7,308 research outputs found
Support vector machine for functional data classification
In many applications, input data are sampled functions taking their values in
infinite dimensional spaces rather than standard vectors. This fact has complex
consequences on data analysis algorithms that motivate modifications of them.
In fact most of the traditional data analysis tools for regression,
classification and clustering have been adapted to functional inputs under the
general name of functional Data Analysis (FDA). In this paper, we investigate
the use of Support Vector Machines (SVMs) for functional data analysis and we
focus on the problem of curves discrimination. SVMs are large margin classifier
tools based on implicit non linear mappings of the considered data into high
dimensional spaces thanks to kernels. We show how to define simple kernels that
take into account the unctional nature of the data and lead to consistent
classification. Experiments conducted on real world data emphasize the benefit
of taking into account some functional aspects of the problems.Comment: 13 page
A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning
Learning sparse combinations is a frequent theme in machine learning. In this
paper, we study its associated optimization problem in the distributed setting
where the elements to be combined are not centrally located but spread over a
network. We address the key challenges of balancing communication costs and
optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW)
algorithm. We obtain theoretical guarantees on the optimization error
and communication cost that do not depend on the total number of
combining elements. We further show that the communication cost of dFW is
optimal by deriving a lower-bound on the communication cost required to
construct an -approximate solution. We validate our theoretical
analysis with empirical studies on synthetic and real-world data, which
demonstrate that dFW outperforms both baselines and competing methods. We also
study the performance of dFW when the conditions of our analysis are relaxed,
and show that dFW is fairly robust.Comment: Extended version of the SIAM Data Mining 2015 pape
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