Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector space of arbitrary dimensionality. Subsequently, the resulting features are meaningful and can be used for visualization or nearest neighbour classification in linear time. This kind of metric learning for sequential data enables the use of algorithms tailored towards fixed length vector spaces such as R^n.
A fully unsupervised approach is to use the parameters estimated by a system identification method (e.g., a linear dynamical system) as features. Recent work includes @cite_8 , in which a complex numbers based system successfully clusters motion capture data.
@cite_8
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Given a motion capture sequence, how to identify the category of the motion? Classifying human motions is a critical task in motion editing and synthesizing, for which manual labeling is clearly inefficient for large databases. Here we study the general problem of time series clustering. We propose a novel method of clustering time series that can (a) learn joint temporal dynamics in the data; (b) handle time lags; and (c) produce interpretable features. We achieve this by developing complex-valued linear dynamical systems (CLDS), which include real-valued Kalman filters as a special case; our advantage is that the transition matrix is simpler (just diagonal), and the transmission one easier to interpret. We then present Complex-Fit, a novel EM algorithm to learn the parameters for the general model and its special case for clustering. Our approach produces significant improvement in clustering quality, 1.5 to 5 times better than well-known competitors on real motion capture sequences.