RULLS: Randomized Union of Locally Linear Subspaces for Feature Engineering

Feature engineering plays an important role in the success of a machine learning model. Most of the effort in training a model goes into data preparation and choosing the right representation. In this paper, we propose a robust feature engineering method, Randomized Union of Locally Linear Subspaces (RULLS). We generate sparse, non-negative, and rotation invariant features in an unsupervised fashion. RULLS aggregates features from a random union of subspaces by describing each point using globally chosen landmarks. These landmarks serve as anchor points for choosing subspaces. Our method provides a way to select features that are relevant in the neighborhood around these chosen landmarks. Distances from each data point to $k$ closest landmarks are encoded in the feature matrix. The final feature representation is a union of features from all chosen subspaces. The effectiveness of our algorithm is shown on various real-world datasets for tasks such as clustering and classification of raw data and in the presence of noise. We compare our method with existing feature generation methods. Results show a high performance of our method on both classification and clustering tasks.