In this paper, we will present a unified view for LDA. We will (1) emphasize that standard LDA solutions are not unique, (2) propose several new LDA formulations: St-orthonormal LDA, Sw-orthonormal LDA and orthogonal LDA which have unique solutions, and (3) show that with St-orthonormal LDA and Sw-orthonormal LDA formulations, solutions to all four major LDA objective functions are identical. F...

Water exists in at least two families of glassy states, broadly categorized as the low-density (LDA) and high-density amorphous ice (HDA). Remarkably, LDA and HDA can be reversibly interconverted via appropriate thermodynamic paths, such as isothermal compression and isobaric heating, exhibiting first-order-like phase transitions. We perform out-of-equilibrium molecular dynamics simulations of ...

The Fisher linear discriminant analysis (LDA) is a classical method for classification and dimension reduction jointly. A major limitation of the conventional LDA is a so-called singularity issue. Many LDA variants, especially two-stage methods such as PCA+LDA and LDA/QR, were proposed to solve this issue. In the two-stage methods, an intermediate stage for dimension reduction is developed befo...

Singularity problems of scatter matrices in Linear Discriminant Analysis (LDA) are challenging and have obtained attention during the last decade. Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant analysis (DLDA) are two popular algorithms to solve the singularity problem. This paper establishes the equivalent relationship between LDA/QR and DLDA. They ca...

Decoding brain states from response patterns with multivariate pattern recognition techniques is a popular method for detecting multivoxel patterns of brain activation. These patterns are informative with respect to a subject's perceptual or cognitive states. Linear discriminant analysis (LDA) cannot be directly applied to fMRI data analysis because of the "few samples and large features" natur...

We propose the local density approximation (LDA) plus an on-site Coulomb self-interaction-like correction (SIC) potential for describing sp-hybridized bonds in semiconductors and insulators. We motivate the present LDA+USIC scheme by comparing the exact exchange (EXX) hole with the LDA exchange hole. The LDA+USIC method yields good band-gap energies Eg and dielectric constants ε(ω≈ 0) of Si, Ge...

In this paper, the performances of appearance-based statistical methods such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and Independent Component Analysis (ICA) are tested and compared for the recognition of colored face images. Three sets of experiments are conducted for relative performance evaluations. In the first set of experiments, the recognition performanc...

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal ...

We present a new approach to the evaluation of the on-site repulsion energy U for use in the LDA+U method of Anisimov and collaborators. Our objectives are to make the method more firmly based, to concentrate primarily on ground state properties rather than spectra, and to test the method in cases where only modest changes in orbital occupations are expected, as well as for highly correlated ma...