Intrinsic dimension estimation for locally undersampled data

Identifying the minimal number of parameters needed to describe a dataset is a challenging problem known in the literature as intrinsic dimension estimation. All the existing intrinsic dimension estimators are not reliable whenever the dataset is locally undersampled, and this is at the core of the so called curse of dimensionality. Here we introduce a new intrinsic dimension estimator that leverages on simple properties of the tangent space of a manifold and extends the usual correlation integral estimator to alleviate the extreme undersampling problem. Based on this insight, we explore a multiscale generalization of the algorithm that is capable of (i) identifying multiple dimensionalities in a dataset, and (ii) providing accurate estimates of the intrinsic dimension of extremely curved manifolds. We test the method on manifolds generated from global transformations of high-contrast images, relevant for invariant object recognition and considered a challenge for state-of-the-art intrinsic dimension estimators

Online Multi-Stage Deep Architectures for Feature Extraction and Object Recognition

Multi-stage visual architectures have recently found success in achieving high classification accuracies over image datasets with large variations in pose, lighting, and scale. Inspired by techniques currently at the forefront of deep learning, such architectures are typically composed of one or more layers of preprocessing, feature encoding, and pooling to extract features from raw images. Training these components traditionally relies on large sets of patches that are extracted from a potentially large image dataset. In this context, high-dimensional feature space representations are often helpful for obtaining the best classification performances and providing a higher degree of invariance to object transformations. Large datasets with high-dimensional features complicate the implementation of visual architectures in memory constrained environments. This dissertation constructs online learning replacements for the components within a multi-stage architecture and demonstrates that the proposed replacements (namely fuzzy competitive clustering, an incremental covariance estimator, and multi-layer neural network) can offer performance competitive with their offline batch counterparts while providing a reduced memory footprint. The online nature of this solution allows for the development of a method for adjusting parameters within the architecture via stochastic gradient descent. Testing over multiple datasets shows the potential benefits of this methodology when appropriate priors on the initial parameters are unknown. Alternatives to batch based decompositions for a whitening preprocessing stage which take advantage of natural image statistics and allow simple dictionary learners to work well in the problem domain are also explored. Expansions of the architecture using additional pooling statistics and multiple layers are presented and indicate that larger codebook sizes are not the only step forward to higher classification accuracies. Experimental results from these expansions further indicate the important role of sparsity and appropriate encodings within multi-stage visual feature extraction architectures

Vibration Monitoring: Gearbox identification and faults detection

L'abstract è presente nell'allegato / the abstract is in the attachmen

Nonlocal Estimation of Manifold Structure

update for BASE on Dec 03 2018International audienceWe claim and present arguments to the effect that a large class of man-ifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality, at 1 the dimension of the true underlying manifold. This observation suggests to explore non-local manifold learning algorithms which attempt to discover shared structure in the tangent planes at different positions. A criterion for such an algorithm is proposed and experiments estimating a tangent plane prediction function are presented, showing its advantages with respect to local manifold learning algorithms: it is able to generalize very far from training data (on learning handwritten character image rotations), where a local non-parametric method fails