4,493 research outputs found
Learning to Transform Time Series with a Few Examples
We describe a semi-supervised regression algorithm that learns to transform one time series into another time series given examples of the transformation. This algorithm is applied to tracking, where a time series of observations from sensors is transformed to a time series describing the pose of a target. Instead of defining and implementing such transformations for each tracking task separately, our algorithm learns a memoryless transformation of time series from a few example input-output mappings. The algorithm searches for a smooth function that fits the training examples and, when applied to the input time series, produces a time series that evolves according to assumed dynamics. The learning procedure is fast and lends itself to a closed-form solution. It is closely related to nonlinear system identification and manifold learning techniques. We demonstrate our algorithm on the tasks of tracking RFID tags from signal strength measurements, recovering the pose of rigid objects, deformable bodies, and articulated bodies from video sequences. For these tasks, this algorithm requires significantly fewer examples compared to fully-supervised regression algorithms or semi-supervised learning algorithms that do not take the dynamics of the output time series into account
Combining Parametric and Non-parametric Algorithms for a Partially Unsupervised Classification of Multitemporal Remote-Sensing Images
In this paper, we propose a classification system based on a multiple-classifier architecture, which is aimed at updating land-cover maps by using multisensor and/or multisource remote-sensing images. The proposed system is composed of an ensemble of classifiers that, once trained in a supervised way on a specific image of a given area, can be retrained in an unsupervised way to classify a new image of the considered site. In this context, two techniques are presented for the unsupervised updating of the parameters of a maximum-likelihood (ML) classifier and a radial basis function (RBF) neural-network classifier, on the basis of the distribution of the new image to be classified. Experimental results carried out on a multitemporal and multisource remote-sensing data set confirm the effectiveness of the proposed system
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
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Local Kernels and the Geometric Structure of Data
We introduce a theory of local kernels, which generalize the kernels used in
the standard diffusion maps construction of nonparametric modeling. We prove
that evaluating a local kernel on a data set gives a discrete representation of
the generator of a continuous Markov process, which converges in the limit of
large data. We explicitly connect the drift and diffusion coefficients of the
process to the moments of the kernel. Moreover, when the kernel is symmetric,
the generator is the Laplace-Beltrami operator with respect to a geometry which
is influenced by the embedding geometry and the properties of the kernel. In
particular, this allows us to generate any Riemannian geometry by an
appropriate choice of local kernel. In this way, we continue a program of
Belkin, Niyogi, Coifman and others to reinterpret the current diverse
collection of kernel-based data analysis methods and place them in a geometric
framework. We show how to use this framework to design local kernels invariant
to various features of data. These data-driven local kernels can be used to
construct conformally invariant embeddings and reconstruct global
diffeomorphisms
Atom-Density Representations for Machine Learning
The applications of machine learning techniques to chemistry and materials
science become more numerous by the day. The main challenge is to devise
representations of atomic systems that are at the same time complete and
concise, so as to reduce the number of reference calculations that are needed
to predict the properties of different types of materials reliably. This has
led to a proliferation of alternative ways to convert an atomic structure into
an input for a machine-learning model. We introduce an abstract definition of
chemical environments that is based on a smoothed atomic density, using a
bra-ket notation to emphasize basis set independence and to highlight the
connections with some popular choices of representations for describing atomic
systems. The correlations between the spatial distribution of atoms and their
chemical identities are computed as inner products between these feature kets,
which can be given an explicit representation in terms of the expansion of the
atom density on orthogonal basis functions, that is equivalent to the smooth
overlap of atomic positions (SOAP) power spectrum, but also in real space,
corresponding to -body correlations of the atom density. This formalism lays
the foundations for a more systematic tuning of the behavior of the
representations, by introducing operators that represent the correlations
between structure, composition, and the target properties. It provides a
unifying picture of recent developments in the field and indicates a way
forward towards more effective and computationally affordable machine-learning
schemes for molecules and materials
A kernel-based approach for fault diagnosis in batch processes
This article explores the potential of kernel-based techniques for discriminating on-specification and off-specification batch runs, combining kernel-partial least squares discriminant analysis and three common approaches to analyze batch data by means of bilinear models: landmark features extraction, batchwise unfolding, and variablewise unfolding. Gower s idea of pseudo-sample projection is exploited to recover the contribution of the initial variables to the final model and visualize those having the highest discriminant power. The results show that the proposed approach provides an efficient fault discrimination and enables a correct identification of the discriminant variables in the considered case studies.Vitale, R.; De Noord, OE.; Ferrer, A. (2014). A kernel-based approach for fault diagnosis in batch processes. Journal of Chemometrics. 28(8):697-707. doi:10.1002/cem.2629S697707288Cao, D.-S., Liang, Y.-Z., Xu, Q.-S., Hu, Q.-N., Zhang, L.-X., & Fu, G.-H. (2011). Exploring nonlinear relationships in chemical data using kernel-based methods. Chemometrics and Intelligent Laboratory Systems, 107(1), 106-115. doi:10.1016/j.chemolab.2011.02.004Walczak, B., & Massart, D. L. (1996). The Radial Basis Functions â Partial Least Squares approach as a flexible non-linear regression technique. Analytica Chimica Acta, 331(3), 177-185. doi:10.1016/0003-2670(96)00202-4Walczak, B., & Massart, D. L. (1996). Application of Radial Basis Functions â Partial Least Squares to non-linear pattern recognition problems: diagnosis of process faults. Analytica Chimica Acta, 331(3), 187-193. doi:10.1016/0003-2670(96)00206-1Gasteiger, J., & Zupan, J. (1993). Neural Networks in Chemistry. Angewandte Chemie International Edition in English, 32(4), 503-527. doi:10.1002/anie.199305031Li, H., Liang, Y., & Xu, Q. (2009). Support vector machines and its applications in chemistry. Chemometrics and Intelligent Laboratory Systems, 95(2), 188-198. doi:10.1016/j.chemolab.2008.10.007Williams, P. (2009). Influence of Water on Prediction of Composition and Quality Factors: The Aquaphotomics of Low Moisture Agricultural Materials. Journal of Near Infrared Spectroscopy, 17(6), 315-328. doi:10.1255/jnirs.862Tan, C., & Li, M. (2008). Mutual information-induced interval selection combined with kernel partial least squares for near-infrared spectral calibration. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 71(4), 1266-1273. doi:10.1016/j.saa.2008.03.033Embrechts, M. J., & Ekins, S. (2006). Classification of Metabolites with Kernel-Partial Least Squares (K-PLS). Drug Metabolism and Disposition, 35(3), 325-327. doi:10.1124/dmd.106.013185Arenas-Garcia, J., & Camps-Valls, G. (2008). Efficient Kernel Orthonormalized PLS for Remote Sensing Applications. IEEE Transactions on Geoscience and Remote Sensing, 46(10), 2872-2881. doi:10.1109/tgrs.2008.918765Sun, R., & Tsung, F. (2003). A kernel-distance-based multivariate control chart using support vector methods. International Journal of Production Research, 41(13), 2975-2989. doi:10.1080/1352816031000075224Lee, J.-M., Yoo, C., Choi, S. W., Vanrolleghem, P. A., & Lee, I.-B. (2004). Nonlinear process monitoring using kernel principal component analysis. Chemical Engineering Science, 59(1), 223-234. doi:10.1016/j.ces.2003.09.012Kewley, R. H., Embrechts, M. J., & Breneman, C. (2000). Data strip mining for the virtual design of pharmaceuticals with neural networks. IEEE Transactions on Neural Networks, 11(3), 668-679. doi:10.1109/72.846738ĂstĂŒn, B., Melssen, W. J., & Buydens, L. M. C. (2007). Visualisation and interpretation of Support Vector Regression models. Analytica Chimica Acta, 595(1-2), 299-309. doi:10.1016/j.aca.2007.03.023Krooshof, P. W. T., UÌstuÌn, B., Postma, G. J., & Buydens, L. M. C. (2010). Visualization and Recovery of the (Bio)chemical Interesting Variables in Data Analysis with Support Vector Machine Classification. Analytical Chemistry, 82(16), 7000-7007. doi:10.1021/ac101338yGOWER, J. C., & HARDING, S. A. (1988). Nonlinear biplots. Biometrika, 75(3), 445-455. doi:10.1093/biomet/75.3.445Postma, G. J., Krooshof, P. W. T., & Buydens, L. M. C. (2011). Opening the kernel of kernel partial least squares and support vector machines. Analytica Chimica Acta, 705(1-2), 123-134. doi:10.1016/j.aca.2011.04.025Smolinska, A., Blanchet, L., Coulier, L., Ampt, K. A. M., Luider, T., Hintzen, R. Q., ⊠Buydens, L. M. C. (2012). Interpretation and Visualization of Non-Linear Data Fusion in Kernel Space: Study on Metabolomic Characterization of Progression of Multiple Sclerosis. PLoS ONE, 7(6), e38163. doi:10.1371/journal.pone.0038163Camacho, J., PicĂł, J., & Ferrer, A. (2008). Bilinear modelling of batch processes. Part I: theoretical discussion. Journal of Chemometrics, 22(5), 299-308. doi:10.1002/cem.1113Wold, S., Kettaneh-Wold, N., MacGregor, J. F., & Dunn, K. G. (2009). Batch Process Modeling and MSPC. Comprehensive Chemometrics, 163-197. doi:10.1016/b978-044452701-1.00108-3Nomikos, P., & MacGregor, J. F. (1995). Multivariate SPC Charts for Monitoring Batch Processes. Technometrics, 37(1), 41-59. doi:10.1080/00401706.1995.10485888GarcĂa-Muñoz, S., Kourti, T., MacGregor, J. F., Mateos, A. G., & Murphy, G. (2003). Troubleshooting of an Industrial Batch Process Using Multivariate Methods. Industrial & Engineering Chemistry Research, 42(15), 3592-3601. doi:10.1021/ie0300023PĂ©rez, N. F., FerrĂ©, J., & BoquĂ©, R. (2009). Calculation of the reliability of classification in discriminant partial least-squares binary classification. Chemometrics and Intelligent Laboratory Systems, 95(2), 122-128. doi:10.1016/j.chemolab.2008.09.005Lindgren, F., Hansen, B., Karcher, W., Sjöström, M., & Eriksson, L. (1996). Model validation by permutation tests: Applications to variable selection. Journal of Chemometrics, 10(5-6), 521-532. doi:10.1002/(sici)1099-128x(199609)10:5/63.0.co;2-jQuintĂĄs, G., Portillo, N., GarcĂa-Cañaveras, J. C., Castell, J. V., Ferrer, A., & Lahoz, A. (2011). Chemometric approaches to improve PLSDA model outcome for predicting human non-alcoholic fatty liver disease using UPLC-MS as a metabolic profiling tool. Metabolomics, 8(1), 86-98. doi:10.1007/s11306-011-0292-5Courrieu, P. (2002). Straight monotonic embedding of data sets in Euclidean spaces. Neural Networks, 15(10), 1185-1196. doi:10.1016/s0893-6080(02)00091-
Coupled Depth Learning
In this paper we propose a method for estimating depth from a single image
using a coarse to fine approach. We argue that modeling the fine depth details
is easier after a coarse depth map has been computed. We express a global
(coarse) depth map of an image as a linear combination of a depth basis learned
from training examples. The depth basis captures spatial and statistical
regularities and reduces the problem of global depth estimation to the task of
predicting the input-specific coefficients in the linear combination. This is
formulated as a regression problem from a holistic representation of the image.
Crucially, the depth basis and the regression function are {\bf coupled} and
jointly optimized by our learning scheme. We demonstrate that this results in a
significant improvement in accuracy compared to direct regression of depth
pixel values or approaches learning the depth basis disjointly from the
regression function. The global depth estimate is then used as a guidance by a
local refinement method that introduces depth details that were not captured at
the global level. Experiments on the NYUv2 and KITTI datasets show that our
method outperforms the existing state-of-the-art at a considerably lower
computational cost for both training and testing.Comment: 10 pages, 3 Figures, 4 Tables with quantitative evaluation
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