Bars Problem

The first experimental problem studied with HNFA+VM was to apply it to artificial data that is an extension of the bars problem [12]. The data set consists of 1000 image patches of size $6 \times 6$ pixels. They have horizontal and vertical bars. In addition to the regular bars, the problem was extended to include horizontal and vertical variance bars that are manifested by increased variance. Samples of the image patches are shown in Figure .

  

Figure 7.1: Samples from the 1000 image patches used in the bars problem.

Data was generated by first choosing whether vertical and/or horizontal orientations are active, each with probability 1/2 independently. When an orientation is active, there is a probability 1/3 for each bar to be active. For both orientations, there are 6 regular bars, one for each row or column, and 3 variance bars that are 2 rows or columns wide. The intensities are drawn from normalised positive exponential distribution. Regular bars are additive and variance bars produce additive Gaussian noise with standard deviation of its intensity. Finally, Gaussian noise with standard deviation 0.1 is added to each pixel.