Related papers: Learning to Normalize on the SPD Manifold under Bu…
Learning with symmetric positive definite (SPD) matrices has many applications in machine learning. Consequently, understanding the Riemannian geometry of SPD matrices has attracted much attention lately. A particular Riemannian geometry of…
Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the…
Batch Normalization (BN) has proven to be an effective algorithm for deep neural network training by normalizing the input to each neuron and reducing the internal covariate shift. The space of weight vectors in the BN layer can be…
In this paper, we comparatively analyze the Bures-Wasserstein (BW) geometry with the popular Affine-Invariant (AI) geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold. Our study begins with an…
In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…
Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…
Distributions of data or sensory stimuli often enjoy underlying invariances. How and to what extent those symmetries are captured by unsupervised learning methods is a relevant question in machine learning and in computational neuroscience.…
The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well…
Normalization layers are crucial for deep learning, but their Euclidean formulations are inadequate for data on manifolds. On the other hand, many Riemannian manifolds in machine learning admit gyro-structures, enabling principled…
In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…
Neuroimaging provides essential tools for characterizing brain activity by quantifying connectivity strength between remote regions, using different modalities that capture different aspects of connectivity. Yet, decoding meaningful neural…
Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…
Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…