We propose a joint channel estimation and signal detection technique for the uplink non-orthogonal multiple access using an unsupervised clustering approach. We apply the Gaussian mixture model to cluster received signals and accordingly optimize the decision regions to enhance the symbol error rate (SER). We show that when the received powers of the users are sufficiently different, the proposed clustering-based approach with no channel state information (CSI) at the receiver achieves an SER performance similar to that of the conventional maximum likelihood detector with full CSI. Since the accuracy of the utilized clustering algorithm depends on the number of the data points available at the receiver, the proposed technique delivers a tradeoff between the accuracy and block length.