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Characterizing the sub-mm Galactic emission has become increasingly criticalespecially in identifying and removing its polarized contribution from the oneemitted by the Cosmic Microwave Background (CMB). In this work, we present aparametric foreground removal performed onto sub-patches identified in thecelestial sphere by means of spectral clustering. Our approach takes intoaccount efficiently both the geometrical affinity and the similarity induced bythe measurements and the accompanying errors. The optimal partition is thenused to parametrically separate the Galactic emission encoding thermal dust andsynchrotron from the CMB one applied on two nominal observations of forthcomingexperiments from the ground and from the space. Performing the parametric fitsingularly on each of the clustering derived regions results in an overallimprovement: both controlling the bias and the uncertainties in the CMB$B-$mode recovered maps. We finally apply this technique using the map of thenumber of clouds along the line of sight, $\mathcal{N}_c$, as estimated from HIemission data and perform parametric fitting onto patches derived by clusteringon this map. We show that adopting the $\mathcal{N}_c$ map as a tracer for thepatches related to the thermal dust emission, results in reducing the $B-$moderesiduals post-component separation. The code is made publicly available.

Improved Galactic Foreground Removal for B-Modes Detection with Clustering Methods