For a kernel-based topographic map formation, kMER (kernel-based maximum entropy learning rule) was proposed by Van Hulle, and some effective learning rules related to kMER have been proposed so far with many applications. However, no discusions have been made concerning the determination of the number of units in kMER. This letter describes a unit-pruning rule, which permits automatic contruction of an appropriate-sized map to acquire the global topographic features underlying the input data. The effectiveness and the validity of the present rule have been confirmed by some preliminary computer simulations.

To elucidate the mechanism of topographic organization, we propose a simple topographic mapping formation model from generalized cell layer to generalized cell layer. Here generalized cell layer means that we consider arbitrary cell neighborhood relations. In our previous work we investigated a topographic mapping formation model between one dimensional cell layers. In this paper we extend the cell layer structure to any dimension. In our model, each cell takes a binary state value and we consider a class of learning principles which are extensions of Hebb's rule and Anti-Hebb's rule. We pay special attention to correlation type learning rules where a synaptic weight value is increased if pre and post synaptic cell states have the same value. We first show that a mapping is stable with respect to the correlational learning if and only if it is semi-embedding. Second, we introduce a special class of weight matrices called band type and show that the set of band type weight matrices is strongly closed and such a weight matrix can not yield a topographic mapping. Third, we show by computer simulations that a mapping, if it is defined by a non band type weight matrix, converges to a topographic mapping under the correlational learning rules.

In this paper, symbols and numerals in topographic maps are recognized by the multi-angled parallelism (MAP) matching method, and small dots and lines are extracted by the MAP operation method. These results are then combined to determine the value, position, and attributes of elevation marks. Also, we reconstruct three dimensional surfaces described by contours, which is difficult even for humans since the elevation symbols are sparse. In reconstruction of the surface, we define an energy function that enfores three constraints: smoothness, fit, and contour. This energy function is minimized by solving a large linear system of simultaneous equations. We describe experiments on 25,000:1 scale topographic maps of the Tsukuba area.

Topographic maps begin to be recognized as one of the major computational structures underlying neural computation in the brain. They provide dimension-reducing projections between feature spaces that seem to be established and maintained under the participation of selforganizing, adaptive processes. In this contribution, we investigate how well the structure of such maps can be replicated by simple adaptive processes of the kind proposed by Kohonen. We will particularly address the important issue, how the dimensionality of the input space affects the spatial organization of the resulting map.