  We have deluge of data in time series format for numerous phenomena. The
number of snapshots, resolution and many other factors come into play as we
look to identify the dynamics in a given problem. The pre-processing and
post-processing steps while working with the data may be related to the
resources in terms of the hardware used to collect data and computations that
we perform on the data to create a model for the problem. Dynamic Mode
Decomposition (DMD) is a data based modeling tool that identifies a matrix to
map a quantity at some time instant to the same quantity in future. It is
possible to generate a model by projecting the high dimensional spatiotemporal
data to a lower dimensional subspace in a probabilistic framework. Sampling and
gaussian projection have been used in the past to increase efficiency in the
computation. Here, we design an optimized version of DMD that utilizes time
delay coordinates and a projection matrix. In our proposal, we discussed about
two projection matrices -- one is inspired by the Krylov subspace and the other
promotes and leverages sparsity to bring computational benefits in producing a
model. Satisfactory results are obtained as they are tested on data related to
Double gyre (present in ocean mixing) and on a 2D compressible signal. The
motivation behind this scheme of DMD comes from the fact that data from many
phenomena are 'big' and 'highly oscillatory.'
