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Abstract:
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.
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