Although sudden changes of the event phase in complex system may indicate underlying essential forces, such events are not frequent. In the present paper, we propose an essential event extractor (E3) scheme to extract relatively rare but cooccurring event sequences in event phase transitions. In E3, the self-organizingmap (SOM) is used as vector quantization (VQ) to encode non-symbolic events and Key-Graph as a co-occurrence graph. Afterwards, event transitions on the co-occurrence graph can be obtained by referring to an occurrence density estimation on the topology map of VQ. We demonstrate the E3 using an acoustic emission (AE) event sequence observed during a damage test of fuel cells and obtain reasonable and essential co-occurring damage sequences that exhibit mechanical effects.