With the first direct detection of gravitational waves, the advanced laser interferometer gravitational-wave observatory (LIGO) has initiated a new field of astronomy by providing an alternative means of sensing the universe. The extreme sensitivity required to make such detections is achieved through exquisite isolation of all sensitive components of LIGO from non-gravitational-wave disturbances. Nonetheless, LIGO is still susceptible to a variety of instrumental and environmental sources of noise that contaminate the data. Of particular concern are noise features known as glitches, which are transient and non-Gaussian in their nature, and occur at a high enough rate so that accidental coincidence between the two LIGO detectors is non-negligible. Glitches come in a wide range of time-frequency-amplitude morphologies, with new morphologies appearing as the detector evolves. Since they can obscure or mimic true gravitational-wave signals, a robust characterization of glitches is paramount in the effort to achieve the gravitational-wave detection rates that are predicted by the design sensitivity of LIGO. This proves a daunting task for members of the LIGO Scientific Collaboration alone due to the sheer amount of data. In this paper we describe an innovative project that combines crowdsourcing with machine learning to aid in the challenging task of categorizing all of the glitches recorded by the LIGO detectors. Through the Zooniverse platform, we engage and recruit volunteers from the public to categorize images of time-frequency representations of glitches into pre-identified morphological classes and to discover new classes that appear as the detectors evolve. In addition, machine learning algorithms are used to categorize images after being trained on human-classified examples of the morphological classes. Leveraging the strengths of both classification methods, we create a combined method with the aim of improving the efficiency and accuracy of each individual classifier. The resulting classification and characterization should help LIGO scientists to identify causes of glitches and subsequently eliminate them from the data or the detector entirely, thereby improving the rate and accuracy of gravitational-wave observations. We demonstrate these methods using a small subset of data from LIGO's first observing run.