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To assist the clinical diagnosis and treatment of speech dysarthria, automatic dysarthric speech detection techniques providing reliable and cost-effective assessment are indispensable. Based on clinical evidence on spectro-temporal distortions associated with dysarthric speech, we propose to automatically discriminate between healthy and dysarthric speakers exploiting spectro-temporal subspaces of speech. Spectro-temporal subspaces are extracted using singular value decomposition, and dysarthric speech detection is achieved by applying a subspace-based discriminant analysis. Experimental results on databases of healthy and dysarthric speakers for different languages and pathologies show that the proposed subspace-based approach using temporal subspaces is more advantageous than using spectral subspaces, also outperforming several state-of-the-art automatic dysarthric speech detection techniques.