Complexity-reduced scheme for feature extraction with linear discriminant analysis

Computational Design of Self-Actuated Deformable Solids via Shape Memory Material

The emerging 4D printing techniques open new horizons for fabricating self-actuated deformable objects by combing strength of 3D printing and stimuli-responsive shape memory materials. This article focuses on designing self-actuated deformable solids for 4D printing such that a solid can be programmed into a temporary shape and later recovers to its original shape after heating. To avoid a high material cost, we choose a dual-material strategy that mixes an expensive thermo-responsive shape memory polymer (SMP) material with a common elastic material, which however leads to undesired deformation at the shape programming stage. We model this shape programming process as two elastic models with different parameters linked by a median shape based on customizing a constitutive model of thermo-responsive SMPs. Taking this material modeling as a foundation, we formulate our design problem as a nonconvex optimization to find the distribution of SMP materials over the whole object as well as the median shape, and develop an efficient and parallelizable method to solve it. We show that our proposed approach is able to design self-actuated deformable objects that cannot be achieved by state of the art approaches, and demonstrate their usefulness with three example applications.

Advanced Application of Raman Spectroscopy and Surface-Enhanced Raman Spectroscopy in Plant Disease Diagnostics: A Review

Plant diseases result in 20-40% of agricultural loss every year worldwide. Timely detection of plant diseases can effectively prevent the development and spread of diseases and ensure the agricultural yield. High-throughput and rapid methods are in great demand. This review investigates the advanced application of Raman spectroscopy (RS) and surface-enhanced Raman spectroscopy (SERS) in the detection of plant diseases. The determination of bacterial diseases and stress-induced diseases, fungal diseases, viral diseases, pests in beans, and mycotoxins related to plant diseases using RS and SERS are discussed in detail. Then, biomarkers for RS and SERS detection are analyzed with regard to plant disease diagnosis. Finally, the advantages and challenges are further illustrated. Additionally, potential alternatives are proposed for the challenges. The review is expected to provide a reference and guidance for the use of RS and SERS in plant disease diagnostics.

DBSDA : Lowering the Bound of Misclassification Rate for Sparse Linear Discriminant Analysis via Model Debiasing

Linear discriminant analysis (LDA) is a well-known technique for linear classification, feature extraction, and dimension reduction. To improve the accuracy of LDA under the high dimension low sample size (HDLSS) settings, shrunken estimators, such as Graphical Lasso, can be used to strike a balance between biases and variances. Although the estimator with induced sparsity obtains a faster convergence rate, however, the introduced bias may also degrade the performance. In this paper, we theoretically analyze how the sparsity and the convergence rate of the precision matrix (also known as inverse covariance matrix) estimator would affect the classification accuracy by proposing an analytic model on the upper bound of an LDA misclassification rate. Guided by the model, we propose a novel classifier, DBSDA , which improves classification accuracy through debiasing. Theoretical analysis shows that DBSDA possesses a reduced upper bound of misclassification rate and better asymptotic properties than sparse LDA (SDA). We conduct experiments on both synthetic datasets and real application datasets to confirm the correctness of our theoretical analysis and demonstrate the superiority of DBSDA over LDA, SDA, and other downstream competitors under HDLSS settings.

On the optimal class representation in linear discriminant analysis

Linear discriminant analysis (LDA) is a widely used technique for supervised feature extraction and dimensionality reduction. LDA determines an optimal discriminant space for linear data projection based on certain assumptions, e.g., on using normal distributions for each class and employing class representation by the mean class vectors. However, there might be other vectors that can represent each class, to increase class discrimination. In this brief, we propose an optimization scheme aiming at the optimal class representation, in terms of Fisher ratio maximization, for LDA-based data projection. Compared with the standard LDA approach, the proposed optimization scheme increases class discrimination in the reduced dimensionality space and achieves higher classification rates in publicly available data sets.

Generalization performance of Fisher linear discriminant based on Markov sampling

Fisher linear discriminant (FLD) is a well-known method for dimensionality reduction and classification that projects high-dimensional data onto a low-dimensional space where the data achieves maximum class separability. The previous works describing the generalization ability of FLD have usually been based on the assumption of independent and identically distributed (i.i.d.) samples. In this paper, we go far beyond this classical framework by studying the generalization ability of FLD based on Markov sampling. We first establish the bounds on the generalization performance of FLD based on uniformly ergodic Markov chain (u.e.M.c.) samples, and prove that FLD based on u.e.M.c. samples is consistent. By following the enlightening idea from Markov chain Monto Carlo methods, we also introduce a Markov sampling algorithm for FLD to generate u.e.M.c. samples from a given data of finite size. Through simulation studies and numerical studies on benchmark repository using FLD, we find that FLD based on u.e.M.c. samples generated by Markov sampling can provide smaller misclassification rates compared to i.i.d. samples.