18,719 research outputs found
Representing complex data using localized principal components with application to astronomical data
Often the relation between the variables constituting a multivariate data
space might be characterized by one or more of the terms: ``nonlinear'',
``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or,
more general, ``complex''. In these cases, simple principal component analysis
(PCA) as a tool for dimension reduction can fail badly. Of the many alternative
approaches proposed so far, local approximations of PCA are among the most
promising. This paper will give a short review of localized versions of PCA,
focusing on local principal curves and local partitioning algorithms.
Furthermore we discuss projections other than the local principal components.
When performing local dimension reduction for regression or classification
problems it is important to focus not only on the manifold structure of the
covariates, but also on the response variable(s). Local principal components
only achieve the former, whereas localized regression approaches concentrate on
the latter. Local projection directions derived from the partial least squares
(PLS) algorithm offer an interesting trade-off between these two objectives. We
apply these methods to several real data sets. In particular, we consider
simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and
Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds),
Lecture Notes in Computational Science and Engineering, Springer, 2007, pp.
180--204,
http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-
Extracting 3D parametric curves from 2D images of Helical objects
Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively
Intraday forecasts of a volatility index: Functional time series methods with dynamic updating
As a forward-looking measure of future equity market volatility, the VIX
index has gained immense popularity in recent years to become a key measure of
risk for market analysts and academics. We consider discrete reported intraday
VIX tick values as realisations of a collection of curves observed sequentially
on equally spaced and dense grids over time and utilise functional data
analysis techniques to produce one-day-ahead forecasts of these curves. The
proposed method facilitates the investigation of dynamic changes in the index
over very short time intervals as showcased using the 15-second high-frequency
VIX index values. With the help of dynamic updating techniques, our point and
interval forecasts are shown to enjoy improved accuracy over conventional time
series models.Comment: 29 pages, 5 figures, To appear at the Annals of Operations Researc
Rate-Distortion Classification for Self-Tuning IoT Networks
Many future wireless sensor networks and the Internet of Things are expected
to follow a software defined paradigm, where protocol parameters and behaviors
will be dynamically tuned as a function of the signal statistics. New protocols
will be then injected as a software as certain events occur. For instance, new
data compressors could be (re)programmed on-the-fly as the monitored signal
type or its statistical properties change. We consider a lossy compression
scenario, where the application tolerates some distortion of the gathered
signal in return for improved energy efficiency. To reap the full benefits of
this paradigm, we discuss an automatic sensor profiling approach where the
signal class, and in particular the corresponding rate-distortion curve, is
automatically assessed using machine learning tools (namely, support vector
machines and neural networks). We show that this curve can be reliably
estimated on-the-fly through the computation of a small number (from ten to
twenty) of statistical features on time windows of a few hundreds samples
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