Within this study, we propose a novel unsupervised representation learning method, harnessing quasiconformal extension, designed for structured data with continuous values. Developing feature representations that substantially enhance predictive performance is crucial, irrespective of the approach being implicit or explicit. Herein, aiming to generate features that contribute to prediction, we extend the feature space using piecewise linear mappings obtained from the relationship between the distribution of each feature and the uniform distribution, via quasiconformal extension, in an unsupervised manner. Quasiconformal extension extends a mapping to a higher dimensional space, having a certain regularity throughout. In experiments conducted across fifteen distinct datasets, our approach improved the performance of neural networks, extremely randomized trees, and support vector machines in both classification and regression tasks, provided that the features contained a sufficient level of information necessary. Furthermore, we apply the proposed method to semi-supervised outlier detection. Specifically, after extending the data’s feature space using our method, we learn the distribution of extended outlier data by generative adversarial networks. By sampling new data from this distribution, we augment the extended outlier data and apply gradient boosting for detection. Experiments with five outlier datasets have confirmed that extended data enhances the performance of outlier detection.