Estimating the error rates of classifiers or regression models is a fundamental task in machine learning which has thus far been studied exclusively using supervised learning techniques. We propose a novel unsupervised framework for estimating these error rates using only unlabeled data. We prove consistency results for the framework and demonstrate its applicability on synthetic and real world data.

Nonnegative factorization of a tensor plays an important role in the analysis of multidimensional data, when data elements are inherently nonnegative. It gives a meaningful lower rank approximation which can further be used for dimensionality reduction as well as visualization. In this work we propose an algorithm for nonnegative tensor factorization (NTF) based on alternating nonnegative least squares (ANLS) and an active set type method called the block pivoting principle. We present experimental results using data sets from real life applications and synthetic data sets to show that the proposed algorithm significantly outperforms other existing algorithms in computational speed.

The growth in size and popularity of the web and other online resources has created enormous quantities of text data. To effectively analyze such data several visualization techniques have been developed. These techniques typically use standard dimensionality reduction methods that implicitly assume a Euclidean geometry. We examine an alternative approach for text visualization that uses user-specified and corpus based geometries. These non-Euclidean geometries exhibit linguistic knowledge gained from expert knowledge and corpus statistics and thus are generally superior to more traditional geometries. We demonstrate our framework with qualitative and quantitative experiments over several document collections. These experiments point the way towards a new visualization paradigm of interactively refining the geometry and the associated dimensionality reduction mechanism.

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