25,762 research outputs found
Worst-Case Linear Discriminant Analysis as Scalable Semidefinite Feasibility Problems
In this paper, we propose an efficient semidefinite programming (SDP)
approach to worst-case linear discriminant analysis (WLDA). Compared with the
traditional LDA, WLDA considers the dimensionality reduction problem from the
worst-case viewpoint, which is in general more robust for classification.
However, the original problem of WLDA is non-convex and difficult to optimize.
In this paper, we reformulate the optimization problem of WLDA into a sequence
of semidefinite feasibility problems. To efficiently solve the semidefinite
feasibility problems, we design a new scalable optimization method with
quasi-Newton methods and eigen-decomposition being the core components. The
proposed method is orders of magnitude faster than standard interior-point
based SDP solvers.
Experiments on a variety of classification problems demonstrate that our
approach achieves better performance than standard LDA. Our method is also much
faster and more scalable than standard interior-point SDP solvers based WLDA.
The computational complexity for an SDP with constraints and matrices of
size by is roughly reduced from to
( in our case).Comment: 14 page
Discriminant analysis under the common principal components model
For two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularised CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations where the CPC model is applicable. This paper extends their work to the context of discriminant analysis for two groups, by plugging the regularised CPC estimator into the ordinary quadratic discriminant function. Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures
Target Contrastive Pessimistic Discriminant Analysis
Domain-adaptive classifiers learn from a source domain and aim to generalize
to a target domain. If the classifier's assumptions on the relationship between
domains (e.g. covariate shift) are valid, then it will usually outperform a
non-adaptive source classifier. Unfortunately, it can perform substantially
worse when its assumptions are invalid. Validating these assumptions requires
labeled target samples, which are usually not available. We argue that, in
order to make domain-adaptive classifiers more practical, it is necessary to
focus on robust methods; robust in the sense that the model still achieves a
particular level of performance without making strong assumptions on the
relationship between domains. With this objective in mind, we formulate a
conservative parameter estimator that only deviates from the source classifier
when a lower or equal risk is guaranteed for all possible labellings of the
given target samples. We derive the corresponding estimator for a discriminant
analysis model, and show that its risk is actually strictly smaller than that
of the source classifier. Experiments indicate that our classifier outperforms
state-of-the-art classifiers for geographically biased samples.Comment: 9 pages, no figures, 2 tables. arXiv admin note: substantial text
overlap with arXiv:1706.0808
A note on stability conditions for planar switched systems
This paper is concerned with the stability problem for the planar linear
switched system , where the real
matrices are Hurwitz and is a measurable function. We give coordinate-invariant
necessary and sufficient conditions on and under which the system
is asymptotically stable for arbitrary switching functions . The new
conditions unify those given in previous papers and are simpler to be verified
since we are reduced to study 4 cases instead of 20. Most of the cases are
analyzed in terms of the function \Gamma(A_1,A_2)={1/2}(\tr(A_1) \tr(A_2)-
\tr(A_1A_2)).Comment: 9 pages, 3 figure
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