BASiS: Batch Aligned Spectral Embedding Space

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely instrumental to design deep network building blocks with spectral graph characteristics. For instance, such a network allows the design of optimal graphs for certain tasks or obtaining a canonical orthogonal lowdimensional embedding of the data. Recent attempts to solve this problem were based on minimizing Rayleighquotient type losses. We propose a different approach of directly learning the graph's eigensapce. A severe problem of the direct approach, applied in batch-learning, is the inconsistent mapping of features to eigenspace coordinates in different batches. We analyze the degrees of freedom of learning this task using batches and propose a stable alignment mechanism that can work both with batch changes and with graph-metric changes. We show that our learnt spectral embedding is better in terms of NMI, ACC, Grassman distnace, orthogonality and classification accuracy, compared to SOTA. In addition, the learning is more stable.