  Transit spectroscopy is a powerful tool to decode the chemical composition of
the atmospheres of extrasolar planets. In this paper we focus on unsupervised
techniques for analyzing spectral data from transiting exoplanets. We
demonstrate methods for i) cleaning and validating the data, ii) initial
exploratory data analysis based on summary statistics (estimates of location
and variability), iii) exploring and quantifying the existing correlations in
the data, iv) pre-processing and linearly transforming the data to its
principal components, v) dimensionality reduction and manifold learning, vi)
clustering and anomaly detection, vii) visualization and interpretation of the
data. To illustrate the proposed unsupervised methodology, we use a well-known
public benchmark data set of synthetic transit spectra. We show that there is a
high degree of correlation in the spectral data, which calls for appropriate
low-dimensional representations. We explore a number of different techniques
for such dimensionality reduction and identify several suitable options in
terms of summary statistics, principal components, etc. We uncover interesting
structures in the principal component basis, namely, well-defined branches
corresponding to different chemical regimes of the underlying atmospheres. We
demonstrate that those branches can be successfully recovered with a K-means
clustering algorithm in fully unsupervised fashion. We advocate for a
three-dimensional representation of the spectroscopic data in terms of the
first three principal components, in order to reveal the existing structure in
the data and quickly characterize the chemical class of a planet.
