Asa　generative　model,　probabilistic　linear　discriminant　analysis　(PLDA)　has　achieved　good　performance　in　supervised　learning　tasks.　The　model　incorporates　both　within-individual　and　between-individual　variation,　and　remaining　unexplained　data　variation　is　assumed　to　follow　Gaussian　distribution.　However,　the　assumption　of　Gaussian　distribution　makes　the　model　sensitive　to　the　presence　of　noise　and　outliers　in　training　set.　To　address　this　issue,　this　paper　proposes　a　robust　probabilistic　linear　discriminant　analysis　model　by　assuming　Laplace　prior　on　the　noise　term.　Instead　of　solving　high-dimensional　linear　systems,　we　embed　a　Kronecker-decomposable　component　in　the　new　model　for　tensor　data,　significantly　reducing　the　size　of　problems.　As　the　non-conjugacy　of　Laplace　distribution　complicates　the　calculation　of　the　posteriors　of　latent　variables,　we　express　it　to　a　hierarchical　architecture　using　an　Inverse　Gamma　distribution　and　then　adopt　variational　expectation　&　ndash;maximization　(EM)　algorithm　to　learn　model　parameters.　The　reconstruction　and　classification　experiments　on　several　public　databases　show　the　superiority　of　the　proposed　model　compared　with　the　state-of-the-art　LDA-based　algorithms.　(c)　2021　Elsevier　Inc.　All　rights　reserved.