Background and Objectives: Identifying risk factors associated with psychiatrist-confirmed anxiety and depression among young lung cancer patients is very difficult because the incidence and prevalence rates are obviously lower than in middle-aged or elderly patients. Due to the nature of these rare events, logistic regression may not successfully identify risk factors. Therefore, this study aimed to propose a novel algorithm for solving this problem. Materials and Methods: A total of 1022 young lung cancer patients (aged 20–39 years) were selected from the National Health Insurance Research Database in Taiwan. A novel algorithm that incorporated a k-means clustering method with v-fold cross-validation into multiple correspondence analyses was proposed to optimally determine the risk factors associated with the depression and anxiety of young lung cancer patients. Results: Five clusters were optimally determined by the novel algorithm proposed in this study. Conclusions: The novel Multiple Correspondence Analysis–k-means (MCA–k-means) clustering algorithm in this study successfully identified risk factors associated with anxiety and depression, which are considered rare events in young patients with lung cancer. The clinical implications of this study suggest that psychiatrists need to be involved at the early stage of initial diagnose with lung cancer for young patients and provide adequate prescriptions of antipsychotic medications for young patients with lung cancer.