# Sample Reduction-Based Pairwise Linear Regression Classification for IoT Monitoring Systems
###### Abstract
When compared with the single image-based recognition task, the set-based video recognition task can directly calculate the labels for whole videos, without classifying each frame of the videos separately, which can effectively accelerate the calculation speed. Since every video includes a wide range of appearance variations, the key to set-based video face recognition lies in two strategies: the representation of the videos and the accurate measurement of the distance between different videos. From the perspective of model representation and measurement learning, many set-based video face-recognition methods have been presented in recent decades, in order to identify the optimal recognition performance, including the discriminant canonical correlations (DCC) algorithm [14], covariance discriminative learning (CDL) algorithm [15], dual-linear regression classification (DLRC) algorithm [16], manifold discriminant analysis (MDA) algorithm [17], pairwise linear regression classification (PLRC) algorithm [18], image set-based collaborative representation and classification (ISCRC) algorithm [19], and set-level joint sparse representation classification (SJSRC) algorithm [20]. Among these algorithms, LRC-based methods have gradually attracted the attention of a greater number of researchers because of their superior performance. Recently, the PLRC algorithm [18] has been proven to be a valid image set-classification method. By analyzing PLRC, the distance between images has been identified as the key point in the construction of unrelated sets. However, previously developed unrelated set construction strategies (i.e., S1 and S2 in [18]) are not optimal distance metric methods. Fortunately, based on collaborative and sparse representation, [PERSON] et al. proposed another two unrelated set construction strategies: S3 and S4 [21]. In addition, when the size of the videos or image sets is small, PLRC can work well (see Figure 4). Therefore, how to make PLRC suitable for large-size videos has become an interesting problem. [PERSON] et al. proposed the kernel PLRC (KPLRC) algorithm [21], with the aim of increasing the dimensionality of image samples in an image set, in order to increase the linear separability and overcome this issue. Unfortunately, KPLRC not only increases the classification accuracy, but also the additional computational overhead. Motivated by this, and starting from the direction of decreasing the number of images in each video, this paper proposes a novel video face recognition or image set classification framework, named sample reduction-based PLRC (SRbPLRC), which consists of divide SRbPLRC (DSRbPLRC), anchor point SRbPLRC (APSRbPLRC), and attention anchor point SRbPLRC (AAPSRbPLRC) methods. Specifically, the DSRbPLRC algorithm was evaluated first, which simply divides large-size videos into several small-size videos/subsets randomly. However, DSRbPLRC increases the number of videos, which may reduce the computing speed, and it does not consider the influence of any noise or outliers that may exist in the videos. Then, we looked at the APSRbPLRC algorithm, which first uses the clustering method to divide each video into several sub-videos, and then the centroid and mean values of each sub-video were used as anchor points. APSRPLCR can greatly reduce the number of samples in videos and does not increase the number of videos. Thus, it can realize set-based video face recognition efficiently and accurately. Additionally, APSRPLCR can overcome the influence of noise and outliers to some extent. Nevertheless, APSRPLCR considers all images within each sub-video to be of equal importance while computing the anchor points; however, we believe that a good anchor point construction strategy should adaptively weigh and combine the images in each sub-video/subset. Thus, the AAPSRbPLRC algorithm was developed, which utilizes an attention mechanism to learn the optimal anchor points.