High-dimensional space includes many subspaces so that anomalies can be hidden in any of them, which leads to obvious difficulties in abnormality detection. Currently, most existing anomaly detection methods tend to measure distances between data points. Unfortunately, the distance between data points becomes more similar as the dimensionality of the input data increases, resulting in difficulties in differentiation between data points. As such, the high dimensionality of input data brings an obvious challenge for anomaly detection. To address this issue, this article proposes a hybrid method of combining a sparse autoencoder with a support vector machine. The principle is that by first using the proposed sparse autoencoder, the low-dimensional features of the input dataset can be captured, so as to reduce its dimensionality. Then, the support vector machine separates abnormal features from normal features in the captured low-dimensional feature space. To improve the precision of separation, a novel kernel is derived based on the Mercer theorem. Meanwhile, to prevent normal points from being mistakenly classified, the upper limit of the number of abnormal points is estimated by theChebyshevtheorem. Experiments on both the synthetic datasets and the UCI datasets show that the proposed method outperforms the state-of-the-art detection methods in the ability of anomaly detection. We find that the newly designed kernel can explore different sub-regions, which is able to better separate anomaly instances from the normal ones. Moreover, our results suggested that anomaly detection models suffer less negative effects from the complexity of data distribution in the space reconstructed by those layered features than in the original space.