Active Learning Classification from a Signal Separation Perspective

In machine learning, classification is usually seen as a function approximation problem, where the goal is to learn a function that maps input features to class labels. In this paper, we propose a novel clustering and classification framework inspired by the principles of signal separation. This approach enables efficient identification of class supports, even in the presence of overlapping distributions. We validate our method on real-world hyperspectral datasets Salinas and Indian Pines. The experimental results demonstrate that our method is competitive with the state of the art active learning algorithms by using a very small subset of data set as training points.

Stability of sorting based embeddings

Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant map $\beta_\Phi : V \to \mathbb{R}^{M \times N}$ given by sorting the coorbits $(\langle v, g \phi_i \rangle_V)_{g \in G}$, where $(\phi_i)_{i=1}^N \in V$, satisfies a bi-Lipschitz condition if and only if it separates orbits. Additionally, we note that any invariant Lipschitz continuous map (into a Hilbert space) factors through the sorting based embedding, and that any invariant continuous map (into a locally convex space) factors through the sorting based embedding as well.