We present a new method for classification using the maximum entropy principle, allowing full use of relevant training data and smoothing the data space. To classify a test point we compute a maximum entropy weight distribution over a subset of training data and constrain the weights to exactly reconstruct the test point. The classification problem is formulated as a linearly constrained optimization problem and solved using a primal-dual logarithmic barrier method, well suited for high-dimensional data. We discuss theoretical advantages and present experimental results on vowel data which demonstrate that the method performs competitively for speech classification tasks.