Related papers: Principal Decomposition with Nested Submanifolds
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs)…
We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…
Suppose we observe data of the form $Y_i = D_i (S_i + \varepsilon_i) \in \mathbb{R}^p$ or $Y_i = D_i S_i + \varepsilon_i \in \mathbb{R}^p$, $i=1,\ldots,n$, where $D_i \in \mathbb{R}^{p\times p}$ are known diagonal matrices, $\varepsilon_i$…
Disentangling complex data to its latent factors of variation is a fundamental task in representation learning. Existing work on sequential disentanglement mostly provides two factor representations, i.e., it separates the data to…
Learning disentangled representations of data is a fundamental problem in artificial intelligence. Specifically, disentangled latent representations allow generative models to control and compose the disentangled factors in the synthesis…
Personalized treatment of patients based on tissue-specific cancer subtypes has strongly increased the efficacy of the chosen therapies. Even though the amount of data measured for cancer patients has increased over the last years, most…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…
We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension. Our technique consists of partitioning the space into simplices and then embedding the data points…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
We propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It includes principal component analysis and principal curve…
In recent years, deep learning-based image compression, particularly through generative models, has emerged as a pivotal area of research. Despite significant advancements, challenges such as diminished sharpness and quality in…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…
We consider the problem of developing interpretable and computationally efficient matrix decomposition methods for matrices whose entries have bounded support. Such matrices are found in large-scale DNA methylation studies and many other…
Learning efficient representations of local features is a key challenge in feature volume-based 3D neural mapping, especially in large-scale environments. In this paper, we introduce Decomposition-based Neural Mapping (DNMap), a…
Data classification techniques partition the data or feature space into smaller sub-spaces, each corresponding to a specific class. To classify into subspaces, physical features e.g., distance and distributions are utilized. This approach…
Very deep convolutional neural networks (CNNs) have been firmly established as the primary methods for many computer vision tasks. However, most state-of-the-art CNNs are large, which results in high inference latency. Recently, depth-wise…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…