  The $k$-segmentation of a video stream is used to partition it into $k$
piecewise-linear segments, so that each linear segment has a meaningful
interpretation. Such segmentation may be used to summarize large videos using a
small set of images, to identify anomalies within segments and change points
between segments, and to select critical subsets for training machine learning
models. Exact and approximate segmentation methods for $k$-segmentation exist
in the literature. Each of these algorithms occupies a different spot in the
trade-off between computational complexity and accuracy. A novel heuristic
algorithm is proposed in this paper to improve upon existing methods. It is
empirically found to provide accuracies competitive with exact methods at a
fraction of the computational expense.
  The new algorithm is inspired by Lloyd's algorithm for K-Means and Lloyd-Max
algorithm for scalar quantization, and is called the LM algorithm for
convenience. It works by iteratively minimizing a cost function from any given
initialisation; the commonly used $L_2$ cost is chosen in this paper. While the
greedy minimization makes the algorithm sensitive to initialisation, the
ability to converge from any initial guess to a local optimum allows the
algorithm to be integrated into other existing algorithms. Three variants of
the algorithm are tested over a large number of synthetic datasets, one being a
standalone LM implementation, and two others that combine with existing
algorithms. One of the latter two -- LM-enhanced-Bottom-Up segmentation -- is
found to have the best accuracy and the lowest computational complexity among
all algorithms. This variant of LM can provide $k$-segmentations over data sets
with up to a million image frames within several seconds.
