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Using Quantum Mechanics to Cluster Time Series
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.
A Family of Metrics for Clustering Algorithms
We give the motivation for scoring clustering algorithms and a metric $M : A \rightarrow \mathbb{N}$ from the set of clustering algorithms to the natural numbers which we realize as \begin{equation} M(A) = \sum_i \alpha_i |f_i - \beta_i|^{w_i} \end{equation} where $\alpha_i,\beta_i, w_i$ are parameters used for scoring the feature $f_i$, which is computed empirically.. We give a method by which one can score features such as stability, noise sensitivity, etc and derive the necessary parameters.
