29,422 research outputs found
On clustering procedures and nonparametric mixture estimation
This paper deals with nonparametric estimation of conditional den-sities in
mixture models in the case when additional covariates are available. The
proposed approach consists of performing a prelim-inary clustering algorithm on
the additional covariates to guess the mixture component of each observation.
Conditional densities of the mixture model are then estimated using kernel
density estimates ap-plied separately to each cluster. We investigate the
expected L 1 -error of the resulting estimates and derive optimal rates of
convergence over classical nonparametric density classes provided the
clustering method is accurate. Performances of clustering algorithms are
measured by the maximal misclassification error. We obtain upper bounds of this
quantity for a single linkage hierarchical clustering algorithm. Lastly,
applications of the proposed method to mixture models involving elec-tricity
distribution data and simulated data are presented
A hybrid supervised/unsupervised machine learning approach to solar flare prediction
We introduce a hybrid approach to solar flare prediction, whereby a
supervised regularization method is used to realize feature importance and an
unsupervised clustering method is used to realize the binary flare/no-flare
decision. The approach is validated against NOAA SWPC data
Making Laplacians commute
In this paper, we construct multimodal spectral geometry by finding a pair of
closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are
jointly diagonalizable and hence have the same eigenbasis. Our construction
naturally extends classical data analysis tools based on spectral geometry,
such as diffusion maps and spectral clustering. We provide several synthetic
and real examples of applications in dimensionality reduction, shape analysis,
and clustering, demonstrating that our method better captures the inherent
structure of multi-modal data
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