The Structure Transfer Machine Theory and Applications

Representation learning is a fundamental but challenging problem, especially when the distribution of data is unknown. We propose a new representation learning method, termed Structure Transfer Machine (STM), which enables feature learning process to converge at the representation expectation in a probabilistic way. We theoretically show that such an expected value of the representation (mean) is achievable if the manifold structure can be transferred from the data space to the feature space. The resulting structure regularization term, named manifold loss, is incorporated into the loss function of the typical deep learning pipeline. The STM architecture is constructed to enforce the learned deep representation to satisfy the intrinsic manifold structure from the data, which results in robust features that suit various application scenarios, such as digit recognition, image classification and object tracking. Compared to state-of-the-art CNN architectures, we achieve the better results on several commonly used benchmarks\footnote{The source code is available. https://github.com/stmstmstm/stm }

A study of the classification of low-dimensional data with supervised manifold learning

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalization performance is that the embedding allow the construction of a sufficiently regular interpolation function in relation with the separation margin of the embedding. We show that for supervised embeddings satisfying this condition, the classification error decays at an exponential rate with the number of training samples. Finally, we examine the separability of supervised nonlinear embeddings that aim to preserve the low-dimensional geometric structure of data based on graph representations. The proposed analysis is supported by experiments on several real data sets