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Mixed-norm regularization for brain decoding.

Flamary R, Jrad N, Phlypo R, Congedo M, Rakotomamonjy A - Comput Math Methods Med (2014)

Bottom Line: For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities.The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection.The multitask approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Lagrange, UMR7293, Université de Nice, 00006 Nice, France.

ABSTRACT
This work investigates the use of mixed-norm regularization for sensor selection in event-related potential (ERP) based brain-computer interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multitask learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multitask learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multitask approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.

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Examples of feature grouping for (a) single task and (b) multiple task learning.
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fig1: Examples of feature grouping for (a) single task and (b) multiple task learning.

Mentions: ℓ1 − ℓq  Mixed-Norm. A way to take into account the fact that features are structured is to use a mixed-norm that will group them and regularize them together. Here, we consider mixed-norm of the form(5)Ω1−q(w)=∑g∈𝒢//wg//q‍  with 1 ≤ q ≤ 2 and 𝒢 being a partition of the set {1,…, d}. Intuitively, this ℓ1 − ℓq mixed-norm can be interpreted as an ℓ1 norm applied to the vector containing the ℓq norm of each group of features. It promotes sparsity on each wg norm and consequently on the wg components as well. For our BCI problem, a natural choice for 𝒢 is to group the features by sensors yielding thus to p groups (one per sensor) of r features as reported in Figure 1. Note that unlike the ℓ1 − ℓ2 norm as used by van Gerven et al. [19] and Tomioka and Müller [20], the use of an inner ℓq norm leads to more flexibility as it spans from the ℓ1 − ℓ1 (equivalent to the ℓ1-norm and leading thus to unstructured feature selection) to the ℓ1 − ℓ2 which strongly ties together the components of a group. Examples of the use of ℓq norm and mixed-norm regularizations in other biomedical contexts can be found for instance in [26, 27].


Mixed-norm regularization for brain decoding.

Flamary R, Jrad N, Phlypo R, Congedo M, Rakotomamonjy A - Comput Math Methods Med (2014)

Examples of feature grouping for (a) single task and (b) multiple task learning.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4016929&req=5

fig1: Examples of feature grouping for (a) single task and (b) multiple task learning.
Mentions: ℓ1 − ℓq  Mixed-Norm. A way to take into account the fact that features are structured is to use a mixed-norm that will group them and regularize them together. Here, we consider mixed-norm of the form(5)Ω1−q(w)=∑g∈𝒢//wg//q‍  with 1 ≤ q ≤ 2 and 𝒢 being a partition of the set {1,…, d}. Intuitively, this ℓ1 − ℓq mixed-norm can be interpreted as an ℓ1 norm applied to the vector containing the ℓq norm of each group of features. It promotes sparsity on each wg norm and consequently on the wg components as well. For our BCI problem, a natural choice for 𝒢 is to group the features by sensors yielding thus to p groups (one per sensor) of r features as reported in Figure 1. Note that unlike the ℓ1 − ℓ2 norm as used by van Gerven et al. [19] and Tomioka and Müller [20], the use of an inner ℓq norm leads to more flexibility as it spans from the ℓ1 − ℓ1 (equivalent to the ℓ1-norm and leading thus to unstructured feature selection) to the ℓ1 − ℓ2 which strongly ties together the components of a group. Examples of the use of ℓq norm and mixed-norm regularizations in other biomedical contexts can be found for instance in [26, 27].

Bottom Line: For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities.The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection.The multitask approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Lagrange, UMR7293, Université de Nice, 00006 Nice, France.

ABSTRACT
This work investigates the use of mixed-norm regularization for sensor selection in event-related potential (ERP) based brain-computer interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multitask learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multitask learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multitask approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.

Show MeSH