Title: Similarity Preserving Representation Learning for Time Series Analysis,
Abstract: A considerable amount of machine learning algorithms take instance-feature
matrices as their inputs. As such, they cannot directly analyze time series
data due to its temporal nature, usually unequal lengths, and complex
properties. This is a great pity since many of these algorithms are effective,
robust, efficient, and easy to use. In this paper, we bridge this gap by
proposing an efficient representation learning framework that is able to
convert a set of time series with equal or unequal lengths to a matrix format.
In particular, we guarantee that the pairwise similarities between time series
are well preserved after the transformation. The learned feature representation
is particularly suitable to the class of learning problems that are sensitive
to data similarities. Given a set of $n$ time series, we first construct an
$n\times n$ partially observed similarity matrix by randomly sampling $O(n \log
n)$ pairs of time series and computing their pairwise similarities. We then
propose an extremely efficient algorithm that solves a highly non-convex and
NP-hard problem to learn new features based on the partially observed
similarity matrix. We use the learned features to conduct experiments on both
data classification and clustering tasks. Our extensive experimental results
demonstrate that the proposed framework is both effective and efficient.