Online Dictionary Learning with Dependent Data

Learning five image dictionary atoms from a video frame of Bruce Lee by processing one frame at a time. All five dictionary atoms are updated online. Four different settings:

  1. (1st row) past2future sampling, fast adaptation to new data;
  2. (2nd row) past2future sampling, slow adaptation to new data;
  3. (3rd row) random i.i.d. sampling, fast adaptation to new data;
  4. (4th row) random i.i.d. sampling, slow adaptation to new data;


The 4-color FCA on square lattice Ζ^2

The κ-color Firefly Cellular Automaton (FCA) is a discrete model for κ-state pulse-coupled oscillators.  While the FCA on lattices for any κ≠4 exhibit local sprials, the 4-color instance on square lattice shows clustering via interacting incomplete spirals.


The 64-state adaptive 4-coupling on uniform spanning tree of Moore lattice

The 4-coupling is a continuum extension of the 4-color FCA. The adaptive 4-coupling is a clock synchronization algorithm based on the 4-coupling, which is able to synchronizes arbitrary initial joint configuration on any trees. If we take a uniform spanning tree of the underlying lattice, the system tries to form spirals but none are completed by topological restriction.



Probability, combinatorics, and complex systems

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