Compression after Lempel and Ziv (LZ78)
When reading about sequence learning and the prediction of elements in a time series you inevitably cross paths with the area of sequence compression at some point, and so did I. In the present post I’d like to outline a…
Mapper Python Implementation
A few posts ago I wrote about the mapper construction by Carlsson-Memoli-Singh and want to follow up on that a little. I wrote a straightforward implementation of the construction in Python. It can be found here: github.com/mirkoklukas/tda-mapper-py.
K-Means, coverings, and Voronoi diagrams
This is the 4th of a series of posts on cluster-algorithms and ideas in data analysis. The $k$-Means algorithm computes a Voronoi partition of the data set such that each landmark is given by the centroid of the corresponding cell….
Mapper – A discrete generalization of the Reeb graph
This is the third of a series of posts on cluster-algorithms and ideas in data analysis. Mapper is a construction that uses a given cluster-algorithm to associate a simplicial complex to a reference map on a given data set. It…
Density-based clustering in spatial data (2)
This is the second of a series of posts on cluster-algorithms and ideas in data analysis (and related fields). Ordering points to identify the clustering structure (OPTICS) is a data clustering algorithm presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter…
Density-based clustering in spatial data (1)
This is the first of a series of posts on cluster-algorithms and ideas in data analysis (and related fields). Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm proposed by Martin Ester, Hans-Peter Kriegel, Jörg Sander…