In the current era of time-domain astronomy, it is increasingly important to have rigorous, data driven models for classifying transients, including supernovae. We present the first application of Principal Component Analysis to the spectra of stripped-envelope core-collapse supernovae. We use one of the largest compiled optical datasets of stripped-envelope supernovae, containing 160 SNe and 1551 spectra. We find that the first 5 principal components capture 79% of the variance of our spectral sample, which contains the main families of stripped supernovae: Ib, IIb, Ic and broad-lined Ic. We develop a quantitative, data-driven classification method using a support vector machine, and explore stripped-envelope supernovae classification as a function of phase relative to V-band maximum light. Our classification method naturally identifies transition supernovae and supernovae with contested labels, which we discuss in detail. We find that the stripped-envelope supernovae types are most distinguishable in the later phase ranges of $10pm5$ days and $15pm5$ days relative to V-band maximum, and we discuss the implications of our findings for current and future surveys such as ZTF and LSST.
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