Rhythm Vector: a Tempo-Invariant Feature

We introduce a tempo-invariant feature named ``rhythm vector,'' since the tempo of the input data is not given in advance and it may vary throughout the data. From our assumption that the tempo is constant or changes slowly, the proportion of consecutive note lengths $x$ is nearly independent from tempo $\tau$ according to Eq.1). Therefore, we introduce rhythm vector as follows:

$$\mbox{\boldmath$r$}_t=(r_t^1,\cdots,r_t^m)\mbox{~~where~~} r_t^i= \frac{x_{t+i}}{x_t + \cdots + x_{t+m-1}} \vspace{-2.5ex}$$ (3)

Here, probabilistic distribution $p(\mbox{\boldmath$r$})$ is assumed to follow the normal distribution ${\cal N}(\mbox{\boldmath$\mu$}, \mbox{\boldmath$\Sigma$})$, whose parameters, mean vector $\mbox{\boldmath$\mu$}$ and covariance matrix $\mbox{\boldmath$\Sigma$}$, can be obtained through statistical training using human-performed MIDI data.