Logarithmic simulated annealing for X-ray diagnosis

We present a new stochastic learning algorithm and first results of computational experiments on fragments of liver CT images. The algorithm is designed to compute a depth-three threshold circuit, where the first layer is calculated by an extension of the Perceptron algorithm by a special type of simulated annealing. The fragments of CT images are of size 119x119 with eight bit grey levels. From 348 positive (focal liver tumours) and 348 negative examples a number of hypotheses of the type w(1)x(1)+. . .;+w(n)x(n)>/=theta were calculated for n=14161. The threshold functions at levels two and three were determined by computational experiments. The circuit was tested on various sets of 50+50 additional positive and negative examples. For depth-three circuits, we obtained a correct classification of about 97%. The input to the algorithm is derived from the DICOM standard representation of CT images. The simulated annealing procedure employs a logarithmic cooling schedule c(k)=Gamma/ln(k+2), where Gamma is a parameter that depends on the underlying configuration space. In our experiments, the parameter Gamma is chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.