A fast image retrieval algorithm with automatically extracted discriminant features

Fisher's discriminant analysis is very powerful for classification but it does not perform well when the number of classes is large but the number of samples in each class is small. We propose to resolve this problem by dynamically grouping classes at different levels in a tree. We recast the problem of classification as a regression problem so that the classification (class labels as output) and regression (numerical values as output) are unified. The proposed HDR tree automatically forms clusters in the input space guided by the desired output, which produces discriminant spaces. These discriminant spaces are organized in a coarse-to-fine structure by a tree. A unified size-dependent negative-log-likelihood is proposed to automatically handle both under-sample situations (where the number of samples of each cluster is smaller than the dimensionality of the discriminant space) and the over-sample situations where the HDR tree can reach near-optimal performance. For fast computation, the HDR tree has a logarithmic retrieval time complexity. The proposed HDR tree has been tested with synthetic data, face image databases, and publicly available data sets that use manually selected features.