An example of an LDS and the models that define it. (a) A few frames of a video of six LEDs flashing independently. (b) Top 20 singular values of the data matrix $[ \\bfy_{1:T} ]$ --- formed by stacking  frames of the video as its columns. Note how the singular values, outside the top six, decay rapidly. This is a consequence of the linear nature of light suggests that the frames of the video lie on a six-dimensional subspace. In practice, deviations from linearity   due to saturation lead to small deviations from the six-dimensional subspace as noted from the decaying singular values. \n(c) Basis vectors associated with a six-dimensional approximation of the data. Blacker pixels denote non-negative entries while whiter pixels denote positive entries. Together, they define a six-dimensional subspace that defines the observation model of the LDS.\n(d) State sequence associated with the six-dimensional approximation. The smooth variation of the state values indicate predictability over small time durations --- one of the key hallmarks of an LDS. These smooth transitions are captured by the state transition model.