The one-class anomaly detection approach has previously been found to be effective in face presentation attack detection, especially in an \textit{unseen} attack scenario, where the system is exposed to novel types of attacks. This work follows the same anomaly-based formulation of the problem and analyses the merits of deploying \textit{client-specific} information for face spoofing detection. We propose training one-class client-specific classifiers (both generative and discriminative) using representations obtained from pre-trained deep convolutional neural networks. Next, based on subject-specific score distributions, a distinct threshold is set for each client, which is then used for decision making regarding a test query. Through extensive experiments using different one-class systems, it is shown that the use of client-specific information in a one-class anomaly detection formulation (both in model construction as well as decision threshold tuning) improves the performance significantly. In addition, it is demonstrated that the same set of deep convolutional features used for the recognition purposes is effective for face presentation attack detection in the class-specific one-class anomaly detection paradigm.