To date, many active learning techniques have been developed for acquiring labels when training data is limited. However, an important aspect of the problem has often been neglected or just mentioned in passing: the curse of dimensionality. Yet, the curse of dimensionality poses even greater challenges in the case of limited data, which is precisely the setup for active learning. Reducing the dimensions is not a trivial task, however, as the correct number of dimensions depends on a number of factors including the training data size, the number of classes, the discriminative power of the features, and the underlying classification model. Moreover, active learning is typically applied in an iterative manner where the number of labels is smaller in the earlier iterations compared to the later ones. We propose an adaptive dimensionality reduction technique that determines the appropriate number of dimensions for each active learning iteration, utilizing the labeled and unlabeled data e...