You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Self-paced learning (SPL) is a recently raised methodology designed through simulating the learning principle of humans animals. A variety of SPL realization schemes have been designed for different computer vision and pattern recognition tasks, and empirically substantiated to be effective in these applications. However, the investigation on its theoretical insight is still a blank. To this issue, this study attempts to provide some new theoretical understanding under the SPL scheme. Specifically, we prove that the solving strategy on SPL accords with a majorization minimization algorithm implemented on a latent objective function. Furthermore, we find that the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty (NSPR) known in statistics and machine learning. Such connection inspires us discovering more intrinsic relationship between SPL regimes and NSPR forms, like SCAD, LOG and EXP. The robustness insight under SPL can then be finely explained. We also analyze the capability of SPL on its easy loss prior embedding property, and provide an insightful interpretation to the effectiveness mechanism under previous SPL variations. Besides, we design a group-partial-order loss prior, which is especially useful to weakly labeled large-scale data processing tasks. Through applying SPL with this loss prior to the FCVID dataset, which is currently one of the biggest manually annotated video dataset, our method achieves state-of-the-art performance beyond previous methods, which further helps supports the proposed theoretical arguments.

Cited Abstract(s):
[1]: Reranking has been a focal technique in multimedia retrieval due to its efficacy in improving initial retrieval results. Current reranking methods, however, mainly rely on the heuristic weighting. In this paper, we propose a novel reranking approach called Self-Paced Reranking (SPaR) for multimodal data. As its name suggests, SPaR utilizes samples from easy to more complex ones in a self-paced fashion. SPaR is special in that it has a concise mathematical objective to optimize and useful properties that can be theoretically verified. It on one hand offers a unified framework providing theoretical justifications for current reranking methods, and on the other hand generates a spectrum of new reranking schemes. This paper also advances the state-of-the-art self-paced learning research which potentially benefits applications in other fields. Experimental results validate the efficacy and the efficiency of the proposed method on both image and video search tasks. Notably, SPaR achieves by far the best result on the challenging TRECVID multimedia event search task.

[2]: Matrix factorization (MF) has been attracting much attention due to its wide applications. However, since MF models are generally non-convex, most of the existing methods are easily stuck into bad local minima, especially in the presence of outliers and missing data. To alleviate this deficiency, in this study we present a new MF learning methodology by gradually including matrix elements into MF training from easy to complex. This corresponds to a recently proposed learning fashion called self-paced learning (SPL), which has been demonstrated to be beneficial in avoiding bad local minima. We also generalize the conventional binary (hard) weighting scheme for SPL to a more effective real-valued (soft) weighting manner. The effectiveness of the proposed self-paced MF method is substantiated by a series of experiments on synthetic, structure from motion and background subtraction data.
where @math is the age parameter for controlling the learning pace, and @math represents the self-paced regularizer (SP-regularizer), whose intrinsic conditions have been theoretically abstracted by [1] [2] . Through jointly learning the model parameter @math and the latent weight @math by AOS with gradually increasing age parameter, more samples can be automatically included into training from easy to complex in a purely self-paced way.