Hybrid analog-digital precoding is challenging for broadband millimeter-wave (mmWave) massive MIMO systems, since the analog precoder is frequency-flat but the mmWave channels are frequency-selective. In this paper, we propose a principal component analysis (PCA)-based broadband hybrid precoder/combiner design, where both the fully-connected array and partially-connected subarray (including the fixed and adaptive subarrays) are investigated. Specifically, we first design the hybrid precoder/combiner for fully-connected array and fixed subarray based on PCA, whereby a low-dimensional frequency-flat precoder/combiner is acquired based on the optimal high-dimensional frequency-selective precoder/combiner. Meanwhile, the near-optimality of our proposed PCA approach is theoretically proven. Moreover, for the adaptive subarray, a low-complexity shared agglomerative hierarchical clustering algorithm is proposed to group the antennas for the further improvement of spectral efficiency (SE) performance. Besides, we theoretically prove that the proposed antenna grouping algorithm is only determined by the slow time-varying channel parameters in the large antenna limit. Simulation results demonstrate the superiority of the proposed solution over state-of-the-art schemes in SE, energy efficiency (EE), bit-error-rate performance, and the robustness to time-varying channels. Our work reveals that the EE advantage of adaptive subarray over fully-connected array is obvious for both active and passive antennas, but the EE advantage of fixed subarray only holds for passive antennas.