Contents I. Introduction
With the rapid development of electronic and electrical technology, large volume of data has been collected by widely applied Internet of Things (IoT) terminals [1]. Among them, optical image data are probably the most popular and common, and are always of high dimensions [1], [36]–[37]. Therefore, high space and computational resources are required to store and process the data and causes the “curse of dimensionality” issue [2]–[3]. Additionally, high-dimensional image data processing has aroused much interests from both scientific and industrial communities [3], [38]–[42]. Dimension reduction (DR) techniques can reduce the dimensionality of data from a large dimension to a smaller and compact dimension, which is beneficial for data storage, transmission and application, as illustrated in Fig. 1. The focus of DR is to transform the original sensing high-dimensional data from the observation space to a reduced and lower dimensional subspace with a linear or nonlinear manner by removing redundant information and noise. In the process, key data knowledge, such as the data structure and discriminative information, should be retained [4]–[5]. Principal component analysis (PCA) [6] and linear discriminative analysis (LDA) [7] are widely applied DR methods owing to their computational simplicity and application effectiveness. PCA is performed without supervised signals and aims to maximize the variance in data. In contrast, LDA can utilize the label prior information of data to concurrently minimize the within-class scatter and maximize the between-class scatter. Similarly, the two methods mainly consider the statistical properties of data when reducing the dimension, and the intrinsic data structure cannot be well revealed. To uncover the essential manifold structure of data, locally linear embedding (LLE) [8] and Laplacian eigenmaps (LE) [9] have been advocated to analyze the data that distribute on or near a low-dimensional manifold. However, these methods are limited to the out of sample problem; that is, the methods cannot handle new samples well [10]. To address this problem, nonlinear methods can be approximately linearized by deriving an explicit projection. Thus, locality-preserving projections (LPPs) [11] has been developed as a linear version of LE, and LLE can be similarly linearized as neighborhood preserving embedding (NPE) [12]. However, the methods focus on the locality or neighborhood properties of data and cannot guarantee the discriminating capability due to their unsupervised nature. A general framework known as graph embedding (GE) has been presented, which can unify many existing DR methods [13]. For instances, PCA, LDA, and LPP can be reformulated via the framework by constructing an intrinsic graph that describes some expected statistical or geometric properties of data. Additionally, scale normalization or a penalty graph that characterizes undesired statistical or geometric properties is generally required as constraint. Following the GE framework, some DR methods have been proposed [14]. As a result, the GE framework can be realized with different intrinsic and penalty graphs constructed according to different principles, and the problem of DR is converted into the difficulty of establishing the statistical or geometric property that should be preserved or inhibited in DR. Classic -nearest neighbors or -radius ball-based graph construction methods are simple but lack effectiveness, and the performances are restricted [15].
Data dimension reduction module in edge computing can simultaneously reduce the dimension of data and preserve data knowledge, which can enable efficient data storage, transmission and application in green IoT.
