Designing volume visualizations showing various structures of interest is critical to the exploratory analysis of volumetric data. The last few years have witnessed dramatic advances in the use of convolutional neural networks for identification of objects in large image collections. Whereas such machine learning methods have shown superior performance in a number of applications, their direct use in volume visualization has not yet been explored. In this paper, we present a deep-learning-assisted volume visualization to depict complex structures, which are otherwise challenging for conventional approaches. A significant challenge in designing volume visualizations based on the high-dimensional deep features lies in efficiently handling the immense amount of information that deep-learning methods provide. In this paper, we present a new technique that uses spectral methods to facilitate user interactions with high-dimensional features. We also present a new deep-learning-assisted technique for hierarchically exploring a volumetric dataset. We have validated our approach on two electron microscopy volumes and one magnetic resonance imaging dataset.