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Clustering is an unsupervised learning technique widely used to group data into homogeneous clusters. For many real-world data containing categorical values, existing algorithms are often computationally costly in high dimensions, do not work well on noisy data with missing values, and rarely provide theoretical guarantees on clustering accuracy. In this thesis, we propose a general categorical data encoding method and a computationally efficient spectral based algorithm to cluster high-dimensional noisy categorical (nominal or ordinal) data. Under a statistical model for data on m attributes from n subjects in r clusters with missing probability epsilon, we show that our algorithm exactly recovers the true clusters with high probability when mn(1-epsilon) >= CMr2 log3M, with M=max(n,m) and a fixed constant C. Moreover, we show that mn(1- epsilon)2 >= r *delta/2 with 0< delta