Valérie Perrier

Hubert Leterme, Kévin Polisano, Valérie Perrier et al.

This paper focuses on improving the mathematical interpretability of convolutional neural networks (CNNs) in the context of image classification. Specifically, we tackle the instability issue arising in their first layer, which tends to learn parameters that closely resemble oriented band-pass filters when trained on datasets like ImageNet. Subsampled convolutions with such Gabor-like filters are prone to aliasing, causing sensitivity to small input shifts. In this context, we establish conditions under which the max pooling operator approximates a complex modulus, which is nearly shift invariant. We then derive a measure of shift invariance for subsampled convolutions followed by max pooling. In particular, we highlight the crucial role played by the filter's frequency and orientation in achieving stability. We experimentally validate our theory by considering a deterministic feature extractor based on the dual-tree complex wavelet packet transform, a particular case of discrete Gabor-like decomposition.

Fethi Harkat, Guillaume Gey, Valérie Perrier et al.

Traditional feature extraction and projection techniques, such as Principal Component Analysis, struggle to adequately represent X-Ray Transmission (XRT) Multi-Energy (ME) images, limiting the performance of neural networks in decision-making processes. To address this issue, we propose a method that approximates the dataset topology by constructing adjacency graphs using the Uniform Manifold Approximation and Projection. This approach captures nonlinear correlations within the data, significantly improving the performance of machine learning algorithms, particularly in processing Hyperspectral Images (HSI) from X-ray transmission spectroscopy. This technique not only preserves the global structure of the data but also enhances feature separability, leading to more accurate and robust classification results.