Electronic density of states (DOS) is a key factor in condensed matter physics and material science that determines the properties of metals. First-principles density-functional theory (DFT) calculations have typically been used to obtain the DOS despite the considerable computation cost. Herein, we report a fast machine learning method for predicting the DOS patterns of not only bulk structures but also surface structures in multi-component alloy systems by a principal component analysis. Within this framework, we use only four features to define the composition, atomic structure, and surfaces of alloys, which are the d-orbital occupation ratio, coordination number, mixing factor, and the inverse of miller indices. While the DFT method scales as O(N3) in which N is the number of electrons in the system size, our pattern learning method can be independent on the number of electrons. Furthermore, our method provides a pattern similarity of 91 ~ 98% compared to DFT calculations. This reveals that our learning method will be an alternative that can break the trade-off relationship between accuracy and speed that is well known in the field of electronic structure calculations.