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Speech analysis could provide an indicator of Alzheimer's disease and help develop clinical tools for automatically detecting and monitoring disease progression. While previous studies have employed acoustic (speech) features for characterisation of Alzheimer's dementia, these studies focused on a few common prosodic features, often in combination with lexical and syntactic features which require transcription. We present a detailed study of the predictive value of purely acoustic features automatically extracted from spontaneous speech for Alzheimer's dementia detection, from a computational paralinguistics perspective. The effectiveness of several state-of-the-art paralinguistic feature sets for Alzheimer's detection were assessed on a balanced sample of DementiaBank's Pitt spontaneous speech dataset, with patients matched by gender and age. The feature sets assessed were the extended Geneva minimalistic acoustic parameter set (eGeMAPS), the emobase feature set, the ComParE 2013 feature set, and new Multi-Resolution Cochleagram (MRCG) features. Furthermore, we introduce a new active data representation (ADR) method for feature extraction in Alzheimer's dementia recognition. Results show that classification models based solely on acoustic speech features extracted through our ADR method can achieve accuracy levels comparable to those achieved by models that employ higher-level language features. Analysis of the results suggests that all feature sets contribute information not captured by other feature sets. We show that while the eGeMAPS feature set provides slightly better accuracy than other feature sets individually (71.34%), “hard fusion” of feature sets improves accuracy to 78.70%.