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 $m$ constraints and matrices of size $d$ by $d$ is roughly reduced from $\mathcal{O}(m^3+md^3+m^2d^2)$ to $\mathcal{O}(d^3)$ ($m>d$ in our case).Comment: 14 page

Joint Bayesian Gaussian discriminant analysis for speaker verification

State-of-the-art i-vector based speaker verification relies on variants of Probabilistic Linear Discriminant Analysis (PLDA) for discriminant analysis. We are mainly motivated by the recent work of the joint Bayesian (JB) method, which is originally proposed for discriminant analysis in face verification. We apply JB to speaker verification and make three contributions beyond the original JB. 1) In contrast to the EM iterations with approximated statistics in the original JB, the EM iterations with exact statistics are employed and give better performance. 2) We propose to do simultaneous diagonalization (SD) of the within-class and between-class covariance matrices to achieve efficient testing, which has broader application scope than the SVD-based efficient testing method in the original JB. 3) We scrutinize similarities and differences between various Gaussian PLDAs and JB, complementing the previous analysis of comparing JB only with Prince-Elder PLDA. Extensive experiments are conducted on NIST SRE10 core condition 5, empirically validating the superiority of JB with faster convergence rate and 9-13% EER reduction compared with state-of-the-art PLDA.Comment: accepted by ICASSP201

Sparse multinomial kernel discriminant analysis (sMKDA)

Dimensionality reduction via canonical variate analysis (CVA) is important for pattern recognition and has been extended variously to permit more flexibility, e.g. by "kernelizing" the formulation. This can lead to over-fitting, usually ameliorated by regularization. Here, a method for sparse, multinomial kernel discriminant analysis (sMKDA) is proposed, using a sparse basis to control complexity. It is based on the connection between CVA and least-squares, and uses forward selection via orthogonal least-squares to approximate a basis, generalizing a similar approach for binomial problems. Classification can be performed directly via minimum Mahalanobis distance in the canonical variates. sMKDA achieves state-of-the-art performance in terms of accuracy and sparseness on 11 benchmark datasets

Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population

This paper focuses on the application of Discriminant Analysis to a set of geometrical objects (bodies) characterized by currents. A current is a relevant mathematical object to model geometrical data, like hypersurfaces, through integration of vector fields along them. As a consequence of the choice of a vector-valued Reproducing Kernel Hilbert Space (RKHS) as a test space to integrate hypersurfaces, it is possible to consider that hypersurfaces are embedded in this Hilbert space. This embedding enables us to consider classification algorithms of geometrical objects. A method to apply Functional Discriminant Analysis in the obtained vector-valued RKHS is given. This method is based on the eigenfunction decomposition of the kernel. So, the novelty of this paper is the reformulation of a size and shape classification problem in Functional Data Analysis terms using the theory of currents and vector-valued RKHS. This approach is applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children's wear