In-memory computing (IMC) is one of the most promising candidates for data-intensive computing accelerators of machine learning (ML). A key ML algorithm for dimensionality reduction and classification is the principal component analysis (PCA), which heavily relies on matrix-vector multiplications(MVM) for which classic von Neumann architectures are not optimized. Here, we provide the experimental demonstration of a new IMC-based PCA algorithm based on power iteration and deflation executed in a 4-kbit array of resistive random-access memory (RRAM). The classification accuracy of breast cancer dataset reaches 95.25%, close to floating-point implementation. Our simulations indicate a 250× improvement in energy efficiency compared to commercial graphic processing units (GPUs), thus supporting IMC for energy-efficient ML in modern data-intensive computing.