Abstract
Multi-instance (MI) learning is a branch of machine learning, where each object (bag) consists of multiple feature vectors (instances)—for example, an image consisting of multiple patches and their corresponding feature vectors. In MI classification, each bag in the training set has a class label, but the instances are unlabeled. The instances are most commonly regarded as a set of points in a multi-dimensional space. Alternatively, instances are viewed as realizations of random vectors with corresponding probability distribution, where the bag is the distribution, not the realizations. By introducing the probability distribution space to bag-level classification problems, dissimilarities between probability distributions (divergences) can be applied. The bag-to-bag Kullback–Leibler information is asymptotically the best classifier, but the typical sparseness of MI training sets is an obstacle. We introduce bag-to-class divergence to MI learning, emphasizing the hierarchical nature of the random vectors that makes bags from the same class different. We propose two properties for bag-to-class divergences, and an additional property for sparse training sets, and propose a dissimilarity measure that fulfils them. Its performance is demonstrated on synthetic and real data. The probability distribution space is valid for MI learning, both for the theoretical analysis and applications.
Highlights
We argue that the equality, orthogonality and monotonicity properties possessed by f -divergences are reasonable for bag-to-class divergences, less likely to occur in practice: The equality property and the monotonicity property are valid for uncertain objects, but in practice it can occur with sparse class sampling, and we argue that these properties are valid for bag-to-class divergences
The bag-to-bag KL information has the minimum misclassification rate, the typical bag sparseness of MI training sets is an obstacle. This is partly solved by bag-to-class dissimilarities and the proposed class-conditional KL information accounts for additional sparsity of bags
(1) Aggregation of instances according to bag label and the additional class-conditioning provide a solution for the bag sparsity problem
Summary
Machine-learning applications include a wide variety of data types, images being one of the most successful areas. It has had an enormous impact on image analysis, especially in replacing small sets of hand-crafted features with large sets of computer readable features, which often lack apparent. The training data consists of K objects, x, with corresponding class labels, y; {(x1 , y1 ), . The task is to build a classifier that correctly labels a new object. The training data is used to adjust the model according to the desired outcome, often maximizing the accuracy of the classifier
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