## Hankel matrices for use in Learning Vector Quantization

- Classification of time series has received an important amount of interest over the past years due to many real-life applications, such as environmental modeling, speech recognition, and computer vision.
In my thesis, I focus on classification of time series by LVQ classifiers. To learn a classifiers, we need a training set. In our case, every data point in the training set contains a sequence (an ordered set) of feature vectors. Thus, the first task is to construct a new feature vector (or matrix) for each sequence.
Inspired by [2], I use Hankel matrices to construct the new feature vectors. This choice comes from a basic assumption that each time series is generated by a single or a set of unknown Linear Time Invariant (LTI) systems.
After generating new feature vectors by Hankel matrices, I use two approaches to learn a classifier: Generalized Learning Vector Quntization (GLVQ) and Median variant of Generalized Learning Vector Quantization (mGLVQ).