This article introduces the Coincidence Algorithm (COIN) to solve several multimodal puzzles. COIN is an algorithm in the category of Estimation of Distribution Algorithms (EDAs) that makes use of probabilistic models to generate solutions. The model of COIN is a joint probability table of adjacent events (coincidence) derived from the population of candidate solutions. A unique characteristic of COIN is the ability to learn from a negative sample. Various experiments show that learning from a negative example helps to prevent premature convergence, promotes diversity and preserves good building blocks.

We present a training algorithm to create a neural network (NN) ensemble that performs classification tasks. It employs a competitive decay of hidden nodes in the component NNs as well as a selective deletion of NNs in ensemble, thus named a pruning algorithm for NN ensembles (PNNE). A node cooperation function of hidden nodes in each NN is introduced in order to support the decaying process. The training is based on the negative correlation learning that ensures diversity among the component NNs in ensemble. The less important networks are deleted by a criterion that indicates over-fitting. The PNNE has been tested extensively on a number of standard benchmark problems in machine learning, including the Australian credit card assessment, breast cancer, circle-in-the-square, diabetes, glass identification, ionosphere, iris identification, and soybean identification problems. The results show that classification performances of NN ensemble produced by the PNNE are better than or competitive to those by the conventional constructive and fixed architecture algorithms. Furthermore, in comparison to the constructive algorithm, NN ensemble produced by the PNNE consists of a smaller number of component NNs, and they are more diverse owing to the uniform training for all component NNs.

This paper deals with the improvement of performance in the transform and subband image coding systems with negatively-correlated input signal. Using a more general source model than the AR(1) model as an input, the coding performance for the transform and subband coding schemes is evaluated in terms of the coding gain over PCM. The source model used here has such resonant band characteristics that its power spectrum has a peak at some frequency between 0 and π/2 for positive autocorrelation and between π/2 and π for negative autocorrelation. It is shown that coding schemes are classified into two classes; one has the pairwise mirror-image property in their filter banks and performs symmetrically regardless of the sign of the autocorrelation, and the other has no that property and performs asymmetrically with inferior performance for negative autocorrelation. Among the well-known transform and subband coding schemes, the DHT and QMF coding systems belong to the former class and the DCT and SSKF coding systems to the latter. In order to remedy the inferior performance, we propose the method in which one modulates the negatively-correlated signal sequences by the alternating sign signal with unity magnitude (-1)n to convert them into positively-correlated sequences. The algorithms are presented for the DCT and SSKF image coding systems with the adaptive signal modulation. In the DCT coding systems, we are particularly concerned with the DCT-based hierarchical progressive coding mode of operation, since the signal modulation works well for that coding mode. The SSKF image coding system has the regular quad-tree structure with three stages. The simulation results for test images show that our method can successfully be applied to the images with a considerable amount of energy in the frequency range higher than π/2 in horizontal or vertical direction, such as fingerprints and textile patterns sampled at a rate close to the Nyquist rate. The paper closes with a brief introduction to the modification of our DCT-based method.