Dimension Reduction Methodology Research Articles

Image enhancement in palmprint recognition: a novel approach for improved biometric authentication

Several researchers have used image enhancement methods to reduce detection errors and increase verification accuracy in palmprint identification. Divergent opinions exist among experts regarding the best method of image filtering to improve image palmprint recognition. Because of the unique characteristics of palmprints and the difficulties in preventing counterfeiting, image-filtering techniques are the subject of this current research. Researchers hope to create the best biometric system possible by utilizing various techniques. These techniques include image enhancement, Gabor orientation scales, dimension reduction techniques, and appropriate matching strategies. This study investigates how different filtering approaches might be combined to improve images. The palmprint identification system uses a 3W filter, which combines wavelet, Wiener, and weighted filters. Optimizing results entails coordinating the 3W filter with Gabor orientation scales, matching processes, and dimension reduction methods. The research shows that accuracy may be considerably increased using a 3W filter with a Gabor orientation scale of [8×7], the kernel principal component analysis (KPCA) dimension reduction methodology, and a cosine matching method. Specifically, a value of 99.722% can be achieved. These results highlight the importance of selecting appropriate settings and techniques for palmprint recognition systems.

Data-driven prediction of dimensionless quantities for semi-infinite target penetration by integrating machine-learning and feature selection methods

This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements. The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables. As a physics-based dimension reduction methodology, this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases. Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering. The results indicate that the selected critical dimensionless feature variables by this synergistic method, without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics, are in accordance with those reported in the reference. Lastly, the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case, and the reliability of regression functions is validated.

A dimension reduction approach for loss valuation in credit risk modeling

This paper addresses the “curse of dimensionality” in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and accurate loss valuation algorithm in credit risk modeling, but it can also be extended to valuation models of other risk types. The proposed methodology is generic, robust and can easily be implemented. Moreover, the accuracy of the proposed methodology in the estimation of expected loss and value-at-risk (VaR) is illustrated by numerical experiments. The results suggest that, compared to the currently most used Principal Component Analysis (PCA) approach, the proposed methodology provides more accurate estimation of expected loss and VaR of a loss distribution.

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube of finite wall thickness from the three-dimensional (3d) finite elasticity theory by applying the dimension reduction methodology proposed by Audoly and Hutchinson (2016). The 1d model makes it much easier to characterize fully nonlinear axisymmetric deformations of a thick-walled tube using simple numerical schemes such as the finite difference method. The new model recovers the diffuse interface model for analyzing bulging in a membrane tube and the 1d model for investigating necking in a stretched solid cylinder as two limiting cases. It is consistent with, but significantly refines, the exact linear and weakly nonlinear bifurcation analyses. Comparisons with finite element simulations show that for the bulging problem, the 1d model is capable of describing the entire bulging process accurately, from initiation, growth, to propagation. The 1d model provides a stepping stone from which similar 1d models can be derived and used to study other effects such as anisotropy and electric loading, and other phenomena such as rupture.

Nonlinear finite element free and forced vibrations of cellular plates having lattice-type metamaterial cores: a strain gradient plate model approach

The main objective of this paper is to develop a theoretically and numerically reliable and efficient methodology based on combining a finite element method and a strain gradient shear deformation plate model accounting for the nonlinear free and forced vibrations of cellular plates having lattice-type metamaterial cores. The proposed model provides a modelling framework computationally more efficient than framework of the conventional three-dimensional elasticity for the simulation of the underlying nonlinear dynamics of cellular plates with microarchitectures. The corresponding governing equations follow Mindlin’s strain gradient elasticity theory including the micro-inertia effect applied to the first-order shear deformation plate theory along with the nonlinear von Kármán kinematics. Standard and higher-order computational homogenization methods determine the classical and strain gradient material constants, respectively. A higher-order C1-continuous 6-node finite element is adopted for the discretization in the spatial domain, and an arc-length continuation technique along with time-periodic discretization is implemented to solve the resulting nonlinear time-dependent problem. Through a set of comparative studies with 3D full-field models as reliable validation references for triangularly prismatic example cores, the accuracy and efficacy of the proposed dimension reduction methodology are demonstrated for a diverse range of problem parameters for analyzing the large-amplitude dynamic structural response. The results show that the proposed strain gradient plate model can accurately capture the microarchitecture effects of cellular plates with low computational costs, which signifies a relevant contribution particularly to the computational analysis of nonlinear dynamics.

Dimension reduction of noisy interacting systems

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally, nonequilibrium setting. We provide a systematic dimension reduction methodology for constructing low-dimensional, reduced-order dynamics based on the cumulants of the probability distribution of the infinite system. We show that the low-dimensional dynamics returns the correct diagnostic properties since it produces a quantitatively accurate representation of the stationary phase diagram of the system that we compare with exact analytical results and numerical simulations. Moreover, we prove that the reduced order dynamics yields also the prognostic, i.e., time-dependent properties, as it provides the correct response of the system to external perturbations. On the one hand, this validates the use of our complexity reduction methodology since it retains information not only of the invariant measure of the system but also of the transition probabilities and time-dependent correlation properties of the stochastic dynamics. On the other hand, the breakdown of linear response properties is a key signature of the occurence of a phase transition. We show that the reduced response operators capture the correct diverging resonant behavior by quantitatively assessing the singular nature of the susceptibility of the system and the appearance of a pole for real values of frequencies. Hence, this methodology can be interpreted as a low-dimensional, reduced order approach to the investigation and detection of critical phenomena in high-dimensional interacting systems in settings where order parameters are not known.

On cross-distance selection algorithm for hybrid sufficient dimension reduction

Given the extensive development of a variety of sufficient dimension reduction (SDR) methodologies, Ye and Weiss (2003) proposed a hybrid SDR method combining two pre-existing SDR methods. In particular, they used a bootstrap approach to select a proper weight. Since bootstrapping is computationally intensive and time-consuming, the hybrid reduction approach has not been widely used, although it is more accurate than conventional single SDR methods. To overcome these deficits, we propose a novel cross-distance selection algorithm. Similar to the bootstrapping method, the proposed selection algorithm is data-driven and has a strong rationale for its performance. The numerical studies demonstrate that the chosen hybrid method from our proposed algorithm offers a good estimation quality and reduces the computing time dramatically at the same time. Furthermore, our real data analysis confirms that the proposed selection algorithm has potential advantages with its practical usefulness over the existing bootstrapping method.

Regulatory analysis of single cell multiome gene expression and chromatin accessibility data with scREG

Technological development has enabled the profiling of gene expression and chromatin accessibility from the same cell. We develop scREG, a dimension reduction methodology, based on the concept of cis-regulatory potential, for single cell multiome data. This concept is further used for the construction of subpopulation-specific cis-regulatory networks. The capability of inferring useful regulatory network is demonstrated by the two-fold increment on network inference accuracy compared to the Pearson correlation-based method and the 27-fold enrichment of GWAS variants for inflammatory bowel disease in the cis-regulatory elements. The R package scREG provides comprehensive functions for single cell multiome data analysis.

Sufficient Dimension Reduction: An Information-Theoretic Viewpoint.

There has been a lot of interest in sufficient dimension reduction (SDR) methodologies, as well as nonlinear extensions in the statistics literature. The SDR methodology has previously been motivated by several considerations: (a) finding data-driven subspaces that capture the essential facets of regression relationships; (b) analyzing data in a ‘model-free’ manner. In this article, we develop an approach to interpreting SDR techniques using information theory. Such a framework leads to a more assumption-lean understanding of what SDR methods do and also allows for some connections to results in the information theory literature.

Fusing sufficient dimension reduction with neural networks

Neural networks are combined with sufficient dimension reduction methodology in order to remove the limitation of small p and n of the latter. NN-SDR applies when the dependence of the response Y on a set of predictors X is fully captured by the regression function g(B′X), for an unknown function g and low rank parameter B matrix. It is shown that the proposed estimator is on par with competing sufficient dimension reduction methods, such as minimum average variance estimation and conditional variance estimation, in small p and n settings in simulations. Its main advantage is its scalability in regressions with large data, for which the other methods are infeasible.

Modeling regional disparity and the reverse commute

• A dimension reduction approach is employed to model the reverse commute. • Greater distances between origin and destination predict the reverse commute. • Higher percent of population African American at origin predict reverse commute. • Lower incomes at origin and higher incomes at destination predict reverse commute. • Effect of metropolitan fragmentation on reverse commute is unclear. This paper measures a) whether the reverse commute – a commute where a worker travels from a home location in the city to a workplace location in the suburbs – is characterized by a uniquely disparate socioeconomic and demographic space between home and workplace, and b) what role greater fragmentation between municipalities in a region might play in this theoretically inequitable circumstance. We employ administrative origin–destination data from the metropolitan Philadelphia, PA area and contemporary dimension reduction methodologies to model the likelihood of an origin destination pair being classified as a reverse commute. Particular attention is given to interactions between socioeconomic and metropolitan fragmentation terms and non-linear specifications of predictor variables. Greater socioeconomic and demographic disparity between home and work geographies is found to uniquely predict the reverse commute. We also find that fragmentation at the metropolitan scale has a multidimensional impact in relation to this socio-economic difference. Together, our findings appear to signal that, while greater regional socioeconomic disparity does indeed correlate with the reverse commute, greater metropolitan fragmentation may not. This portrait highlights new areas for transport research around political fragmentation and makes the case for renewed, equity-oriented policy investment in the reverse commuting problem.

On hierarchical clustering in sufficient dimension reduction

The K-means clustering algorithm has had successful application in sufficient dimension reduction. Unfortunately, the algorithm does have reproducibility and nestness, which will be discussed in this paper. These are clear deficits for the K-means clustering algorithm; however, the hierarchical clustering algorithm has both reproducibility and nestness, but intensive comparison between K-means and hierarchical clustering algorithm has not yet been done in a sufficient dimension reduction context. In this paper, we rigorously study the two clustering algorithms for two popular sufficient dimension reduction methodology of inverse mean and clustering mean methods throughout intensive numerical studies. Simulation studies and two real data examples confirm that the use of hierarchical clustering algorithm has a potential advantage over the K-means algorithm.

Envelopes in multivariate regression models with nonlinearity and heteroscedasticity

SummaryEnvelopes have been proposed in recent years as a nascent methodology for sufficient dimension reduction and efficient parameter estimation in multivariate linear models. We extend the classical definition of envelopes in Cook et al. (2010) to incorporate a nonlinear conditional mean function and a heteroscedastic error. Given any two random vectors ${X}\in\mathbb{R}^{p}$ and ${Y}\in\mathbb{R}^{r}$, we propose two new model-free envelopes, called the martingale difference divergence envelope and the central mean envelope, and study their relationships to the standard envelope in the context of response reduction in multivariate linear models. The martingale difference divergence envelope effectively captures the nonlinearity in the conditional mean without imposing any parametric structure or requiring any tuning in estimation. Heteroscedasticity, or nonconstant conditional covariance of ${Y}\mid{X}$, is further detected by the central mean envelope based on a slicing scheme for the data. We reveal the nested structure of different envelopes: (i) the central mean envelope contains the martingale difference divergence envelope, with equality when ${Y}\mid{X}$ has a constant conditional covariance; and (ii) the martingale difference divergence envelope contains the standard envelope, with equality when ${Y}\mid{X}$ has a linear conditional mean. We develop an estimation procedure that first obtains the martingale difference divergence envelope and then estimates the additional envelope components in the central mean envelope. We establish consistency in envelope estimation of the martingale difference divergence envelope and central mean envelope without stringent model assumptions. Simulations and real-data analysis demonstrate the advantages of the martingale difference divergence envelope and the central mean envelope over the standard envelope in dimension reduction.

Fused clustering mean estimation of central subspace

Recently, Yoo (Statistics 50:1086–1099, 2016) newly defines an informative predictor subspace to contain the central subspace. The method to estimate the informative predictor subspace does not require any of the conditions assumed to hold in usual sufficient dimension reduction methodologies. However, like sliced inverse regression (Li in J Am Stat Assoc 86:316–342, 1991) and sliced average variance estimation (Cook and Weisberg in J Am Stat Assoc 86:328–332, 1991), its non-asymptotic behavior in the estimation is sensitive to the choices of the categorization of the predictors and response. The paper develops an estimation approach that is robust to the categorization choices. For this, sample kernel matrices are combined in two ways. Numerical studies and real data analysis are presented to confirm the potential usefulness of the proposed approach in practice.

A Hierarchical Dimension Reduction Approach for Big Data with Application to Fault Diagnostics

Abstract About four zetta bytes of data, which falls into the category of big data, is generated by complex manufacturing systems annually. Big data can be utilized to improve the efficiency of an aging manufacturing system, provided, several challenges are handled. In this paper, a novel methodology is presented to detect faults in manufacturing systems while overcoming some of these challenges. Specifically, a generalized distance measure is proposed in conjunction with a novel hierarchical dimension reduction (HDR) approach. It is shown that the HDR can tackle challenges that are frequently observed during distance calculation in big data scenarios, such as norm concentration, redundant dimensions, and a non-invertible correlation matrices. Subsequently, a probabilistic methodology is developed for isolation and detection of faults. Here, Edgeworth expansion based expressions are derived to approximate the density function of the data. The performance of the dimension reduction methodology is demonstrated to be efficient with simulation results involving the use of big data sets. It is shown that HDR is able to explain almost 90% of the total information. Furthermore, the proposed dimension reduction methodology is seen to outperform standard dimension reduction approaches and is able to improve the performance of standard classification methodologies in high dimensional scenarios.

Bayesian personalized treatment selection strategies that integrate predictive with prognostic determinants.

The evolution of "informatics" technologies has the potential to generate massive databases, but the extent to which personalized medicine may be effectuated depends on the extent to which these rich databases may be utilized to advance understanding of the disease molecular profiles and ultimately integrated for treatment selection, necessitating robust methodology for dimension reduction. Yet, statistical methods proposed to address challenges arising with the high-dimensionality of omics-type data predominately rely on linear models and emphasize associations deriving from prognostic biomarkers. Existing methods are often limited for discovering predictive biomarkers that interact with treatment and fail to elucidate the predictive power of their resultant selection rules. In this article, we present a Bayesian predictive method for personalized treatment selection that is devised to integrate both the treatment predictive and disease prognostic characteristics of a particular patient's disease. The method appropriately characterizes the structural constraints inherent to prognostic and predictive biomarkers, and hence properly utilizes these complementary sources of information for treatment selection. The methodology is illustrated through a case study of lower grade glioma. Theoretical considerations are explored to demonstrate the manner in which treatment selection is impacted by prognostic features. Additionally, simulations based on an actual leukemia study are provided to ascertain the method's performance with respect to selection rules derived from competingmethods.

Generalized principal Hessian directions for mixture multivariate skew elliptical distributions

Principal Hessian directions (pHd) based on the Hessian matrix is a moment-based method and a promising methodology for sufficient dimension reduction because of its easy implementation. However, it requires strong conditions on the distribution of the predictors, which must be nearly Gaussian. We investigate here whether and how this method is applicable when the distribution is a mixture multivariate skew elliptical (MMSE) distribution, and if not, how to adapt the technique. Further, we propose two new estimation algorithms for an extended version of pHd. The theoretical results also serve as a reminder for researchers and users to pay attention to the theoretical conditions on which pHd critically relies. Numerical studies are conducted to examine its performance in finite-sample cases.

Investigation of nonlinear characteristics of the motor-gear transmission system by trajectory-based stability preserving dimension reduction methodology

Gear-motor system is a typically nonlinear system because of many nonlinear factors, such as time-varying meshing stiffness, backlash, and the nonlinear relationship between the electric motor torque and speed. At present, the nonlinear analytical methods can only be used for simplified gear dynamic model. Though the numerical methods can be used for the complicated dynamic model, the quantitative analysis of stability is difficult and rarely conducted. Therefore, a kind of trajectory-based stability preserving dimension reduction (TSPDR) methodology is proposed to investigate nonlinear dynamic characteristics of the gear-motor system. In the TSPDR methodology herein, the complementary cluster center of inertia-relative motion (CCCOI-RM) transformation is chosen and the stability margins are specially defined for distinguishing the stable motion modes of the motor-gear system, to make the TSPDR methodology used in the nonlinear analysis of the gear-motor system. Furthermore, the critical values are obtained for alteration of different motion modes and the nonlinear characteristics of each motion modes are analyzed. At last, combined with modal analysis, the relationship between the stability and resonance of the gear-motor system is revealed.

Ontological Optimization for Latent Semantic Indexing of Arabic Corpus

The dimensionality reduction is a critical problem in the information retrieval process. The higher dimensions directly affect the search performance in terms of Recall and Precision. The dimensionality reduction enabling the search to be semantically based instead of lexically based as the dimensions are defined in terms of the semantic concepts instead of traditional terms or keywords. Latent Semantic Indexing (LSI) is a mathematical extension of the classical Vector Space Model (VSM). LSI is used to discover the latent semantic in the search space by extracting concepts from the original terms in the space. LSI is based on the Singular Value Decomposition (SVD) to reduce the dimension of the term space into a lower dimensional LSI space. In this paper, we propose a methodology for extra optimal LSI dimension reduction via two reduction levels. The first reduction level is based on an ontological conceptualization process. The Universal Wordnet ontology (UWN) is used to develop an ontological based concept space instead of the term space. As a second reduction level, the SVD is applied to the extracted concept space for getting an optimal LSI conceptualization. The experimental results of this research indicate an improvement in the search results in terms of both Precision and Recall as the proposed methodology addresses the Synonymy and Polysemy problems effectively.

Automated Skin Detection using Fuzzy Logic based Pixel Matching Algorithm

Objectives: Skin detection is the initial process of any automatic face recognition system. One of the fore most common approaches to detect the faces in facial pictures can be done by an automatic face detection method. In this paper, a new type of facial skin detection using the combination of Fuzzy and Pixel matching algorithms is proposed. Method/Statistical Analysis: The proposed system has three steps. Initially, the input facial color image is transformed in to a grey scale image and then, it is sharpened using a filter. Secondly, the pixels of the different types of facial grey scale images are computed. Finally, the computed pixels are compared with the original grey scale image based on the fuzzy rules. This process is done for the first pixel to the last pixel so that all the pixels which are present in the entire image can be included in the overall process. Findings: The algorithm is tested for different types of facial images for both the accuracy and the time taken to complete the skin detection process. The results of the experiments reveal that an accurate skin detection rate of 94.42% for the combination of fuzzy based pixel matching along with the dimension reduction methodology. Application/ Improvements: Future enhancements in this work are to propose an efficient algorithm to detect the facial images of group of faces present in a single image. Keywords: Dimension Reduction, Facial Image, Fuzzy Logic, Pixel Matching Algorithm, Skin Texture Analysis, Skin Detection