text: In this paper we present an unsupervised method to learn the weights with which the scores of multiple classifiers must be combined in classifier fusion settings. We also introduce a novel metric for ranking instances based on an index which depends upon the rank of weighted scores of test points among the weighted scores of training points. We show that the optimized index can be used for computing measures such as average precision. Unlike most classifier fusion methods where a single weight is learned to weigh all examples our method learns instance-specific weights. The problem is formulated as learning the weight which maximizes a clarity index; subsequently the index itself and the learned weights both are used separately to rank all the test points. Our method gives an unsupervised method of optimizing performance on actual test data, unlike the well known stacking-based methods where optimization is done over a labeled training set. Moreover, we show that our method is tolerant to noisy classifiers and can be used for selecting N-best classifiers.
  @cite_13: In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which each entry characterizes the comparative relationship of scores of two test samples. Our hypothesis is that the relative score relations are consistent among component models up to certain sparse deviations, despite the large variations that may exist in the absolute values of the raw scores. Then we formulate the score fusion problem as seeking a shared rank-2 pairwise relationship matrix based on which each original score matrix from individual model can be decomposed into the common rank-2 matrix and sparse deviation errors. A robust score vector is then extracted to fit the recovered low rank score relation matrix. We formulate the problem as a nuclear norm and l 1 norm optimization objective function and employ the Augmented Lagrange Multiplier (ALM) method for the optimization. Our method is isotonic (i.e., scale invariant) to the numeric scales of the scores originated from different models. We experimentally show that the proposed method achieves significant performance gains on various tasks including object categorization and video event detection.
  @cite_10: Late fusion addresses the problem of combining the prediction scores of multiple classifiers, in which each score is predicted by a classifier trained with a specific feature. However, the existing methods generally use a fixed fusion weight for all the scores of a classifier, and thus fail to optimally determine the fusion weight for the individual samples. In this paper, we propose a sample-specific late fusion method to address this issue. Specifically, we cast the problem into an information propagation process which propagates the fusion weights learned on the labeled samples to individual unlabeled samples, while enforcing that positive samples have higher fusion scores than negative samples. In this process, we identify the optimal fusion weights for each sample and push positive samples to top positions in the fusion score rank list. We formulate our problem as a L∞ norm constrained optimization problem and apply the Alternating Direction Method of Multipliers for the optimization. Extensive experiment results on various visual categorization tasks show that the proposed method consistently and significantly beats the state-of-the-art late fusion methods. To the best knowledge, this is the first method supporting sample-specific fusion weight learning.
summary: To the best of our knowledge, few recent works have actually looked into instance-specific weight learning @cite_10 @cite_13 . Some of the most promising results are reported in @cite_10 . The basic idea in this work is to propagate fusion weights of labeled instances to the individual unlabeled instances along a graph built on low-level features. The method has been shown to outperform other fusion methods on a variety of datasets. However, although the learned weights are instance specific, the method not only still requires a held-out set for which labels are known, it also requires knowledge of the low-level features of instances. On the other hand, our method does not require held-out data. Moreover, our solution is a meta algorithm that requires no knowledge of the low-level features of the instances. Another issue with @cite_10 is that the weights learned for different test instances are not disjoint from each other. This has the undesirable aspect that newer test instances cannot be independently introduced into the set.