Carbon-based black pigments, a widely used class of pigments, are difficult to differentiate with the noninvasive techniques currently used in cultural heritage science. We use pump-probe microscopy, coupled with a support vector machine, to distinguish common carbon-based black pigments as pure pigments, as two-component black pigment mixtures, and as a mixture of a black and a colorful pigment. This work showcases the potential of pump-probe microscopy to spatially differentiate carbon-based black pigments, which would have interesting applications to works of art.