Hierarchical Multiresolution Feature- and Prior-based Graphs for Classification
This work addresses classification challenges in domains requiring spatial and hierarchical modeling, but it appears incremental as it builds on existing graph-based methods like random walker graphs.
The authors tackled the problem of incorporating spatial, hierarchical, and prior information into classification by formulating it on multiresolution neighborhood graphs and a hierarchical conditional random field, resulting in a system of linear equations and energy minimization that can be solved efficiently.
To incorporate spatial (neighborhood) and bidirectional hierarchical relationships as well as features and priors of the samples into their classification, we formulated the classification problem on three variants of multiresolution neighborhood graphs and the graph of a hierarchical conditional random field. Each of these graphs was weighted and undirected and could thus incorporate the spatial or hierarchical relationships in all directions. In addition, each variant of the proposed neighborhood graphs was composed of a spatial feature-based subgraph and an aspatial prior-based subgraph. It expanded on a random walker graph by using novel mechanisms to derive the edge weights of its spatial feature-based subgraph. These mechanisms included implicit and explicit edge detection to enhance detection of weak boundaries between different classes in spatial domain. The implicit edge detection relied on the outlier detection capability of the Tukey's function and the classification reliabilities of the samples estimated by a hierarchical random forest classifier. Similar mechanism was used to derive the edge weights and thus the energy function of the hierarchical conditional random field. This way, the classification problem boiled down to a system of linear equations and a minimization of the energy function which could be done via fast and efficient techniques.