Swamp: an Isometric Frontend for Speaker Clustering

In this paper, we describe a non-linear feature normalization based on Riemannian differential geometry. This feature normalization will yield parameters that are invariant under any bijective stationary transformation. Moreover, it is robust to additive noise that is uncorrelated with speech and quasi-stationary. The only requirement is that of ergodicity. The frontend is called SWAMP (Sweeping Metric Parameterization). The frontend assumes that speech resides in a small, smooth manifold that is entirely and densely explored during the course of an utterance. It first observes the tangent spaces on every point of the manifold. This defines a local Riemannian geometry. Under this geometry, we are able to measure geodesic lengths on the manifold. These lengths are invariant under non-linear transformations. Therefore, we are able to locate a point invariantly by measuring its relative distance to all other observed points. Through classical multi-dimensional scaling, we map this triangulation to a canonical, Euclidean, isometric space inherent of the observed manifold. Combined with standard features, SWAMP features are shown to improve speaker clustering on Broadcast News.