Minimum distance classification for dynamical systems and sensors

• Martinez Dominique
• Boutayeb Mohamed

• Classification
• Dynamical systems
• Machine Learning
• Support vector machines
• State-space models
• Smart sensors
• Gas sensors
• Metal-oxide sensors

Sensors and systems often exhibit different dynamics in response to various stimuli. The problem of determining which of the dynamics has generated a given observation sequence is referred to as a multiclass discrimination problem. We propose a solution to this problem as a minimum distance classifier that assigns the observation sequence to the dynamics to which it is closest in terms of a similarity metric. One of the main contributions is to compute this metric in a high-dimensional feature space using the Kronecker product so that the projected data of each class lie on distinct hyperplanes. These are trained using singular value decomposition or quadratic programing in the spirit of twin support vector machines. The other main contribution is to show that the minimum distance classifier exists for state-space models if and only if the observability matrices are all different even when the models are not observable in a control-theoric sense. We validated our method on numerical examples of dynamical systems and on gas identification using metal-oxide sensors. Results confirm the theoretical condition for the existence of the classifier and demonstrate the efficiency of the learning process with classification accuracy matching or exceeding state-of-the art performance. In particular, learning the classifier directly from training data is more robust and more generally applicable than determining it from classical system identification methods. The minimum distance classifier is thus relevant to the classication of dynamical sensing systems.