Predicting Periodic Phenomena with Self-Organising Maps

Self-Organising Maps are a form of neural network allowing unsupervised learning. In this work, we use a 2-dimensional network. Given a set of data, the neural network learns the distribution of data points, and provides a mapping from the set of data points to the neural network. The mapping has the property that similar data points map to nearby neurons in the network. Figure 2. Self-Organising Map after learning sample data for 132 months. Light squares indicate high values, and dark squares indicate low values. Circles indicate neurons corresponding to data points, colour-coded by month. The time sequence is anticlockwise, with January at the top centre. We are particularly concerned with learning the distribution of periodic data, where the period may be a day, a week, or a year. Each point in time therefore has an associated phase angle corresponding to the position within the daily, weekly, or annual cycle. We allow for these cycles by using the helical encoding of time illustrated in Figure 1. If the time t corresponds to the data point (di1, ..., di∆), and a phase angle of θ, then we use the vector (di1, ..., di∆, t, sin θ, cos θ ) for training the Self-Organising Map. We can predict missing data values by interpolating within the network. This technique is stochastic, since the predicted value will depend on random aspects of the self-organisation process. However, averaging a number of predictions reduces this random element. In reporting the performance of our prediction technique, we use an adjusted error which makes allowance for the standard deviation of the stochastic prediction.