Hierarchical Linear Dynamical Systems: A new model for clustering of time series

Hierarchical linear dynamical systems for unsupervised musical note recognition

“…Therefore, similar time structure (same musical note) presented at the observation layer will drive the top layer state to similar locations in state space, while differences in the input time structure will push the top layer state mean values to different points in the space, creating invariant representations (clusters) for musical data as we have illustrated in previous works [17], [18]. This multilayer state model is still linear, and can be trained using recursive state estimators since it is a special case of the system model defined in the Kalman Filter [19], which further exploits computational efficiency.…”

“…Classification accuracy of HLDS, SWIPE' and YIN are 93.33%, 91.37% and 92.41% respectively [18]. A key property of our model is that it needs a fixed amount of sample frames to reach a cluster and past that the rhythm does not affect the assignment (i.e.…”

“…However, we found that some of the mistakes in note classification in songs is derived from too sluggish convergence. One alternative is to tune the noise parameters that affect the learned coefficients, but a time domain implementation of the observation model instead of using FFTs will provide convergence time less than 50ms [18] which is significantly shorter compared to the frequency domain implementation presented in this paper.…”

“…It is possible to predict the transient response of the model given the parameters, but it is difficult to reach conclusions easily because of the matrices product. So it is more practical to study the convergence time experimentally as done in [18].…”

“…without windows, as shown in the time domain implementation of HLDS in [18]) and without labels can be interpreted as a clustering-in-time operation. For time series clustering, the state of the art methods require windowing and create non injective solutions, which are detrimental (clusters change with the window size) [15].…”