# Regularized Instance Embedding for Deep Multi-Instance Learning
## 2 Related Work
### Research Background of MIL  
MIL deals with a dataset called a bag and only supervises the whole bag, but does not provide specific labels of instances in the bag. Especially, in recent years, the formulation of this problem has attracted much attention from the research community. The data volume of the problem is exponential and requires a lot of labeling work. As a weakly supervised learning method, MIL can effectively reduce this burden because weak supervision is usually easier to obtain. For example, you can train object detectors with images collected from the web, using their associated tags as weak supervision, rather than a dataset of local annotations, such as object bounding box annotation and pixel-wise annotation [10; 11]. MIL is widely used in medical image analysis problems. A computer-aided-diagnosis (CAD) algorithm can be trained with medical images instead of expensive local annotations provided by experts. There are several types of problems that can be naturally expressed as MIL problems. For example, in a drug-activity-prediction problem [12], the goal is to predict whether a molecule induces a given effect. A molecule can have many conformations, and it is impossible to observe the influence of individual conformation without the expected effect. Therefore, the molecule must be observed as a set of conformations, so MIL formulation is used. Due to these attractive features, MIL has been increasingly used in many other applications in the past 20 years, such as image and video classification [13; 14; 15; 16; 17; 18], document classification [19; 20], and sound classification [21]. Motivated by the great effectiveness of MIL in real applications, the research goal of this paper is to propose a state-of-the-art MIL method. When developing MIL algorithms, there are two tasks: bag classification task and instance classification task. Bag classification is the most common task for MIL algorithms. It involves assigning a class label to a set of instances. The single instance label is not necessarily important depending on the algorithm and the type of hypothesis. Instance classification requires predicting instance labels though the instance labels in training set are not given. As described in [22], the loss functions of the two tasks are different. When the goal is bag classification, misclassification of the instance does not necessarily affect bag-level loss. For example, in a positive bag, if there are few real negative instances that are wrongly classified as positive instances, and bag labels remain the same; therefore, in the structure of the problem, such as the number of instances per-bag, the loss function plays an important role [22]. Moreover, many methods perform bag classification in the bag space without reasoning in instance space; therefore, they are often unable to perform instance classification. The proposed method can predict both bag labels and instance labels, which makes it more useful in applications. MIL classification is not limited to assigning a single label to an instance or bag. Assigning multiple labels to bags is particularly relevant because they can contain instances that represent different concepts. This multi-label MIL idea has been the focus of several publications [23; 24; 25]. Besides classification, MIL can be applied in for regression problems (see, e.g., [26; 27; 28]). The simplest way is to replace the bag-level classifier with a regressor [28]. Other methods proposed to rank bags instead of assigning a class tag or score. This problem is different from regression, because the goal is not to obtain accurate real-value labels, but to compare the predicted scores for sorting. Ranking can be performed at bag-level [29] or instance-level [30]. It is also possible to implement clustering tasks, including searching for clusters or structures in the set of an unlabeled bag. In some cases, clustering is performed in bag spaces using standard algorithms and set-based distance measures.