A1923
Title: High-dimensional factor and clustering analysis via projected and truncated sample covariance matrix
Authors: Long Yu - Shanghai University of Finance and Economics (China) [presenting]
Abstract: Spike identification in high-dimensional mixture factor models is addressed, where spiked eigenvalues arising from cluster-mean differences may be comparable in size to those from latent common factors. This overlap poses a significant challenge to existing methods. A novel projected and truncated sample covariance matrix is introduced, which, with suitable thresholding, consistently recovers the factor loading space regardless of the relative strength of the factor-driven eigenvalues. Importantly, this consistency holds even when the subspaces induced by the factor structure and the cluster means are partially confounded. Given the estimated factor space, a projected spectral clustering procedure is proposed that removes the factor component to reveal the underlying cluster structure. Furthermore, an iterative refinement algorithm is developed that builds upon these steps to enhance estimation accuracy. All proposed methods are supported by rigorous theoretical guarantees and validated through extensive simulations and real data analysis.
