Filtrage vaste marge pour letiquetage sequentiel `a noyaux de signaux

We address in this paper the problem of multi-channel signal sequence labeling. In particular, we consider the problem where the signals are contaminated by noise or may present some dephasing with respect to their labels. For that, we propose to jointly learn a SVM sample classifier with a temporal filtering of the channels. This will lead to a large margin filtering that is adapted to the specificity of each channel (noise and time-lag). We derive algorithms to solve the optimization problem and we discuss different filter regularizations for automated scaling or selection of channels. Our approach is tested on a non-linear toy example and on a BCI dataset. Results show that the classification performance on these problems can be improved by learning a large margin filtering.

💡 Research Summary

The paper tackles the challenging problem of multi‑channel sequential labeling when the observed signals are noisy and may be temporally misaligned with respect to their ground‑truth labels. Traditional pipelines treat preprocessing (e.g., filtering) and classification as separate stages, which is sub‑optimal for applications such as brain‑computer interfaces (BCI) where each electrode exhibits a distinct signal‑to‑noise ratio and a variable latency relative to the intended action. To overcome these limitations, the authors propose a unified learning framework that simultaneously optimizes a large‑margin Support Vector Machine (SVM) classifier and a set of channel‑specific temporal filters.

Model formulation
For each channel (c) a finite‑impulse‑response (FIR) filter (\mathbf{h}c) of length (L) is introduced. The filtered observation at time (t) is (\tilde{x}c(t)=\sum{l=0}^{L-1}h{c,l},x_c(t-l)). The decision function of the SVM is then a linear combination of the filtered signals across all channels:
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