Extracting Continuous Relevant Features
The problem of extracting the relevant aspects of data, in face of multiple conflicting structures, is inherent to modeling of complex data. Extracting continuous structures in one random variable that are relevant for another variable has been principally addressed recently via the method of Sufficient dimensionality reduction. However, such auxiliary variables often contain both structures that are relevant and others that are irrelevant for the task in hand. Identifying the relevant structures was shown in the context of clustering to be considerably improved by minimizing the information about another, irrelevant, variable. In this paper we address the problem of extracting continuous relevant structures and derive its formal, as well as algorithmic, solution. Its operation is demonstrated in a synthetic example and in a real world application of face images, showing its superiority over current methods such as oriented principal component analysis.