Probabilistic distance functions, including several variants of value difference metrics, minimum risk metric and ShortFukunaga metrics, are used with prototype-based rules (P-rules) to provide a very concise and comprehensible classification model. Application of probabilistic metrics to nominal or discrete features is straightforward. Heterogeneous metrics that handle continuous attributes wi...

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian process. We treat the corresponding latent v...

Models of the perceived distance between pairs of pitch collections are a core component of broader models of music cognition. Numerous distance measures have been proposed, including voice-leading [1], psychoacoustic [2–4], and pitch and interval class distances [5]; but, so far, there has been no attempt to bind these different measures into a single mathematical or conceptual framework, nor ...