Unsupervised learning with normalised data and non-Euclidean norms

The measurement of distance is one of the key steps in the unsupervised learning process, as it is through these distance measurements that patterns and correlations are discovered. We examined the characteristics of both non-Euclidean norms and data normalisation within the unsupervised learning environment. We empirically assessed the performance of the K-means, Neural Gas, Growing Neural Gas and Self-Organising Map algorithms with a range of real-world data sets and concluded that data normalisation is both beneficial in learning class structure, and in reducing the unpredictable influence of the norm.