1,778 research outputs found
Solution Path Algorithm for Twin Multi-class Support Vector Machine
The twin support vector machine and its extensions have made great
achievements in dealing with binary classification problems, however, which is
faced with some difficulties such as model selection and solving
multi-classification problems quickly. This paper is devoted to the fast
regularization parameter tuning algorithm for the twin multi-class support
vector machine. A new sample dataset division method is adopted and the
Lagrangian multipliers are proved to be piecewise linear with respect to the
regularization parameters by combining the linear equations and block matrix
theory. Eight kinds of events are defined to seek for the starting event and
then the solution path algorithm is designed, which greatly reduces the
computational cost. In addition, only few points are combined to complete the
initialization and Lagrangian multipliers are proved to be 1 as the
regularization parameter tends to infinity. Simulation results based on UCI
datasets show that the proposed method can achieve good classification
performance with reducing the computational cost of grid search method from
exponential level to the constant level
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
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
Joint measurements via quantum cloning
We explore the possibility of achieving optimal joint measurements of
noncommuting observables on a single quantum system by performing conventional
measurements of commuting self adjoint operators on optimal clones of the
original quantum system. We consider the case of both finite dimensional and
infinite dimensional Hilbert spaces. In the former we study the joint
measurement of three orthogonal components of a spin 1/2, in the latter we
consider the case of the joint measurements of any pair of noncommuting
quadratures of one mode of the electromagnetic field. We show that universally
covariant cloning is not ideal for joint measurements, and a suitable non
universally covariant cloning is needed.Comment: 8 page
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