78,758 research outputs found
Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models
The expectation-maximization (EM) algorithm is an iterative method for
finding maximum likelihood estimates when data are incomplete or are treated as
being incomplete. The EM algorithm and its variants are commonly used for
parameter estimation in applications of mixture models for clustering and
classification. This despite the fact that even the Gaussian mixture model
likelihood surface contains many local maxima and is singularity riddled.
Previous work has focused on circumventing this problem by constraining the
smallest eigenvalue of the component covariance matrices. In this paper, we
consider constraining the smallest eigenvalue, the largest eigenvalue, and both
the smallest and largest within the family setting. Specifically, a subset of
the GPCM family is considered for model-based clustering, where we use a
re-parameterized version of the famous eigenvalue decomposition of the
component covariance matrices. Our approach is illustrated using various
experiments with simulated and real data
Decomposition methods for machine learning with small, incomplete or noisy datasets
In many machine learning applications, measurements are sometimes incomplete or noisy resulting in missing features. In other cases, and for different reasons, the datasets are originally small, and therefore, more data samples are required to derive useful supervised or unsupervised classification methods. Correct handling of incomplete, noisy or small datasets in machine learning is a fundamental and classic challenge. In this article, we provide a unified review of recently proposed methods based on signal decomposition for missing features imputation (data completion), classification of noisy samples and artificial generation of new data samples (data augmentation). We illustrate the application of these signal decomposition methods in diverse selected practical machine learning examples including: brain computer interface, epileptic intracranial electroencephalogram signals classification, face recognition/verification and water networks data analysis. We show that a signal decomposition approach can provide valuable tools to improve machine learning performance with low quality datasets.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Sole Casals, Jordi. Center for Advanced Intelligence; JapónFil: Marti Puig, Pere. University of Catalonia; EspañaFil: Sun, Zhe. RIKEN; JapónFil: Tanaka,Toshihisa. Tokyo University of Agriculture and Technology; Japó
Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
In many machine learning applications, measurements are sometimes incomplete or noisy resulting in missing features. In other cases, and for different reasons, the datasets are originally small, and therefore, more data samples are required to derive useful supervised or unsupervised classification methods. Correct handling of incomplete, noisy or small datasets in machine learning is a fundamental and classic challenge. In this article, we provide a unified review of recently proposed methods based on signal decomposition for missing features imputation (data completion), classification of noisy samples and artificial generation of new data samples (data augmentation). We illustrate the application of these signal decomposition methods in diverse selected practical machine learning examples including: brain computer interface, epileptic intracranial electroencephalogram signals classification, face recognition/verification and water networks data analysis. We show that a signal decomposition approach can provide valuable tools to improve machine learning performance with low quality datasets.Instituto Argentino de Radioastronomí
The Matrix Ridge Approximation: Algorithms and Applications
We are concerned with an approximation problem for a symmetric positive
semidefinite matrix due to motivation from a class of nonlinear machine
learning methods. We discuss an approximation approach that we call {matrix
ridge approximation}. In particular, we define the matrix ridge approximation
as an incomplete matrix factorization plus a ridge term. Moreover, we present
probabilistic interpretations using a normal latent variable model and a
Wishart model for this approximation approach. The idea behind the latent
variable model in turn leads us to an efficient EM iterative method for
handling the matrix ridge approximation problem. Finally, we illustrate the
applications of the approximation approach in multivariate data analysis.
Empirical studies in spectral clustering and Gaussian process regression show
that the matrix ridge approximation with the EM iteration is potentially
useful
Large-Scale Multi-Label Learning with Incomplete Label Assignments
Multi-label learning deals with the classification problems where each
instance can be assigned with multiple labels simultaneously. Conventional
multi-label learning approaches mainly focus on exploiting label correlations.
It is usually assumed, explicitly or implicitly, that the label sets for
training instances are fully labeled without any missing labels. However, in
many real-world multi-label datasets, the label assignments for training
instances can be incomplete. Some ground-truth labels can be missed by the
labeler from the label set. This problem is especially typical when the number
instances is very large, and the labeling cost is very high, which makes it
almost impossible to get a fully labeled training set. In this paper, we study
the problem of large-scale multi-label learning with incomplete label
assignments. We propose an approach, called MPU, based upon positive and
unlabeled stochastic gradient descent and stacked models. Unlike prior works,
our method can effectively and efficiently consider missing labels and label
correlations simultaneously, and is very scalable, that has linear time
complexities over the size of the data. Extensive experiments on two real-world
multi-label datasets show that our MPU model consistently outperform other
commonly-used baselines
Molecular dynamics simulations of lead clusters
Molecular dynamics simulations of nanometer-sized lead clusters have been
performed using the Lim, Ong and Ercolessi glue potential (Surf. Sci. {\bf
269/270}, 1109 (1992)). The binding energies of clusters forming crystalline
(fcc), decahedron and icosahedron structures are compared, showing that fcc
cuboctahedra are the most energetically favoured of these polyhedral model
structures. However, simulations of the freezing of liquid droplets produced a
characteristic form of ``shaved'' icosahedron, in which atoms are absent at the
edges and apexes of the polyhedron. This arrangement is energetically favoured
for 600-4000 atom clusters. Larger clusters favour crystalline structures.
Indeed, simulated freezing of a 6525-atom liquid droplet produced an imperfect
fcc Wulff particle, containing a number of parallel stacking faults. The
effects of temperature on the preferred structure of crystalline clusters below
the melting point have been considered. The implications of these results for
the interpretation of experimental data is discussed.Comment: 11 pages, 18 figues, new section added and one figure added, other
minor changes for publicatio
Probabilistic Methodology and Techniques for Artefact Conception and Development
The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology
and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art
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