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In classic supervised learning, a learning algorithm takes a fixed training data of several classes to build a classifier. In this paper, we propose to study a new problem, i.e., building a learning system that learns cumulatively. As time goes by, the system sees and learns more and more classes of data and becomes more and more knowledgeable. We believe that this is similar to human learning. We humans learn continuously, retaining the learned knowledge, identifying and learning new things, and updating the existing knowledge with new experiences. Over time, we cumulate more and more knowledge. A learning system should be able to do the same. As algorithmic learning matures, it is time to tackle this cumulative machine learning (or simply cumulative learning) problem, which is a kind of lifelong machine learning problem. It presents two major challenges. First, the system must be able to detect data from …