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Slow feature analysis (SFA) extracts slowly varying features out of the input data and has been successfully applied on pattern recognition. However, SFA heavily relies on the constructed time series when SFA is applied on databases that neither have obvious temporal structure nor have label information. Traditional SFA constructs time series based on k-nearest neighborhood (k-NN) criterion. Specifically, the time series set constructed by k-NN criterion is likely to include noisy time series or lose suitable time series because the parameter k is difficult to determine. To overcome these problems, a method called adaptive unsupervised slow feature analysis (AUSFA) is proposed. First, AUSFA designs an adaptive criterion to generate time series for characterizing submanifold. The constructed time series have two properties: (1) two points of time series lie on the same submanifold and (2) the submanifold of the time series is smooth. Second, AUSFA seeks projections that simultaneously minimize the slowness scatter and maximize the fastness scatter to extract slow discriminant features. Extensive experimental results on three benchmark face databases demonstrate the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]