In real-world applications, the oracle who can label all instances correctly may not exist or may be too expensive to acquire. Alternatively, crowdsourcing provides an easy way to get labels at a low cost from multiple non-expert annotators. During the past few years, much attention has been paid to learning from such crowdsourcing data, namelyLearning from Crowds(LFC). Despite their proper statistical foundations, the existing methods for LFC still suffer from several disadvantages, such as needing prior knowledge to select the expertise model to represent the behavior of annotators, involving non-convex optimization problems, or restricting the classifier type being used. This paper addresses LFC from a quality-sensitive perspective and presents a novel framework named QS-LFC. Through reformulating the original LFC problem as a quality-sensitive learning problem, the above-mentioned disadvantages of existing methods can be avoided. Further, a support vector machine (SVM) implementation of QS-LFC is proposed. Experimental results on both synthetic and real-world data sets demonstrate that QS-LFC can achieve better generalization performance and is more robust to the noisy labels, than the existing methods.

Learning from crowds, which the labels of the instances are collected through crowdsourcing ways, has become an important research topic recently. Personal Classifier (PC) approach is a representative approach for learning from crowds due to its convex optimization formulation. PC approach makes assumptions about parameters' distribution, thus it is a parametric approach. However, these assumptions may not always hold, especially for real-world data sets. In this paper, we propose a new non-parametric approach, called NP approach, for learning from crowds. NP approach has a convex optimization formulation but without assumptions about parameters' distribution. In addition, NP approach can be generalized to the non-linear case directly, while the PC approach does not. Experimental studies show that NP approach outperforms other two compared approaches.

The convex hull has been extensively studied in computational geometry and its applications have spread over an impressive number of fields. How to find the convex hull is an important and challenging problem. Although many algorithms had been proposed for that, most of them can only tackle the problem in two or three dimensions and the biggest issue is that those algorithms rely on the samples' coordinates to find the convex hull. In this paper, we propose an approximation algorithm named FVDM, which only utilizes the information of the samples' distance matrix to find the convex hull. Experiments demonstrate that FVDM can effectively identify the vertices of the convex hull.

In this paper we consider a dynamic lot sizing model with mixed backlogging and outsourcing and bounded inventory, in which outsourcing may occur in a period even if the inventory level at that period is positive. The production cost may include setup cost and the production level is unlimited. The holding, backlogging and outsourcing cost functions are linear. Furthermore, backlogging level at each period is limited, and outsourcing level at each period cannot exceed the demand of that period. The goal is to minimize the total cost of production, inventory holding/backlogging and outsourcing. We show that this problem can be solved in O(T4log T) time where T is the length of the planning horizon. Finally, the proposed algorithm is implemented in C++ and evaluated on a large variety of instances generated randomly.