Unsupervised learning with associative cubes for robust gray-scale image recognition

We consider a class of auto-associative memories, namely, "associative cubes" in which 2D gray-level images and the hidden orthogonal basis functions such as Walsh-Hadamard or Fourier kernels, are mixed and updated in the weight cubes, "C". First, we develop an unsupervised learning procedure based upon the adaptive recursive algorithm. Here, each 2D training image is mapped into the associated 1D wavelet in the least-squares sense during the training phase. Second, we show how the recall procedure minimizes the recognition errors with a competitive network in the hidden layer. As 2D images corrupted by noises are applied to an associative cube, the nearest one among the original training images would be retrieved in the sense of the minimum euclidean squared norm during the recall phase. The simulation results confirm the perfect recall for the original training images as well as the robustness of associative cubes even if the test data are heavily distorted by noises.