  One of the most interesting tools that have recently entered the data science
toolbox is topological data analysis (TDA). With the explosion of available
data sizes and dimensions, identifying and extracting the underlying structure
of a given dataset is a fundamental challenge in data science, and TDA provides
a methodology for analyzing the shape of a dataset using tools and prospects
from algebraic topology. However, the computational complexity makes it quickly
infeasible to process large datasets, especially those with high dimensions.
Here, we introduce a preprocessing strategy called the Characteristic Lattice
Algorithm (CLA), which allows users to reduce the size of a given dataset as
desired while maintaining geometric and topological features in order to make
the computation of TDA feasible or to shorten its computation time. In
addition, we derive a stability theorem and an upper bound of the barcode
errors for CLA based on the bottleneck distance.
