Label-free cell analysis is essential to personalized genomics, cancer diagnostics, and drug development as it avoids adverse effects of staining reagents on cellular viability and cell signaling. However, currently available label-free cell assays mostly rely only on a single feature and lack accuracy. Also, the sample size analyzed by these assays is limited due to their low throughput. We have integrated feature extraction and deep learning with high-throughput quantitative phase imaging enabled by photonic time stretch, achieving record high accuracy in label-free blood cell classification. Our system captures quantitative phase and intensity images and extracts 16 biophysical features from each cell. These biophysical measurements form a hyperdimensional feature space in which supervised learning is performed for cell classification. We show classification of white blood T-cells against colon cancer cells, as well as lipid accumulating algal strains for biofuel production. This system opens up a new path to data-driven phenotypic diagnosis and better understanding of the heterogeneous gene expressions in cells.