Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/sylvchev/mdla

Multivariate Dictionary Learning Algorithm
https://github.com/sylvchev/mdla

dictionary-learning eeg manifold multivariate-dictionaries

Last synced: about 22 hours ago
JSON representation

Multivariate Dictionary Learning Algorithm

Awesome Lists containing this project

README 

        
# MDLA - Multivariate Dictionary Learning Algorithm



[![Build Status](https://github.com/sylvchev/mdla/workflows/Test-and-Lint/badge.svg)](https://github.com/sylvchev/mdla/actions?query=branch%3Amaster)

[![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/psf/black)

[![codecov](https://codecov.io/gh/sylvchev/mdla/branch/master/graph/badge.svg?token=Vba6g9c5pM)](https://codecov.io/gh/sylvchev/mdla)



## Dictionary Learning for the multivariate dataset



This dictionary learning variant is tailored for dealing with multivariate datasets and

especially timeseries, where samples are matrices and the dataset is seen as a tensor.

Dictionary Learning Algorithm (DLA) decompose input vector on a dictionary matrix with a

sparse coefficient vector, see (a) on figure below. To handle multivariate data, a first

approach called **multichannel DLA**, see (b) on figure below, is to decompose the matrix

vector on a dictionary matrix but with sparse coefficient matrices, assuming that a

multivariate sample could be seen as a collection of channels explained by the same

dictionary. Nonetheless, multichannel DLA breaks the "spatial" coherence of multivariate

samples, discarding the column-wise relationship existing in the samples. **Multivariate

DLA**, (c), on figure below, decompose the matrix input on a tensor dictionary, where each

atom is a matrix, with sparse coefficient vectors. In this case, the spatial relationship

are directly encoded in the dictionary, as each atoms has the same dimension than an input

samples.



![dictionaries](https://github.com/sylvchev/mdla/raw/master/img/multidico.png)



(figure from [Chevallier et al., 2014](#biblio) )



To handle timeseries, two major modifications are brought to DLA:



1. extension to **multivariate** samples

2. **shift-invariant** approach, The first point is explained above. To implement the

   second one, there is two possibility, either slicing the input timeseries into small

   overlapping samples or to have atoms smaller than input samples, leading to a

   decomposition with sparse coefficients and offsets. In the latter case, the

   decomposition could be seen as sequence of kernels occuring at different time steps.



![shift invariance](https://github.com/sylvchev/mdla/raw/master/img/audio4spikegram.png)



(figure from [Smith & Lewicki, 2005](#biblio))



The proposed implementation is an adaptation of the work of the following authors:



- Q. Barthélemy, A. Larue, A. Mayoue, D. Mercier, and J.I. Mars. _Shift & 2D rotation

  invariant sparse coding for multi- variate signal_. IEEE Trans. Signal Processing,

  60:1597–1611, 2012.

- Q. Barthélemy, A. Larue, and J.I. Mars. _Decomposition and dictionary learning for 3D

  trajectories_. Signal Process., 98:423–437, 2014.

- Q. Barthélemy, C. Gouy-Pailler, Y. Isaac, A. Souloumiac, A. Larue, and J.I. Mars.

  _Multivariate temporal dictionary learning for EEG_. Journal of Neuroscience Methods,

  215:19–28, 2013.



## Dependencies



The only dependencies are scikit-learn, matplotlib, numpy and scipy.



No installation is required.



## Example



A straightforward example is:



```python

import numpy as np

from mdla import MultivariateDictLearning

from mdla import multivariate_sparse_encode

from numpy.linalg import norm



rng_global = np.random.RandomState(0)

n_samples, n_features, n_dims = 10, 5, 3

X = rng_global.randn(n_samples, n_features, n_dims)



n_kernels = 8

dico = MultivariateDictLearning(n_kernels=n_kernels, max_iter=10).fit(X)

residual, code = multivariate_sparse_encode(X, dico)

print ('Objective error for each samples is:')

for i in range(len(residual)):

    print ('Sample', i, ':', norm(residual[i], 'fro') + len(code[i]))

```



## Bibliography



- Chevallier, S., Barthelemy, Q., & Atif, J. (2014). [_Subspace metrics for multivariate

  dictionaries and application to EEG_][1]. In Acoustics, Speech and Signal Processing

  (ICASSP), IEEE International Conference on (pp. 7178-7182).

- Smith, E., & Lewicki, M. S. (2005). [_Efficient coding of time-relative structure using

  spikes_][2]. Neural Computation, 17(1), 19-45

- Chevallier, S., Barthélemy, Q., & Atif, J. (2014). [_On the need for metrics in

  dictionary learning assessment_][3]. In European Signal Processing Conference (EUSIPCO),

  pp. 1427-1431.



[1]: http://dx.doi.org/10.1109/ICASSP.2014.6854993 "Chevallier et al., 2014"

[2]: http://dl.acm.org/citation.cfm?id=1119614 "Smith and Lewicki, 2005"

[3]: https://hal-uvsq.archives-ouvertes.fr/hal-01352054/document