Advancing Joint Dimension Reduction and Clustering through Hyperparameter Tuning

Clustering high-dimensional data requires dimensionality reduction to improve performance. However, joint models that unify both tasks often rely on hyperparameter tuning, which is challenging in the absence of labels. In this work, we propose a method that transforms external metrics, such as the V-measure, into internal metrics by comparing clustering results in the reduced and original spaces. This enables unsupervised tuning of key parameters, such as dimensionality and regularization strength. We evaluate our approach on several models (DKM, DCN, RSDE) and datasets spanning image and text data. The results show that our method outperforms default settings and correlates more strongly with ground-truth-based metrics than standard internal criteria, such as silhouette or Davies-Bouldin scores. Our method offers a robust, label-free alternative for hyperparameter selection in joint dimension reduction and clustering.