A comparison of generalized linear discriminant analysis algorithms

Linear discriminant analysis (LDA) is a dimension reduction method which finds an optimal linear transformation that maximizes the class separability. However, in undersampled problems where the number of data samples is smaller than the dimension of data space, it is difficult to apply LDA due to the singularity of scatter matrices caused by high dimensionality. In order to make LDA applicable, several generalizations of LDA have been proposed recently. In this paper, we present theoretical and algorithmic relationships among several generalized LDA algorithms and compare their computational complexities and performances in text classification and face recognition. Towards a practical dimension reduction method for high dimensional data, an efficient algorithm is proposed, which reduces the computational complexity greatly while achieving competitive prediction accuracies. We also present nonlinear extensions of these LDA algorithms based on kernel methods. It is shown that a generalized eigenvalue problem can be formulated in the kernel-based feature space, and generalized LDA algorithms are applied to solve the generalized eigenvalue problem, resulting in nonlinear discriminant analysis. Performances of these linear and nonlinear discriminant analysis algorithms are compared extensively.     

Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis

In this paper, we present a new approach for fingerprint classification based on discrete Fourier transform (DFT) and nonlinear discriminant analysis. Utilizing the DFT and directional filters, a reliable and efficient directional image is constructed from each fingerprint image, and then nonlinear discriminant analysis is applied to the constructed directional images, reducing the dimension dramatically and extracting the discriminant features. The proposed method explores the capability of DFT and directional filtering in dealing with low-quality images and the effectiveness of nonlinear feature extraction method in fingerprint classification. Experimental results demonstrates competitive performance compared with other published results.     

Electrokinetically driven concentration of particles and cells by dielectrophoresis with DC-offset AC electric field

Insulator-based dielectrophoresis (iDEP) has been successfully used for on-chip manipulations of biological samples. Despite its effectiveness, iDEP typically requires high DC voltages to achieve sufficient electric field; this is mainly due to the coupled phenomena among linear electrokinetics: electroosmosis (EO) and electrophoresis (EP) and nonlinear electrokinetics: dielectrophoresis (DEP). This paper presents a microfluidic technique using DC-offset AC electric field for electrokinetic concentration of particles and cells by repulsive iDEP. This technique introduces AC electric field for producing iDEP which is decoupled from electroosmosis (EO) and electrophoresis (EP). The repulsive iDEP is generated in a PDMS tapered contraction channel that induces non-uniform electric field. The benefits of introducing AC electric field component are threefold: (i) it contributes to DEP force acting on particles, (ii) it suppresses EO flow and (iii) it does not cause any EP motion. As a result, the required DC field component that is mainly used to transport particles on the basis of EO and EP can be significantly reduced. Experimental results supported by numerical simulations showed that the total DC-offset AC electric field strength required to concentrate 15-μm particles is significantly reduced up to 85.9% as compared to using sole DC electric field. Parametric experimental studies showed that the higher buffer concentration, larger particle size and higher ratio of AC-to-DC electric field are favorable for particle concentration. In addition, the proposed technique was demonstrated for concentration of yeast cells.     

Quasi-Parallax for Nearly Parallel Frontal Eyes

In this paper, we explore how a visual system equipped with a pair of frontally-placed eyes/cameras can rapidly estimate egomotion and depths for the task of locomotion by exploiting the eye topography. We eschew the traditional approach of motion-stereo integration, as finding stereo correspondence is a computationally expensive operation. Instead, we propose a quasi-parallax scheme by pairing appropriate visual rays together, thus obviating the need for stereo correspondence and yet being able to leverage on the redundant information present in the binocular overlap. Our model covers realistic visual systems where the two eyes might deviate from the strictly frontal-parallel configuration, and yet the results show that the advantages of the parallax-based approach are retained. In particular, it offers better disambiguation of translation and rotation over conventional two-frame structure from motion approaches, despite not having views covering diametrically opposing directions like that of spherical eyes or laterally-placed eyes. The rapid processing that such scheme entails seems to offer a more realizable and useful alternative for depth recovery during locomotion.     

Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin

We present a continuous feedback stabilizer for nonlinear systems in the strict-feedback form, whose chained integrator part has the power of positive odd rational numbers. Since the power is not restricted to be larger than or equal to one, the linearization of the system at the origin may fail. Nevertheless, we show that the closed loop system is globally asymptotically stable (GAS) with the proposed continuous (but, possibly not differentiable) feedback. We formulate a condition that enables our design by characterizing the powers of the given system. The condition also shows that our result is an extension of Qian and Lin [Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems Control Lett. 42 (2001) 185–200] where the power of odd positive integers has been considered. New result on the global finite time stabilization problem is also presented.     

Text classification without negative examples revisit

Traditionally, building a classifier requires two sets of examples: positive examples and negative examples. This paper studies the problem of building a text classifier using positive examples (P) and unlabeled examples (U). The unlabeled examples are mixed with both positive and negative examples. Since no negative example is given explicitly, the task of building a reliable text classifier becomes far more challenging. Simply treating all of the unlabeled examples as negative examples and building a classifier thereafter is undoubtedly a poor approach to tackling this problem. Generally speaking, most of the studies solved this problem by a two-step heuristic: first, extract negative examples (N) from U. Second, build a classifier based on P and N. Surprisingly, most studies did not try to extract positive examples from U. Intuitively, enlarging P by P' (positive examples extracted from U) and building a classifier thereafter should enhance the effectiveness of the classifier. Throughout our study, we find that extracting P' is very difficult. A document in U that possesses the features exhibited in P does not necessarily mean that it is a positive example, and vice versa. The very large size of and very high diversity in U also contribute to the difficulties of extracting P'. In this paper, we propose a labeling heuristic called PNLH to tackle this problem. PNLH aims at extracting high quality positive examples and negative examples from U and can be used on top of any existing classifiers. Extensive experiments based on several benchmarks are conducted. The results indicated that PNLH is highly feasible, especially in the situation where |P| is extremely small.     

Molecular modeling study of CodX reveals importance of N-terminal and C-terminal domain in the CodWX complex structure of Bacillus subtilis

In Bacillus subtilis, CodW peptidase and CodX ATPase function together as a distinctive ATP-dependent protease called CodWX, which participates in protein degradation and regulates cell division. The molecular structure of CodX and the assembly structure of CodW-CodX have not yet been resolved. Here we present the first three-dimensional structure of CodX N-terminal (N) and C-terminal (C) domain including possible structure of intermediate (I) domain based on the crystal structure of homologous Escherichia coli HslU ATPase. Moreover, the biologically relevant CodWX (W(6)W(6)X(6)) octadecamer complex structure was constructed using the recently identified CodW-HslU hybrid crystal structure. Molecular dynamics (MD) simulation shows a reasonably stable structure of modeled CodWX and explicit behavior of key segments in CodX N and C domain: nucleotide binding residues, GYVG pore motif and CodW-CodX interface. Predicted structure of the possible I domain is flexible in nature with highly coiled hydrophobic region (M153-M206) that could favor substrate binding and entry. Electrostatic surface potential observation unveiled charge complementarity based CodW-CodX interaction pattern could be a possible native interaction pattern in the interface of CodWX. CodX GYVG pore motif structural features, flexible nature of glycine (G92 and G95) residues and aromatic ring conformation preserved Y93 indicated that it may follow the similar mode during the proteolysis mechanism as in the HslU closed state. This molecular modeling study uncovers the significance of CodX N and C domain in CodWX complex and provides possible explanations which would be helpful to understand the CodWX-dependent proteolysis mechanism of B. subtilis.     

Efficient mixing of viscoelastic fluids in a microchannel at low Reynolds number

In this paper, we examined mixing of various two-fluid flows in a silicon/glass microchannel based on the competition of dominant forces in a flow field, namely viscous/elastic, viscous/viscous and viscous/inertial. Experiments were performed over a range of Deborah and Reynolds numbers (0.36 < De < 278, 0.005 < Re < 24.2). Fluorescent dye and microshperes were used to characterize the flow kinematics. Employing abrupt convergent/divergent channel geometry, we achieved efficient mixing of two-dissimilar viscoelastic fluids at very low Reynolds number. Enhanced mixing was achieved through elastically induced flow instability at negligible diffusion and inertial effects (i.e. enormous Peclet and Elasticity numbers). This viscoelastic mixing was achieved over a short effective mixing length and relatively fast flow velocities.