Package: iva-order-selection
Comple Model Identification using Independent Vector Analysis (CMI-IVA)This package contains the Python versions of CMI-IVA [1].For CMI-IVA please visit:https://mlsp.umbc.edu/SiddiqueFor IVA please visit:http://mlsp.umbc.edu/jointBSS_introduction.htmlhttps://github.com/SSTGroup/independent_vector_analysisInstalling iva_order_selectionpip install independent_vector_analysis####################################################Pre-requisite:Installing independent_vector_analysisThe only pre-requisite is to havePython 3(>= version 3.6) installed.
The iva package can be installed withpip install independent_vector_analysisRequired third party packages will automatically be installed.###################################################First, the imports:import numpy as np
from independent_vector_analysis import *
from independent_vector_analysis.data_generation import MGGD_generationExample:
N = 10 # No. Sources
T = 1000 # No. Samples
K = 15 # No. datasets (subjects)
rho = [0.9,0.8,0.7]# Common and distinct source generation
source_mat = np.zeros((N,T,K))
scv_cov_mat = np.zeros((K,K,N))

# Common sources across K datasets
for i in range(len(rho)):
	(temp,scv_cov_mat[:,:,i]) = MGGD_generation(T,K,'uniform',rho[i],0.5)
	source_mat[i,:,:] = temp.T

# Common sources with sub-group structure across K datasets
(temp,scv_cov_mat[:,:,len(rho)]) = MGGD_generation(T,K,'block',{'val': 0.01, 'blocks': [(0.9, 0, 3), (0.01, 3,14)]},0.5)
source_mat[len(rho),:,:] = temp.T

# Distinct sources across K datasets
for i in range(len(rho)+1,N,1):
	(temp,scv_cov_mat[:,:,i]) = MGGD_generation(T,K,'ar',0.01,0.5)
	source_mat[i,:,:] = temp.T


# Create datasets by mixing with randomly generated mixing matrices
mix_mat = np.random.randn(N,N,K)
data_mat = np.zeros((N,T,K))
for k in range(K):
	data_mat[:,:,k] = mix_mat[:,:,k]@source_mat[:,:,k]

# Apply CMI-IVA
iva_results, Order, Corr_struct = order_selection_iva(data_mat)

 Output:
    iva_results: tuple
         -iva_results[0] = W : np.ndarray
             The estimated demixing matrices of dimensions N x N x K so that ideally
             W[k] @ A[k] = P @ D[k], where P is any arbitrary permutation matrix and D[k] is any
             diagonal invertible (scaling) matrix. Note that P is common to all datasets. This is
             to indicate that the local permutation ambiguity between dependent sources
             across datasets should ideally be resolved by IVA.

         -iva_results[1] = cost : float
             The cost for each iteration

         -iva_results[2] = Sigma_N : np.ndarray
             Covariance matrix of each source component vector, with dimensions K x K x N

         -iva_results[3] = isi : float

    Order: dict
         -'mdl': int 
              Common order estimated by the minimum description length (MDL) criteria 
         -'aic': int
              Common order estimated by the akaike information criterion (AIC)
         -'mdl_results': np.ndarray
              Number of subgroup in each SCV estimated by MDL (N)
         -'aic_results': np.ndarray
              Number of subgroup in each SCV estimated by AIC (N)

    Corr_struct: dict
        -'eig': np.ndarray
              Estimated eigenvalues for each SCV (K x N)
        -'eig_str': np.ndarray
              Estimated correlation structire in each SCV (K x K x N)Contactakhondams@nih.govormo32@umbc.eduCitingIf you use this package in an academic paper, please cite [1].@INPROCEEDINGS{9523414,
author={Akhonda, M. A. B. S. and Gabrielson, Ben and Calhoun, Vince D. and Adali, TÃ¼lay},
booktitle={2021 IEEE Data Science and Learning Workshop (DSLW)}, 
title={Complete Model Identification Using Independent Vector Analysis: Application to the Fusion of Task FMRI Data}, 
year={2021},
volume={},
number={},
pages={1-6},
doi={10.1109/DSLW51110.2021.9523414}}[1]  M. A. B. S. Akhonda, B. Gabrielson, V. D. Calhoun and T. Adali,"Complete Model Identification Using Independent Vector Analysis: Application to the Fusion of Task FMRI Data," 2021 IEEE Data Science and Learning Workshop (DSLW), Toronto, ON, Canada, 2021, pp. 1-6, doi: 10.1109/DSLW51110.2021.9523414.