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This paper proposes a novel temporal knowledge representation and learning framework to perform large-scale temporal signature mining of longitudinal heterogeneous event data. The framework enables the representation, extraction, and mining of high-order latent event structure and relationships within single and multiple event sequences. The proposed knowledge representation maps the heterogeneous event sequences to a geometric image by encoding events as a structured spatial-temporal shape process. We present a doubly constrained convolutional sparse coding framework that learns interpretable and shift-invariant latent temporal event signatures. We show how to cope with the sparsity in the data as well as in the latent factor model by inducing a double sparsity constraint on the β-divergence to learn an overcomplete sparse latent factor model. A novel stochastic optimization scheme performs large-scale incremental learning of group-specific temporal event signatures. We validate the framework on synthetic data and on an electronic health record dataset.