  In this article we present a method by which we can reduce a time series into
a single point in $\mathbb{R}^{13}$. We have chosen 13 dimensions so as to
prevent too many points from being labeled as "noise." When using a Euclidean
(or Mahalanobis) metric, a simple clustering algorithm will with near certainty
label the majority of points as "noise." On pure physical considerations, this
is not possible. Included in our 13 dimensions are four parameters which
describe the coefficients of a cubic polynomial attached to a Gaussian picking
up a general trend, four parameters picking up periodicity in a time series,
two each for amplitude of a wave and period of a wave, and the final five
report the "leftover" noise of the detrended and aperiodic time series. Of the
final five parameters, four are the centralized probabilistic moments, and the
final for the relative size of the series. The first main contribution of this
work is to apply a theorem of quantum mechanics about the completeness of the
solutions to the quantum harmonic oscillator on $L^2(\mathbb{R})$ to estimating
trends in time series. The second main contribution is the method of fitting
parameters. After many numerical trials, we realized that methods such a
Newton-Rhaphson and Levenberg-Marquardt converge extremely fast if the initial
guess is good. Thus we guessed many initial points in our parameter space and
computed only a few iterations, a technique common in Keogh's work on time
series clustering. Finally, we have produced a model which gives incredibly
accurate results quickly. We ackowledge that there are faster methods as well
of more accurate methods, but this work shows that we can still increase
computation speed with little, if any, cost to accuracy in the sense of data
clustering.
