This paper presents a fully event-driven feedforward architecture that accounts for rapid categorization. The proposed algorithm processes the address event data generated either from an image or from Address-Event-Representation (AER) temporal contrast vision sensor. Bio-inspired, cortex-like, spike-based features are obtained through event-driven convolution and neural competition. The extracted spike feature patterns are then classified by a network of leaky integrate-and-fire (LIE) spiking neurons, in which the weights are trained using tempotron learning rule. One appealing characteristic of our system is the fully event-driven processing. The input, the features, and the classification are all based on address events (spikes). Experimental results on three datasets have proved the efficacy of the proposed algorithm.