Direction of arrival estimation using the spherical microphone array usually requires a search in the whole 3-dimensional space, hence computationally demanding. This work presents a machine learning approach to sectorizing the 3-dimensional space, as an intermediate step for direction-of-arrival estimation using spherical microphone array. A new feature based on the outer product of spherical harmonic vectors was proposed for the classification. This spherical harmonic matrix nominally offers lower dimensionality compared to the commonly used covariance matrix of received data. The dimension of the input matrix was further reduced using the neighborhood component analysis. The extracted features were then used to train a support vector machine (SVM), 2-layer multilayer perceptron (MLP) and a convolutional neural network (CNN) for classification purposes. The results show that the models were able to classify the spherical sector with up to 90 % accuracy for all models and number of sectors under consideration. Also, the MLP and CNN trained with simulated samples were able to accurately classify samples from real data that were not included in training samples.