Fuzzy clustering of multiple instance data

We introduce a new algorithm to identify multiple target concepts when data are represented by multiple instances. A multiple instance data sample is characterized by a bag that contains multiple feature vectors, or instances. Each bag is labeled as either positive or negative. However, the labels of the instances within each bag are unknown. A bag is labeled as positive if and only if at least one of its instances is positive and negative if and only if all of its instances are negative. First, we define a fuzzy Multi-target concept Diverse Density (MDD) metric. The MDD is maximized when the target concepts correspond to dense regions in the feature space with maximal correlation to instances from positive samples, and minimal correlation to instances from negative samples. Then, we develop an iterative algorithm to optimize the MDD and identify K target concepts simultaneously. The proposed algorithm, called Fuzzy Clustering of Multiple Instance data (FCMI), is tested and validated by using it to analyze data of buried landmines collected using a ground penetrating radar sensor. We show that the FCMI algorithm can identify distinct target concepts that correspond to mines of different types buried at different depths. We also show that FCMI can be used to label individual instances within each bag.