Matching and learning structural and spatial representations with neural networks
Steven Gold · 1996
The matching and learning of structural and spatial representations with Hopfield like recurrent neural networks is explored, by formulating and minimizing different energy functions. Building upon recent techniques from statistical physics, such as deterministic annealing which helps avoid some local minima, and the softmax which enforces a one-way constraint without a penalty term, a new optimization technique is introduced--the softassign. The softassign is specifically geared to the types of problems being examined--matching problems--which often require two-way (assignment) constraints. It eliminates the need for penalty terms in these objective functions. The softassign is applied to three types of problems, the first of which is the matching of structural representations--graphs, A new algorithm is introduced which can match unweighted, weighted and attributed relational graphs. This algorithm employs a sparse distance measure between the links of the two graphs. Experiments on randomly generated graphs, and on graphs generated from images are presented. The second problem is the matching of spatial representations--two sets of feature points located in two dimensional space. The feature points may be specified solely by their Cartesian coordinates, or there may be a feature vector associated with them. It is assumed the two sets of feature points are related by an affine transformation. Within Computer Vision this is known as a pose estimation and correspondence problem. A new algorithm is introduced and experiments on randomly generated point sets are run. Experiments on hand-written characters are presented. Finally the problem of learning spatial and structural representations is addressed. A new algorithm for clustering is introduced, which uses as distance measures versions of the point matching and graph matching algorithms. Point set and graph prototypes are learned in an unsupervised fashion. Experiments on randomly generated data sets, and data sets generated from hand-written characters are run.