37,464 research outputs found
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Deep Adaptive Feature Embedding with Local Sample Distributions for Person Re-identification
Person re-identification (re-id) aims to match pedestrians observed by
disjoint camera views. It attracts increasing attention in computer vision due
to its importance to surveillance system. To combat the major challenge of
cross-view visual variations, deep embedding approaches are proposed by
learning a compact feature space from images such that the Euclidean distances
correspond to their cross-view similarity metric. However, the global Euclidean
distance cannot faithfully characterize the ideal similarity in a complex
visual feature space because features of pedestrian images exhibit unknown
distributions due to large variations in poses, illumination and occlusion.
Moreover, intra-personal training samples within a local range are robust to
guide deep embedding against uncontrolled variations, which however, cannot be
captured by a global Euclidean distance. In this paper, we study the problem of
person re-id by proposing a novel sampling to mine suitable \textit{positives}
(i.e. intra-class) within a local range to improve the deep embedding in the
context of large intra-class variations. Our method is capable of learning a
deep similarity metric adaptive to local sample structure by minimizing each
sample's local distances while propagating through the relationship between
samples to attain the whole intra-class minimization. To this end, a novel
objective function is proposed to jointly optimize similarity metric learning,
local positive mining and robust deep embedding. This yields local
discriminations by selecting local-ranged positive samples, and the learned
features are robust to dramatic intra-class variations. Experiments on
benchmarks show state-of-the-art results achieved by our method.Comment: Published on Pattern Recognitio
Unsupervised Feature Selection with Adaptive Structure Learning
The problem of feature selection has raised considerable interests in the
past decade. Traditional unsupervised methods select the features which can
faithfully preserve the intrinsic structures of data, where the intrinsic
structures are estimated using all the input features of data. However, the
estimated intrinsic structures are unreliable/inaccurate when the redundant and
noisy features are not removed. Therefore, we face a dilemma here: one need the
true structures of data to identify the informative features, and one need the
informative features to accurately estimate the true structures of data. To
address this, we propose a unified learning framework which performs structure
learning and feature selection simultaneously. The structures are adaptively
learned from the results of feature selection, and the informative features are
reselected to preserve the refined structures of data. By leveraging the
interactions between these two essential tasks, we are able to capture accurate
structures and select more informative features. Experimental results on many
benchmark data sets demonstrate that the proposed method outperforms many state
of the art unsupervised feature selection methods
Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings
The recovery of the intrinsic geometric structures of data collections is an
important problem in data analysis. Supervised extensions of several manifold
learning approaches have been proposed in the recent years. Meanwhile, existing
methods primarily focus on the embedding of the training data, and the
generalization of the embedding to initially unseen test data is rather
ignored. In this work, we build on recent theoretical results on the
generalization performance of supervised manifold learning algorithms.
Motivated by these performance bounds, we propose a supervised manifold
learning method that computes a nonlinear embedding while constructing a smooth
and regular interpolation function that extends the embedding to the whole data
space in order to achieve satisfactory generalization. The embedding and the
interpolator are jointly learnt such that the Lipschitz regularity of the
interpolator is imposed while ensuring the separation between different
classes. Experimental results on several image data sets show that the proposed
method outperforms traditional classifiers and the supervised dimensionality
reduction algorithms in comparison in terms of classification accuracy in most
settings
On the evolution of flow topology in turbulent Rayleigh-BĂ©nard convection
Copyright 2016 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Benard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 10(8) and 10(10), inside an air-filled rectangular cell of aspect ratio unity and pi span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (Q(G), R-G) has displayed the so-calledPeer ReviewedPostprint (author's final draft
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