Interpretable online network dictionary learning for inferring long-range chromatin interactions
Fig 2
(a) Organization of a dictionary comprising K dictionary elements that are convex combinations of real representative subnetworks. Each dictionary element itself is a sparse convex combination of a set of representatives which are small subnetworks of the input real-world network. In the example, there are 6 options for the representatives, and inclusion of a representative into a dictionary element is indicated by a colored entry in a 6-dimensional indicator column-vector. Each of the 6 representatives corresponds to a subnetwork of the input network with a fixed number of nodes (3 for our example). The dictionary element is generated by a convex combination of the corresponding adjacency matrices of its corresponding representative subnetworks. For the example, the resulting dictionary elements are 9 × 9 matrices. (b) Illustration of the representative region update. When an online data sample is observed, the distance of the sample to each of the current dictionary elements is computed and the sample is assigned to the representative region of the nearest dictionary element. From this expanded set of representatives, one representative is carefully selected for removal to improve the objective. The new dictionary element is then obtained as an optimized convex combination of the updated set of representatives.