  Machine learning is a promising technique for angle-of-arrival (AOA)
estimation of waves impinging a sensor array. However, the majority of the
methods proposed so far only consider a known, fixed number of impinging waves,
i.e., a fixed source number. This paper proposes a machine-learning-based
estimator designed for the case when the source number is variable and hence
unknown a priori. The proposed estimator comprises a framework of single-label
classifiers. Each classifier predicts if waves are present within certain
randomly selected segments of the array's field of view (FOV), resulting from
discretising the FOV with a certain (FOV) resolution. The classifiers'
predictions are combined into a probabilistic angle spectrum, whereupon the
source number and the AOAs are estimated jointly by applying a probability
threshold whose optimal level is learned from data. The estimator's performance
is assessed using a new performance metric: the joint AOA estimation success
rate. Numerical simulations show that for low SNR (-10 dB), a low FOV
resolution (2$^\circ$) yields a higher success rate than a high resolution
(1$^\circ$), whereas the opposite applies for mid (0 dB) and high (10 dB) SNRs.
In nearly all simulations, except one at low SNR and a high FOV resolution, the
proposed estimator outperforms the MUSIC algorithm if the maximum allowed AOA
estimation error is approximately equal to (or larger than) the FOV resolution.
