14,293 research outputs found
Fuzzy Least Squares Twin Support Vector Machines
Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an
efficient and fast algorithm for binary classification. It combines the
operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it
constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of
linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still
unable to cope with two features of real-world problems. First, in many
real-world applications, labels of samples are not deterministic; they come
naturally with their associated membership degrees. Second, samples in
real-world applications may not be equally important and their importance
degrees affect the classification. In this paper, we propose Fuzzy LST-SVM
(FLST-SVM) to deal with these two characteristics of real-world data. Two
models are introduced for FLST-SVM: the first model builds up crisp hyperplanes
using training samples and their corresponding membership degrees. The second
model, on the other hand, constructs fuzzy hyperplanes using training samples
and their membership degrees. Numerical evaluation of the proposed method with
synthetic and real datasets demonstrate significant improvement in the
classification accuracy of FLST-SVM when compared to well-known existing
versions of SVM
The StarScan plate measuring machine: overview and calibrations
The StarScan machine at the U.S. Naval Observatory (USNO) completed measuring
photographic astrograph plates to allow determination of proper motions for the
USNO CCD Astrograph Catalog (UCAC) program. All applicable 1940 AGK2 plates,
about 2200 Hamburg Zone Astrograph plates, 900 Black Birch (USNO Twin
Astrograph) plates, and 300 Lick Astrograph plates have been measured. StarScan
comprises of a CCD camera, telecentric lens, air-bearing granite table, stepper
motor screws, and Heidenhain scales to operate in a step-stare mode. The
repeatability of StarScan measures is about 0.2 micrometer. The CCD mapping as
well as the global table coordinate system has been calibrated using a special
dot calibration plate and the overall accuracy of StarScan x,y data is derived
to be 0.5 micrometer. Application to real photographic plate data shows that
position information of at least 0.65 micrometer accuracy can be extracted from
course grain 103a-type emulsion astrometric plates. Transformations between
"direct" and "reverse" measures of fine grain emulsion plate measures are
obtained on the 0.3 micrometer level per well exposed stellar image and
coordinate, which is at the limit of the StarScan machine.Comment: 24 pages, 8 figures, accepted for PAS
Positive Semidefinite Metric Learning with Boosting
The learning of appropriate distance metrics is a critical problem in image
classification and retrieval. In this work, we propose a boosting-based
technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One
of the primary difficulties in learning such a metric is to ensure that the
Mahalanobis matrix remains positive semidefinite. Semidefinite programming is
sometimes used to enforce this constraint, but does not scale well.
\BoostMetric is instead based on a key observation that any positive
semidefinite matrix can be decomposed into a linear positive combination of
trace-one rank-one matrices. \BoostMetric thus uses rank-one positive
semidefinite matrices as weak learners within an efficient and scalable
boosting-based learning process. The resulting method is easy to implement,
does not require tuning, and can accommodate various types of constraints.
Experiments on various datasets show that the proposed algorithm compares
favorably to those state-of-the-art methods in terms of classification accuracy
and running time.Comment: 11 pages, Twenty-Third Annual Conference on Neural Information
Processing Systems (NIPS 2009), Vancouver, Canad
Support matrix machine: A review
Support vector machine (SVM) is one of the most studied paradigms in the
realm of machine learning for classification and regression problems. It relies
on vectorized input data. However, a significant portion of the real-world data
exists in matrix format, which is given as input to SVM by reshaping the
matrices into vectors. The process of reshaping disrupts the spatial
correlations inherent in the matrix data. Also, converting matrices into
vectors results in input data with a high dimensionality, which introduces
significant computational complexity. To overcome these issues in classifying
matrix input data, support matrix machine (SMM) is proposed. It represents one
of the emerging methodologies tailored for handling matrix input data. The SMM
method preserves the structural information of the matrix data by using the
spectral elastic net property which is a combination of the nuclear norm and
Frobenius norm. This article provides the first in-depth analysis of the
development of the SMM model, which can be used as a thorough summary by both
novices and experts. We discuss numerous SMM variants, such as robust, sparse,
class imbalance, and multi-class classification models. We also analyze the
applications of the SMM model and conclude the article by outlining potential
future research avenues and possibilities that may motivate academics to
advance the SMM algorithm
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