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<h1 class="title toc-ignore">Software</h1>
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<p><br></p>
<div id="r-package-tda-statistical-tools-for-topological-data-analysis"
class="section level2">
<h2>R package TDA: Statistical Tools for Topological Data Analysis</h2>
<ul>
<li><p>Authors: Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clement
Maria, David L. Millman, Vincent Rouvreau.</p></li>
<li><p>Maintainer: Jisu KIM ( jisu [DOT] kim [AT] inria [DOT] fr
)</p></li>
<li><p>[ <a
href="https://cran.r-project.org/web/packages/TDA/index.html">CRAN</a> |
<a href="https://cran.r-project.org/web/packages/TDA/TDA.pdf">Reference
Manual</a> | <a
href="https://cran.r-project.org/web/packages/TDA/vignettes/article.pdf">Vignettes</a>
| <a
href="http://www.stat.cmu.edu/~flecci/software/index.html">Fabrizio’s
page</a> | <a href="http://arxiv.org/abs/1504.05438">arXiv</a>
]</p></li>
</ul>
<p>The R package TDA provides some tools for Topological Data Analysis.
In particular, it includes implementations of functions that, given some
data, provide topological information about the underlying space, such
as the distance function, the distance to a measure, the kNN density
estimator, the kernel density estimator, and the kernel distance. The
salient topological features of the sublevel sets (or superlevel sets)
of these functions can be quantified with persistent homology. We
provide an R interface for the efficient algorithms of the C++ libraries
<a href="https://project.inria.fr/gudhi">GUDHI</a>, <a
href="http://www.mrzv.org/software/dionysus">Dionysus</a> and <a
href="https://bitbucket.org/phat-code/phat">PHAT</a>, including a
function for the persistent homology of the Rips filtration, and one for
the persistent homology of sublevel sets (or superlevel sets) of
arbitrary functions evaluated over a grid of points. The significance of
the features in the resulting persistence diagrams can be analyzed with
functions that implement the methods discussed in <span
class="citation">(Fasy et al. 2014)</span>, <span
class="citation">(Chazal, Fasy, Lecci, Rinaldo, et al. 2014)</span> and
<span class="citation">(Chazal, Fasy, Lecci, Michel, et al.
2014)</span>. The R package TDA also includes the implementation of an
algorithm for density clustering, which allows us to identify the
spatial organization of the probability mass associated to a density
function and visualize it by means of a dendrogram, the cluster
tree.</p>
<pre class="r"><code>library("TDA")
set.seed(0)
X <- circleUnif(100)
lim <- rep(c(-1.6, 1.6), 2)
by <- 0.05
Xseq <- seq(lim[1], lim[2], by = by)
Yseq <- seq(lim[3], lim[4], by = by)
Grid <- expand.grid(Xseq, Yseq)
m0 <- 0.1
Diag <- gridDiag(X = X, FUN = dtm, lim = lim,
by = by, sublevel = TRUE, library = "Dionysus",
printProgress = FALSE, m0 = m0)
B <- 20
alpha <- 0.1
band <- bootstrapBand(X = X, FUN = dtm, Grid = Grid, B = B,
parallel = FALSE, alpha = alpha, m0 = m0)
par(mfrow = c(1, 2))
plot(X, pch = 16, cex = 0.5, xlab = "", ylab = "")
plot(Diag[["diagram"]], band = 2 * band[["width"]])</code></pre>
<p><img src="software_files/figure-html/unnamed-chunk-1-1.png" width="672" /></p>
<hr />
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-ChazalFLMRW2014" class="csl-entry">
Chazal, Frédéric, Brittany Terese Fasy, Fabrizio Lecci, Bertrand Michel,
Alessandro Rinaldo, and Larry Wasserman. 2014. <span>“Robust Topological
Inference: Distance-to-a-Measure and Kernel Distance.”</span>
<em>Technical Report</em>.
</div>
<div id="ref-ChazalFLRW2014" class="csl-entry">
Chazal, Frédéric, Brittany Terese Fasy, Fabrizio Lecci, Alessandro
Rinaldo, and Larry Wasserman. 2014. <span>“Stochastic Convergence of
Persistence Landscapes and Silhouettes.”</span> In <em>Annual Symposium
on Computational Geometry</em>, 474–83. ACM.
</div>
<div id="ref-FasyLRWBS2014" class="csl-entry">
Fasy, Brittany Terese, Fabrizio Lecci, Alessandro Rinaldo, Larry
Wasserman, Sivaraman Balakrishnan, and Aarti Singh. 2014.
<span>“Confidence Sets for Persistence Diagrams.”</span> <em>Annals of
Statistics</em>.
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