The ability to detect anomalies in signals from sensors is imperative for structural health monitoring (SHM) applications. Many of the candidate algorithms for these applications either require a lot of training examples or are very computationally inefficient for large sample sizes. The damage detection framework presented in this paper uses a combination of Linear Discriminant Analysis (LDA) along with Support Vector Machines (SVM) to obtain a computationally efficient classification scheme for rapid damage state determination. LDA was used for feature extraction of damage signals from piezoelectric sensors on a composite plate and these features were used to train the SVM algorithm in parts, reducing the computational intensity associated with the quadratic optimization problem that needs to be solved during training. SVM classifiers were organized into a binary tree structure to speed up classification, which also reduces the total training time required. This framework was validated on composite plates that were impacted at various locations. The results show that the algorithm was able to correctly predict the different impact damage cases in composite laminates using less than 21 percent of the total available training data after data reduction.