Deep learning models have been widely applied across various domains and industries. However, many fields still face challenges due to limited and insufficient data. This paper proposes a Feature Augmentation on Adaptive Geodesic Curve (FAAGC) method in the pre-shape space to increase data. In the pre-shape space, objects with identical shapes lie on a great circle. Thus, we project deep model representations into the pre-shape space and construct a geodesic curve, i.e., an arc of a great circle, for each class. Feature augmentation is then performed by sampling along these geodesic paths. Extensive experiments demonstrate that FAAGC improves classification accuracy under data-scarce conditions and generalizes well across various feature types.

Deep learning has yielded remarkable outcomes in various domains. However, the challenge of requiring large-scale labeled samples still persists in deep learning. Thus, data augmentation has been introduced as a critical strategy to train deep learning models. However, data augmentation suffers from information loss and poor performance in small sample environments. To overcome these drawbacks, we propose a feature augmentation method based on shape space theory, i.e., feature augmentation on Geodesic curve, called FAGC in brevity.First, we extract features from the image with the neural network model. Then, the multiple image features are projected into a pre-shape space as features. In the pre-shape space, a Geodesic curve is built to fit the features. Finally, the many generated features on the Geodesic curve are used to train the various machine learning models. The FAGC module can be seamlessly integrated with most machine learning methods. And the proposed method is simple, effective and insensitive for the small sample datasets.Several examples demonstrate that the FAGC method can greatly improve the performance of the data preprocessing model in a small sample environment.

This paper considers joint analysis of multiple functionally related structures in classification tasks. In particular, our method developed is driven by how functionally correlated brain structures vary together between autism and control groups. To do so, we devised a method based on a novel combination of (1) non-Euclidean statistics that can faithfully represent non-Euclidean data in Euclidean spaces and (2) a non-parametric integrative analysis method that can decompose multi-block Euclidean data into joint, individual, and residual structures. We find that the resulting joint structure is effective, robust, and interpretable in recognizing the underlying patterns of the joint variation of multi-block non-Euclidean data. We verified the method in classifying the structural shape data collected from cases that developed and did not develop into Autistic Spectrum Disorder (ASD).