We introduce an improved version of the principal path method, an algorithm conceived to find smooth paths between objects in space. Some key steps of the algorithm have been changed, making the solution intrinsically local and preventing it from being attracted by a global manifold. Judiciously performing the initialization step with the Dijkstra algorithm and a proper metric, the functional now only performs a final refinement of the initial solution. Hence the algorithm is stabler as the space of possible solutions has been considerably reduced with respect to the original method. We tested the proposed algorithm in 2D toy data sets (to understand the behaviour) and in high-dimensional data sets. Compared to the previous version of the algorithm, we obtained significantly stabler and more realistic generated samples.

SUMMARY: A primary problem in high-throughput genomics experiments is finding the most important genes involved in biological processes (e.g. tumor progression). In this applications note, we introduce spathial, an R package for navigating high-dimensional data spaces. spathial implements the Principal Path algorithm, which is a topological method for locally navigating on the data manifold. The package, together with the core algorithm, provides several high-level functions for interpreting the results. One of the analyses we propose is the extraction of the genes that are mainly involved in the progress from one state to another. We show a possible application in the context of tumor progression using RNA-Seq and single-cell datasets, and we compare our results with two commonly used algorithms, edgeR and monocle3, respectively. AVAILABILITY AND IMPLEMENTATION: The R package spathial is available on the Comprehensive R Archive Network (https://cran.r-project.org/web/packages/spathial/index.html) and on GitHub (https://github.com/erikagardini/spathial). It is distributed under the GNU General Public License (version 3). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.