Space Dimension Reduction Research Articles

Low-Complexity Reduced-Dimension Space–Time Adaptive Processing for Navigation Receivers

In this paper, we propose a low-complexity adaptive reduced-rank interference suppression scheme based on alternating low-rank decomposition techniques for navigation receivers. The proposed scheme, which employs a generalized sidelobe canceler structure, makes use of a projection matrix for rank reduction followed by a reduced-dimension receive filter. An alternating optimization strategy based on recursive least squares is devised to compute the basis vectors of the projection matrix and the receive filter adaptively. Simulation results show that the proposed algorithm achieves a better performance than existing methods with a reduced computational complexity.

Measuring Horizon-Specific Systematic Risk via Spectral Betas

We represent risk factors as sums of orthogonal components capturing fluctuations with cycles of different length. The representation leads to novel spectral factor models in which systematic risk is allowed (without being forced) to vary across frequencies. Frequency-specific systematic risk is captured by a notion of spectral beta. We show that traditional factor models restrict the spectral betas to be constant over frequencies. The restriction can hide horizon-specific pricing effects which spectral factor models are designed to reveal. We illustrate how the methods may lead to economically-meaningful dimensionality reduction in the factor space.

An Integrated Gaussian Process Modeling Framework for Residential Load Prediction

While adding new capabilities, the distributed energy resource (DER) proliferation raises great concern about challenges such as dynamic fluctuations of voltages. For robust and efficient operational planning purposes, we propose an integrated Gaussian process (IGP) modeling framework for reliable hourly load prediction. The proposed IGP modeling framework has the following unique features: 1) the IGP utilizes not only the data streams generated by the target customer, but also those generated by relevant customers in the power system; an effective input space dimension reduction method is proposed to significantly improve the computational efficiency, while maintaining the high predictive accuracy of the IGP; and 2) an adaptive data communication rate controlling scheme is proposed to further enhance the predictive performance of the IGP by optimally and dynamically adjusting the data communication rate used for each customer under the total data communication bandwidth constraint often imposed. Taking into account the highly uncertain load and generation behaviors of DERs, the proposed IGP framework is tested on various standard IEEE test cases with load and renewable generation data collected from real-world power systems with DERs. The superiority and efficacy of the IGP are verified by our simulation results.

Improved trust-region gradient-search algorithm for accelerated optimization of wideband antenna input characteristics

Full-wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM-based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate-assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust-region-embedded gradient search with numerical derivatives is proposed for reduced-cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand-alone optimization routine or as a building block of surrogate-assisted procedures.

CLUSTER ANALYSIS OF MEDICAL TEXT DOCUMENTS BY USING SEMI-CLUSTERING APPROACH BASED ON GRAPH REPRESENTATION

The development of Internet resulted in an increasing number of online text re-positories. In many cases, documents are assigned to more than one class and automatic multi-label classification needs to be used. When the number of labels exceeds the number of the documents, effective label space dimension reduction may signifi-cantly improve classification accuracy, what is a major priority in the medical field. In the paper, we propose document clustering for label selection. We use semi-clustering method, by considering graph representation, where documents are represented by vertices and edge weights are calculated according to their mutual similarity. Assigning documents to semi-clusters helps in reducing number of labels, further used in multilabel classification process. The performance of the method is examined by experiments conducted on real medical datasets.

Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models.

Improving Scalability of Generic Online Calibration for Real-Time Dynamic Traffic Assignment Systems

Flexible calibration of dynamic traffic assignment (DTA) systems in real time has important applications in effective traffic management. However, the existing approaches are either limited to small networks or to a specific class of parameters. In this light, this study presents a framework to systematically reduce the dimension of the generic online calibration problem, making it more scalable. Specifically, a state–space formulation of the problem in the reduced dimension space is proposed. Following this the problem is solved using the constrained extended Kalman filter, which is made tractable because of the low dimensionality of the formulated problem. The effectiveness of the proposed approach is demonstrated using a real-world network leading to better state estimation by 13% and better state predictions by 11%—with a 50 fold dimensionality reduction. Insights into choosing the right degree of dimensionality reduction are also discussed. This work has the potential for a more widespread application of real-time DTA systems in practice.

Statistical inference on asymptotic properties of two estimators for the partially linear single-index models

ABSTRACTThe outer product of gradients (OPG) estimation procedure based on least squares (LS) approach has been presented by Xia et al. [An adaptive estimation of dimension reduction space. J Roy Statist Soc Ser B. 2002;64:363–410] to estimate the single-index parameter in partially linear single-index models (PLSIM). However, its asymptotic property has not been established yet and the efficiency of LS-based method can be significantly affected by outliers and heavy-tailed distributions. In this paper, we firstly derive the asymptotic property of OPG estimator developed by Xia et al. [An adaptive estimation of dimension reduction space. J Roy Statist Soc Ser B. 2002;64:363–410] in theory, and a novel robust estimation procedure combining the ideas of OPG and local rank (LR) inference is further developed for PLSIM along with its theoretical property. Then, we theoretically derive the asymptotic relative efficiency (ARE) of the proposed LR-based procedure with respect to LS-based method, which is shown to possess an expression that is closely related to that of the signed-rank Wilcoxon test in comparison with the t-test. Moreover, we demonstrate that the new proposed estimator has a great efficiency gain across a wide spectrum of non-normal error distributions and almost not lose any efficiency for the normal error. Even in the worst case scenarios, the ARE owns a lower bound equalling to 0.864 for estimating the single-index parameter and a lower bound being 0.8896 for estimating the nonparametric function respectively, versus the LS-based estimators. Finally, some Monte Carlo simulations and a real data analysis are conducted to illustrate the finite sample performance of the estimators.

Recurrence network modeling and analysis of spatial data.

Nonlinear dynamical systems exhibit complex recurrence behaviors. Recurrence plot is widely used to graphically represent the patterns of recurrence dynamics and further facilitates the quantification of recurrence patterns, namely, recurrence quantification analysis. However, traditional recurrence methods tend to be limited in their ability to handle spatial data due to high dimensionality and geometric characteristics. Prior efforts have been made to generalize the recurrence plot to a four-dimensional space for spatial data analysis, but this framework can only provide graphical visualization of recurrence patterns in the projected reduced-dimension space (i.e., two- or three- dimensions). In this paper, we propose a new weighted recurrence network approach for spatial data analysis. A weighted network model is introduced to represent the recurrence patterns in spatial data, which account for both pixel intensities and spatial distance simultaneously. Note that each network node represents a location in the high-dimensional spatial data. Network edges and weights preserve complex spatial structures and recurrence patterns. Network representation is shown to be an effective means to provide a complete picture of recurrence patterns in the spatial data. Furthermore, we leverage network statistics to characterize and quantify recurrence properties and features in the spatial data. Experimental results in both simulation and real-world case studies show that the generalized recurrence network approach yields superior performance in the visualization of recurrence patterns in spatial data and in the extraction of salient features to characterize recurrence dynamics in spatial systems.

A methodology using Gaussian-based density map approximation to assess sets of cryo-electron microscopy density maps

This article presents a methodology to assess a set of density maps, as used in the Blind Assessment Phase of the 2015/2016 Map Challenge (EMDataBank Validation Challenges). The synthetic and experimental cryo-electron microscopy (cryo-EM) density maps obtained by different single particle analysis protocols and by different participants, submitted in the Challenge Phase for assessment, were analyzed with this methodology and the obtained results are presented and discussed here. The goal of using such a methodology was to blindly identify the density maps with globally similar structural information, meaning the maps with the structural information mostly "reproduced" by different protocols. To this end, the density maps are "coarsened" using Gaussian-based approximations, with the same input approximation parameters for all maps of the target biological complex. The approximated maps are then represented in a common reduced-dimension (here, 3D) space of their correlation-coefficient-based distances, in which close maps mean similar maps. The distance analysis allows identifying maps with the most "reproduced" structural information by different protocols. The obtained results are also discussed taking into account the detailed information about the protocols that has been released after the end of the Blind Assessment Phase.

Multi-view label embedding

Multi-label classification has been successfully applied to image annotation, information retrieval, text categorization, etc. When the number of classes increases significantly, the traditional multi-label learning models will become computationally impractical. Label space dimension reduction (LSDR) is then developed to alleviate the effect of the high dimensionality of labels. However, almost all the existing LSDR methods focus on single-view learning. In this paper, we develop a multi-view label embedding (MVLE) model by exploiting the multi-view correlations. The label space and feature space of each view are bridged by a latent space. To exploit the consensus among different views, multi-view latent spaces are correlated by Hilbert–Schmidt independence criterion(HSIC). For a test sample, it is firstly embedded to the latent space of each view and then projected to the label space. The prediction is conducted by combining the multi-view outputs. Experiments on benchmark databases show that MVLE outperforms the state-of-the-art LSDR algorithms in both multi-view settings and different multi-view learning strategies.

Face Recognition Using Fisherface Method

Fisherface is one of the popular algorithms used in face recognition, and is widely believed to be superior to other techniques, such as eigenface because of the effort to maximize the separation between classes in the training process. The purpose of this research is to establish a program of face recognition application using fisherface method by utilizing GUI applications and databases that are used in the form of a Papuan facial image. Image recognition using fisherface method is based on the reduction of face space dimension using Principal Component Analysis (PCA) method, then apply Fisher’s Linear Discriminant (FDL) method or also known as Linear Discriminant Analysis (LDA) method to obtain feature of image characteristic. The algorithm used in the process for image recognition is fisherfaces algorithm while for identification or matching face image using minimum euclidean. The method used in this study is literature study that is studying and reviewing various books or literature related to mathematical concepts that underlies the formation of fisherface algorithm to recognize the image of a person’s face which is then applied in programming language, especially programming language Matlab7.10. While in the process of preprocessing used Adobe Photoshop CS4 application program, its goal is to make the face image to be uniform in terms of size and format so that the image is ready to be used by the system. The results show that for image recognition where the image of testing is the same as the training image, the percentage of program success is 100%, while for 73 facial test images with various expressions and various positions, 70 faces are recognized correctly and 3 faces are recognized incorrectly, so the percentage of success is 93%.

Visualizing histopathologic deep learning classification and anomaly detection using nonlinear feature space dimensionality reduction

BackgroundThere is growing interest in utilizing artificial intelligence, and particularly deep learning, for computer vision in histopathology. While accumulating studies highlight expert-level performance of convolutional neural networks (CNNs) on focused classification tasks, most studies rely on probability distribution scores with empirically defined cutoff values based on post-hoc analysis. More generalizable tools that allow humans to visualize histology-based deep learning inferences and decision making are scarce.ResultsHere, we leverage t-distributed Stochastic Neighbor Embedding (t-SNE) to reduce dimensionality and depict how CNNs organize histomorphologic information. Unique to our workflow, we develop a quantitative and transparent approach to visualizing classification decisions prior to softmax compression. By discretizing the relationships between classes on the t-SNE plot, we show we can super-impose randomly sampled regions of test images and use their distribution to render statistically-driven classifications. Therefore, in addition to providing intuitive outputs for human review, this visual approach can carry out automated and objective multi-class classifications similar to more traditional and less-transparent categorical probability distribution scores. Importantly, this novel classification approach is driven by a priori statistically defined cutoffs. It therefore serves as a generalizable classification and anomaly detection tool less reliant on post-hoc tuning.ConclusionRoutine incorporation of this convenient approach for quantitative visualization and error reduction in histopathology aims to accelerate early adoption of CNNs into generalized real-world applications where unanticipated and previously untrained classes are often encountered.

Data-driven reduced-order models for rank-ordering the high cycle fatigue performance of polycrystalline microstructures

Computationally efficient estimation of the fatigue response of polycrystalline materials is critical for the development of next generation materials in application domains such as transportation, health, security, and energy industries. This is non-trivial for fatigue of polycrystalline metals since the initiation and growth of fatigue cracks depends strongly on attributes of the microstructure, such as the sizes, shapes, orientations, and neighbors of individual grains. Furthermore, regions of microstructure most likely to initiate cracks correspond to the tails of the distributions of the microstructure features. This requires the execution of large numbers of experiments or simulations to capture the response of the material in a statistically meaningful manner. In this work, a linkage is described to connect polycrystalline microstructures to the statistically signified driving forces controlling the high cycle fatigue (HCF) responses. This is achieved through protocols that quantify these microstructures using 2-pt spatial correlations and represent them in a reduced-dimensional space using principal component analysis. Reduced-order relationships are then constructed to link microstructures to performance characteristics related to their HCF responses. These protocols are demonstrated for α-titanium, which exhibits heterogeneous microstructure features along with significant elastic and inelastic anisotropies at both the microscale and the macroscale.

Large-Scale Location-Aware Services in Access: Hierarchical Building/Floor Classification and Location Estimation Using Wi-Fi Fingerprinting Based on Deep Neural Networks

ABSTRACTWe report the results of our investigation on the use of deep neural networks (DNNs) for building/floor classification and floor-level location estimation based on Wi-Fi fingerprinting. We propose a new DNN architecture based on a stacked autoencoder for feature space dimension reduction and a feed-forward classifier for multi-label classification with arg max functions to convert multi-label classification results into multi-class classification ones. We also demonstrate a prototype system for floor-level location estimation using received signal strengths measured on XJTLU campus. Our results show the strengths of DNN-based approaches, providing near state-of-the-art performance with less parameter tuning and higher scalability.

A scalable deep neural network architecture for multi-building and multi-floor indoor localization based on Wi-Fi fingerprinting

BackgroundOne of the key technologies for future large-scale location-aware services covering a complex of multi-story buildings is a scalable indoor localization technique. In this paper, we report the current status of our investigation on the use of deep neural networks (DNNs) for the scalable building/floor classification and floor-level position estimation based on Wi-Fi fingerprinting. Exploiting the hierarchical nature of the building/floor estimation and floor-level coordinates estimation of a location, we propose a new DNN architecture consisting of a stacked autoencoder for the reduction of feature space dimension and a feed-forward classifier for multi-label classification of building/floor/location, on which the multi-building and multi-floor indoor localization system based on Wi-Fi fingerprinting is built.ResultsWe evaluate the performance of building/floor estimation and floor-level coordinates estimation of a given location using the UJIIndoorLoc dataset covering three buildings with four or five floors in the Jaume I University (UJI) campus, Spain. Experimental results demonstrate the feasibility of the proposed DNN-based indoor localization system, which can provide near state-of-the-art performance using a single DNN.ConclusionsThe proposed scalable DNN architecture for multi-building and multi-floor indoor localization based on Wi-Fi fingerprinting can achieve near state-of-the-art performance with just a single DNN and enables the implementation with lower complexity and energy consumption at mobile devices.

A label compression method for online multi-label classification

Many modern applications deal with multi-label data, such as functional categorizations of genes, image labeling and text categorization. Classification of such data with a large number of labels and latent dependencies among them is a challenging task, and it becomes even more challenging when the data is received online and in chunks. Many of the current multi-label classification methods require a lot of time and memory, which make them infeasible for practical real-world applications. In this paper, we propose a fast linear label space dimension reduction method that transforms the labels into a reduced encoded space and trains models on the obtained pseudo labels. Additionally, it provides an analytical method to update the decoding matrix which maps the labels into the original space and is used during the test phase. Experimental results show the effectiveness of this approach in terms of running times and the prediction performance over different measures.

On consistency and sparsity for sliced inverse regression in high dimensions

We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by \cite{Li:1991}. Under mild conditions, the asymptotic ratio $\rho= \lim p/n$ is the phase transition parameter and the SIR estimator is consistent if and only if $\rho= 0$. When dimension $p$ is greater than $n$, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm. This method provides us with an estimate of the eigen-space of the covariance matrix of the conditional expectation $var(\mathbf{E}[\boldsymbol{x}|y])$. The desired dimension reduction space is then obtained by multiplying the inverse of the covariance matrix on the eigen-space. Under certain sparsity assumptions on both the covariance matrix of predictors and the loadings of the directions, we prove the consistency of DT-SIR in estimating the dimension reduction space in high dimensional data analysis. Extensive numerical experiments demonstrate superior performances of the proposed method in comparison to its competitors.

Personalized market response analysis for a wide variety of products from sparse transaction data

Advanced database marketing is designed to ascertain individual customers’ market responses with a discount or display of widely various products from transaction data. However, transaction data recorded in a supermarket or electric commerce are fundamentally sparse because most customers purchase only a few products from all products in shops. Existing methods are not applicable to elucidate the personalized response because of a lack of sample size of purchased data. This paper proposes a personalized market response estimation method for a wide set of customers and products from these sparse data. The method compresses a sparse transaction data with information related to response to marketing variables into a reduced-dimensional space for feasible parameter estimation. Then, they are decompressed into original space using augmented latent variables to obtain individual response parameters. Results show that the method can find suitable marketing promotions for individual customers to every analyzed product.

A computerised framework for prediction of fatty and dense breast tissue using principal component analysis and multi-resolution texture descriptors

The present work proposes a computerised framework for prediction of fatty and dense breast tissue using principal component analysis and multi-resolution texture descriptors. For this study, 480 MLO view digitised screen film mammograms have been taken from the DDSM dataset. A fixed ROIs size of 128 × 128 pixels are cropped from the centre location of each mammographic image. Three texture features are computed in multi-resolution transform domain, where each ROI is decomposed up to 2nd level using ten different compact support wavelet filters resulting 16 sub-band feature images. Two step feature optimisation approach (feature pruning followed by feature space dimensionality reduction using PCA) is applied. In feature pruning stage, the TFV corresponding to best basis feature is selected; result of feature pruning stage is PTFV. This PTFV is subjected to PCA for feature space dimensionality reductions. After the application, PCA accuracy increases from 92.1% to 97.9%.