This paper presents a new approach to classification of high dimensional spectroscopy data and demonstrates that it outperforms other current state-of-the art approaches. The specific task we consider is identifying whether samples contain chlorinated solvents or not, based on their Raman spectra. We also examine robustness to classification of outlier samples that are not represented in the training set (negative outliers). A novel application of a locally-connected neural network (NN) for the binary classification of spectroscopy data is proposed and demonstrated to yield improved accuracy over traditionally popular algorithms. Additionally, we present the ability to further increase the accuracy of the locally-connected NN algorithm through the use of synthetic training spectra and we investigate the use of autoencoder based one-class classifiers and outlier detectors. Finally, a two-step classification process is presented as an alternative to the binary and one-class classification paradigms. This process combines the locally-connected NN classifier, the use of synthetic training data, and an autoencoder based outlier detector to produce a model which is shown to both produce high classification accuracy, and be robust to the presence of negative outliers.