## 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…