Recognition of protein-DNA binding sites in genomic sequences is a crucial step for discovering biological functions of genomic sequences. Explosive growth in availability of sequence information has resulted in a demand for binding site detection methods with high specificity. The motivation of the work presented here is to address this demand by a systematic approach based on Maximum Likelihood Estimation. A general framework is developed in which a large class of binding site detection methods can be described in a uniform and consistent way. Protein-DNA binding is determined by binding energy, which is an approximately linear function within the space of sequence words. All matrix based binding word detectors can be regarded as different linear classifiers which attempt to estimate the linear separation implied by the binding energy function. The standard approaches of consensus sequences and profile matrices are described using this framework. A maximum likelihood approach for determining this linear separation leads to a novel matrix type, called the binding matrix. The binding matrix is the most specific matrix based classifier which is consistent with the input set of known binding words. It achieves significant improvements in specificity compared to other matrices. This is demonstrated using 95 sets of experimentally determined binding words provided by the TRANSFAC database.