We perform multi-class classification of LIBS spectroscopy data of four proteins: Bovine Serum Albumin (the most abundant protein in blood plasma), Osteopontin, Leptin and Insulin-like Growth Factor II (potential biomarkers for ovarian cancer). Principal Component Analysis (PCA) is applied on the data as a feature extraction technique to select features that both are easy to compute and preserve useful discriminatory information for the classification algorithms. Classification of these proteins is performed using five classification techniques: K-nearest neighbor, classification and regression trees (CART), neural networks, support vector machines (SVMs), and adaptive local hyperplane (ALH). The aim is to show that this methodology can lead to separable classes of complex proteins in higher dimensional feature space which can result in automatic classification achieving high classification accuracy. Automatic classification of these complex proteins can lead to identification of elemental fingerprints of biological and chemical components that are vital in the detection of certain diseases (i.e. ovarian cancer). Our approach demonstrates that highly accurate automatic classification of complex protein samples is possible on laser-induced breakdown spectroscopy (LIBS) data, using principal component analysis (PCA) with sufficiently large number of extracted features and appropriate machine learning classification techniques.