We cast the query by example spoken term detection (QbE-STD) problem as subspace detection where query and background subspaces are modeled as union of low-dimensional subspaces. The speech exemplars used for subspace modeling are class-conditional posterior probabilities estimated using deep neural network (DNN). The query and background training exemplars are exploited to model the underlying low-dimensional subspaces through dictionary learning for sparse representation. Given the dictionaries characterizing the query and background subspaces, QbE-STD is performed based on the ratio of the two corresponding sparse representation reconstruction errors. The proposed subspace detection method can be formulated as the generalized likelihood ratio test for composite hypothesis testing. The experimental evaluation demonstrate that the proposed method is able to detect the query given a single example and performs significantly better than a highly competitive QbE-STD baseline system based on template matching.