Protein binding microarrays (PBM) are a high throughput technology used to characterize protein-DNA binding. The arrays measure a protein's affinity toward thousands of double-stranded DNA sequences at once, producing a comprehensive binding specificity catalog. We present a linear model for predicting the binding affinity of a protein toward DNA sequences based on PBM data. Our model represents the measured intensity of an individual probe as a sum of the binding affinity contributions of the probe's subsequences. These subsequences characterize a DNA binding motif and can be used to predict the intensity of protein binding against arbitrary DNA sequences. Our method was the best performer in the Dialogue for Reverse Engineering Assessments and Methods 5 (DREAM5) transcription factor/DNA motif recognition challenge. For the DREAM5 bonus challenge, we also developed an approach for the identification of transcription factors based on their PBM binding profiles. Our approach for TF identification achieved the best performance in the bonus challenge.