The randomization methods that are applied for privacy-preserving data mining are commonly subject to reconstruction, linkage, and semantic-related attacks. Some existing works employed random noise addition to realize probabilistic anonymity, aiming only at linkage attacks. Random noise addition is vulnerable to reconstruction attacks, and is unable to achieve semantic closeness, particularly on high-dimensional data, to prevent semantic-related attacks. For linkage attacks, the main security vulnerability of their proposed probabilistic anonymity lies in the assumption that the attacker had a priori knowledge of the quasi-identifiers of all individuals. When only some individuals leak their quasi-identifiers, the proposed model will become incapable, because the attacker can deploy a different linkage attack that has not been studied before. This type of attack is much easier to deploy and is thus very harmful. In this paper, we propose new frameworks of probabilistic (1, k)and (k, k)-anonymity to defend against all these linkage attacks, and realize the frameworks on a hybrid randomization model. The model is also secure against reconstruction attacks. We further achieve statistical semantic closeness of high-dimensional data to prevent semantic-related attacks on the model. The frameworks also allow us to re-design the traditional K-nearest neighbor algorithm to leverage the introduced data uncertainty and improve the mining results. This paper demonstrates the promising applications in large-scale and high-dimensional data mining in clouds, by providing high efficiency and security to protect data privacy, guaranteeing high data utility for mining purposes, on-time processing, and non-interactive data publishing