Bearing　fault　diagnosis　collects　massive　amounts　of　vibration　data　about　a　rotating　machinery　system,　whose　fault　classification　largely　depends　on　feature　extraction.　Features　reflecting　bearing　work　states　are　directly　extracted　using　time-frequency　analysis　of　vibration　signals,　which　leads　to　high　dimensional　feature　data.　To　address　the　problem　of　feature　dimension　reduction,　a　compressive　sensing-based　feature　extraction　algorithm　is　developed　to　construct　a　concise　fault　feature　set.　Next,　a　heuristic　PSO-BP　neural　network,　whose　learning　process　perfectly　combines　particle　swarm　optimization　and　the　Levenberg-Marquardt　algorithm,　is　constructed　for　fault　classification.　Numerical　simulation　experiments　are　conducted　on　four　datasets　sampled　under　different　severity　levels　and　load　conditions,　which　verify　that　the　proposed　fault　diagnosis　method　achieves　efficient　feature　extraction　and　high　classification　accuracy.