36 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
Functional Mixture Discriminant Analysis with hidden process regression for curve classification
We present a new mixture model-based discriminant analysis approach for
functional data using a specific hidden process regression model. The approach
allows for fitting flexible curve-models to each class of complex-shaped curves
presenting regime changes. The model parameters are learned by maximizing the
observed-data log-likelihood for each class by using a dedicated
expectation-maximization (EM) algorithm. Comparisons on simulated data with
alternative approaches show that the proposed approach provides better results.Comment: In Proceedings of the XXth European Symposium on Artificial Neural
Networks, Computational Intelligence and Machine Learning (ESANN), Pages
281-286, 2012, Bruges, Belgiu
Consistency of Derivative Based Functional Classifiers on Sampled Data
International audienceIn some applications, especially spectrometric ones, curve classifiers achieve better performances if they work on the -order derivatives of their inputs. This paper proposes a smoothing spline based approach that give a strong theoretical background to this common practice
Mixtures of Spatial Spline Regressions
We present an extension of the functional data analysis framework for
univariate functions to the analysis of surfaces: functions of two variables.
The spatial spline regression (SSR) approach developed can be used to model
surfaces that are sampled over a rectangular domain. Furthermore, combining SSR
with linear mixed effects models (LMM) allows for the analysis of populations
of surfaces, and combining the joint SSR-LMM method with finite mixture models
allows for the analysis of populations of surfaces with sub-family structures.
Through the mixtures of spatial splines regressions (MSSR) approach developed,
we present methodologies for clustering surfaces into sub-families, and for
performing surface-based discriminant analysis. The effectiveness of our
methodologies, as well as the modeling capabilities of the SSR model are
assessed through an application to handwritten character recognition
Unexpected properties of bandwidth choice when smoothing discrete data for constructing a functional data classifier
The data functions that are studied in the course of functional data analysis
are assembled from discrete data, and the level of smoothing that is used is
generally that which is appropriate for accurate approximation of the
conceptually smooth functions that were not actually observed. Existing
literature shows that this approach is effective, and even optimal, when using
functional data methods for prediction or hypothesis testing. However, in the
present paper we show that this approach is not effective in classification
problems. There a useful rule of thumb is that undersmoothing is often
desirable, but there are several surprising qualifications to that approach.
First, the effect of smoothing the training data can be more significant than
that of smoothing the new data set to be classified; second, undersmoothing is
not always the right approach, and in fact in some cases using a relatively
large bandwidth can be more effective; and third, these perverse results are
the consequence of very unusual properties of error rates, expressed as
functions of smoothing parameters. For example, the orders of magnitude of
optimal smoothing parameter choices depend on the signs and sizes of terms in
an expansion of error rate, and those signs and sizes can vary dramatically
from one setting to another, even for the same classifier.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1158 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Un r\'esultat de consistance pour des SVM fonctionnels par interpolation spline
This Note proposes a new methodology for function classification with Support
Vector Machine (SVM). Rather than relying on projection on a truncated Hilbert
basis as in our previous work, we use an implicit spline interpolation that
allows us to compute SVM on the derivatives of the studied functions. To that
end, we propose a kernel defined directly on the discretizations of the
observed functions. We show that this method is universally consistent.Comment: 6 page