Generalized Category Discovery (GCD) aims to recognize both known and novel categories in an unlabeled dataset using labeled data with only known categories. Existing methods often struggle with noisy representations and poorly defined category boundaries, limiting novel category discovery. We propose Chaotic Sparsity Matching and Transfer (CSMT) to address these issues. CSMT selects robust prototypes with Iterative Truncated Mean, transfers knowledge via Sparsity Matching to reduce noise, and enhances learning through instance-level alignment using chaotic feature perturbations, and category-level alignment with a Margin Constraint to improve separability. Experiments on three benchmarks show that CSMT achieves state-of-the-art performance in discovering novel categories.