A common way to represent a time series is to divide it into
short-duration blocks, each of which is then represented by a set of
basis functions. A limitation of this approach, however, is that the
temporal alignment of the basis functions with the underlying
structure in the time series is arbitrary. We present an algorithm
for encoding a time series that does not require blocking the data.
The algorithm finds an efficient representation by inferring the best
temporal positions for functions in a kernel basis. These can have
arbitrary temporal extent and are not constrained to be orthogonal.
This allows the model to capture structure in the signal that may
occur at arbitrary temporal positions and preserves the relative
temporal structure of underlying events. The model is shown to be
equivalent to a very sparse and highly overcomplete basis. Under this
model, the mapping from the data to the representation is nonlinear,
but can be computed efficiently. This form also allows the use of
existing methods for adapting the basis itself to data.
compressed postscript (7 pages, 70kB)
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