iva(X, which_iva='iva_l_sos', n_runs=500)

where iva_results is a dict containing:

• 'W' : estimated demixing matrix of dimensions N x N x K
• 'W_change' : change in W for each iteration
• 'S' : estimated sources of dimensions N x T x K
• 'A' : estimated mixing matrix of dimensions N x N x K
• 'scv_cov' : covariance matrices of the SCVs, of dimensions K x K x N (the same as Sigma_n in iva_g / iva_l_sos)
• 'cross_isi' : cross joint ISI for each run compated with all other runs

Citing

If you use this package in an academic paper, please cite [1]

@inproceedings{Lehmann2022,
  author  = {Lehmann, Isabell and Acar, Evrim and Hasija, Tanuj and Akhonda, M.A.B.S. and Calhoun, Vince D. and Schreier, Peter J. and Adali, Tulay},
  title   = {Multi-task fMRI Data Fusion Using IVA and PARAFAC2},
  journal = {unpublished work}
}

[1] Isabell Lehmann, Evrim Acar, et. al, Multi-task fMRI Data Fusion Using IVA and PARAFAC2, unpublished work.