Locality-Preserving Partial Least Squares Regression

This chapter proposes another nonlinear PLS method, named as locality-preserving partial least squares (LPPLS), which embeds the nonlinear degenerative and structure-preserving properties of LPP into the PLS model. The core of LPPLS is to replace the role of PCA in PLS with LPP. When extracting the principal components of $$\boldsymbol{t}_i$$ t i and $$\boldsymbol{u}_i$$ u i , two conditions must satisfy: (1) $$\boldsymbol{t}_i$$ t i and $$\boldsymbol{u}_i$$ u i retain the most information about the local nonlinear structure of their respective data sets. (2) The correlation between $$\boldsymbol{t}_i$$ t i and $$\boldsymbol{u}_i$$ u i is the largest. Finally, a quality-related monitoring strategy is established based on LPPLS.

Improved Locality Preserving Projection for Hyperspectral Image Classification in Probabilistic Framework

Unlabeled samples and transformation matrix are two main parts of unsupervised and semi-supervised feature extraction (FE) algorithms. In this manuscript, a semi-supervised FE method, locality preserving projection in the probabilistic framework (LPPPF), to find a sufficient number of reliable and unmixed unlabeled samples from all classes and constructing an optimal projection matrix is proposed. The LPPPF has two main steps. In the first step, a number of reliable unlabeled samples are selected based on the training samples, spectral features, and spatial information in the probabilistic framework. In this way, the spectral and spatial probability distribution function is calculated for each unlabeled sample. Therefore, the spectral features and spatial information are integrated together with a joint probability distribution function. Finally, a sufficient number of unlabeled samples with the highest joint probability distribution are selected. In the second step, the selected unlabeled samples are applied to construct the transformation matrix based on the spectral and spatial information of the unlabeled samples. The adjacency graph is improved by using new weights based on spectral and spatial information. This method is evaluated on three data sets: Indian Pines, Pavia University, and Kennedy Space Center (KSC) and compared with some recent and well-known supervised, semi-supervised, and unsupervised FE methods. Various experiments demonstrate the efficiency of the LPPPF in comparison with the other FE methods. LPPPF has also considerable performance with limited training samples.

A multimode process monitoring strategy via improved variational inference Gaussian mixture model based on locality preserving projections

For multimode process monitoring, accurate mode information is difficult to be obtained, and each mode is monitored separately, which increases the complexity of the system. This paper proposes a multimode process monitoring strategy via improved variational inference Gaussian mixture model based on locality preserving projections (IVIGMM-LPP). First, the raw data are projected to the feature space where samples still maintain the original neighbor structure. Second, a new discriminant condition is introduced to reduce the influence of the initial category parameter on the iteration results in the VIGMM model. Then, the data are updated utilizing modal information, so that the scales of different modes are adjusted to the same level. Next, the deviation vector is introduced to eliminate the multi-center structure of data. Finally, the statistic is built to monitor the process. IVIGMM-LPP establishes one model for monitoring the premise of knowing the mode information, which reduces the complexity of the monitoring process and improves the fault detection rate. The experimental results of a numerical case and the Tennessee Eastman (TE) process verify the effectiveness of IVIGMM-LPP.

Joint Analysis of Functional and Structural Connectomes Between Preterm and Term Infant Brains via Canonical Correlation Analysis With Locality Preserving Projection

Preterm is a worldwide problem that affects infants’ lives significantly. Moreover, the early impairment is more than limited to isolated brain regions but also to global and profound negative outcomes later, such as cognitive disorder. Therefore, seeking the differences of brain connectome between preterm and term infant brains is a vital step for understanding the developmental impairment caused by preterm. Existing studies revealed that studying the relationship between brain function and structure, and further investigating their differentiable connectomes between preterm and term infant brains is a way to comprehend and unveil the differences that occur in the preterm infant brains. Therefore, in this article, we proposed a novel canonical correlation analysis (CCA) with locality preserving projection (LPP) approach to investigate the relationship between brain functional and structural connectomes and how such a relationship differs between preterm and term infant brains. CCA is proposed to study the relationship between functional and structural connections, while LPP is adopted to identify the distinguishing features from the connections which can differentiate the preterm and term brains. After investigating the whole brain connections on a fine-scale connectome approach, we successfully identified 89 functional and 97 structural connections, which mostly contributed to differentiate preterm and term infant brains from the functional MRI (fMRI) and diffusion MRI (dMRI) of the public developing Human Connectome Project (dHCP) dataset. By further exploring those identified connections, the results innovatively revealed that the identified functional connections are short-range and within the functional network. On the contrary, the identified structural connections are usually remote connections across different functional networks. In addition, these connectome-level results show the new insights that longitudinal functional changes could deviate from longitudinal structural changes in the preterm infant brains, which help us better understand the brain-behavior changes in preterm infant brains.

An Optimization Technique for Linear Manifold Learning-Based Dimensionality Reduction: Evaluations on Hyperspectral Images

Manifold learning tries to find low-dimensional manifolds on high-dimensional data. It is useful to omit redundant data from input. Linear manifold learning algorithms have applicability for out-of-sample data, in which they are fast and practical especially for classification purposes. Locality preserving projection (LPP) and orthogonal locality preserving projection (OLPP) are two known linear manifold learning algorithms. In this study, scatter information of a distance matrix is used to construct a weight matrix with a supervised approach for the LPP and OLPP algorithms to improve classification accuracy rates. Low-dimensional data are classified with SVM and the results of the proposed method are compared with some other important existing linear manifold learning methods. Class-based enhancements and coefficients proposed for the formulization are reported visually. Furthermore, the change on weight matrices, band information, and correlation matrices with p-values are extracted and visualized to understand the effect of the proposed method. Experiments are conducted on hyperspectral imaging (HSI) with two different datasets. According to the experimental results, application of the proposed method with the LPP or OLPP algorithms outperformed traditional LPP, OLPP, neighborhood preserving embedding (NPE) and orthogonal neighborhood preserving embedding (ONPE) algorithms. Furthermore, the analytical findings on visualizations show consistency with obtained classification accuracy enhancements.

Locality Preserving and Label-Aware Constraint-Based Hybrid Dictionary Learning for Image Classification

Dictionary learning has been an important role in the success of data representation. As a complete view of data representation, hybrid dictionary learning (HDL) is still in its infant stage. In previous HDL approaches, the scheme of how to learn an effective hybrid dictionary for image classification has not been well addressed. In this paper, we proposed a locality preserving and label-aware constraint-based hybrid dictionary learning (LPLC-HDL) method, and apply it in image classification effectively. More specifically, the locality information of the data is preserved by using a graph Laplacian matrix based on the shared dictionary for learning the commonality representation, and a label-aware constraint with group regularization is imposed on the coding coefficients corresponding to the class-specific dictionary for learning the particularity representation. Moreover, all the introduced constraints in the proposed LPLC-HDL method are based on the l2-norm regularization, which can be solved efficiently via employing an alternative optimization strategy. The extensive experiments on the benchmark image datasets demonstrate that our method is an improvement over previous competing methods on both the hand-crafted and deep features.

Wukong

Querying graph data is becoming increasingly prevalent and important across many application domains, like social networking, urban monitoring, electronic payment, and semantic webs. In the last few years, we have ben working on improving the performance of graph querying by leveraging new hardware features and system designs. Moving towards this goal, we have designed and developed Wukong, a distributed in-memory framework that provides low latency and high throughput for concurrent query processing over large and fast-evolving graph data. This article overviews our architecture and presents four systems that aim to satisfy diverse challenging requirements on graph querying (e. g. high concurrency, evolving graphs, workload heterogencity, and locality preserving). Our systems also significantly outperform state-of-the-art systems in both latency and throughput, usually by orders of magnitude.

Robust Image Representation via Low Rank Locality Preserving Projection

Locality preserving projection (LPP) is a dimensionality reduction algorithm preserving the neighhorhood graph structure of data. However, the conventional LPP is sensitive to outliers existing in data. This article proposes a novel low-rank LPP model called LR-LPP. In this new model, original data are decomposed into the clean intrinsic component and noise component. Then the projective matrix is learned based on the clean intrinsic component which is encoded in low-rank features. The noise component is constrained by the ℓ 1 -norm which is more robust to outliers. Finally, LR-LPP model is extended to LR-FLPP in which low-dimensional feature is measured by F-norm. LR-FLPP will reduce aggregated error and weaken the effect of outliers, which will make the proposed LR-FLPP even more robust for outliers. The experimental results on public image databases demonstrate the effectiveness of the proposed LR-LPP and LR-FLPP.