A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Survey of Locally Linear Embedding and its variants.
Generative LLE modifies LLE to generate stochastic embeddings.
Non-linear Hopf manifolds can be embedded into linear ones and admit LCK metrics.
A new method simplifies HLLE for better robustness.
This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.
LLE produces unwanted results without regularization, which can be prevented with regularization.
Proves local isometric embedding of low-differentiability metrics in 3D space.
Local model for Poisson manifolds around submanifolds.
Most of existing manifold learning methods rely on Mean Squared Error (MSE) or norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image dist…
Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…
Background: Functional magnetic resonance imaging (fMRI) provides non-invasive measures of neuronal activity using an endogenous Blood Oxygenation-Level Dependent (BOLD) contrast. This article introduces a nonlinear dimensionality reduction (Locally Linear Embedding) to extract informative measures of the underlying ne…
Proposes a boundary detection method inspired by LLE for high-dimensional data.
LNPE enhances local connections in embeddings using extended neighbor propagation.
LOCA learns standardized data coordinates from measurements.
We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear equation whose type is explicitly determined by the Gaussian curvature.
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…
Locally-contextual CRFs improve sequence labeling performance.
In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each set. We show that the resulting random feature map, when used in conjunction with …
SA-REMBO adapts to nonstationary high-dimensional optimization.
A new method for creating simpler models from complex ones.
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
The paper proves local isometric embeddings for singular metrics near a point.
First explicit isometric immersion of a flat Klein bottle in 3D space.
A new method estimates rare failure events in complex systems.
The ability to characterize the color content of natural imagery is an important application of image processing. The pixel by pixel coloring of images may be viewed naturally as points in color space, and the inherent structure and distribution of these points affords a quantization, through clustering, of the color i…
New subgroups found in CAT(0) groups with exotic finiteness properties.
Study reveals how manifold geometry impacts linear regression solutions.
In this paper, we propose a semi-supervised dictionary learning method that uses both the information in labelled and unlabelled data and jointly trains a linear classifier embedded on the sparse codes. The manifold structure of the data in the sparse code space is preserved using the same approach as the Locally Linea…
The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…
The paper studies which branched covers can be lifted to braided embeddings.
The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and prediction tractable by assuming that the training label matrix is low-rank and hen…
Adding attributes for nodes to network embedding helps to improve the ability of the learned joint representation to depict features from topology and attributes simultaneously. Recent research on the joint embedding has exhibited a promising performance on a variety of tasks by jointly embedding the two spaces. Howeve…
Classifies linear embeddings of grassmannians and ind-grassmannians.
Two log-linear approximations speed up optimal transport for deep learning applications.
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as clustering similar words and inferring learning relationships, many challenges …
We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global and/or local geometric structure of a dataset. However, in practice one is often mo…
Flexible Kernels for Protein Property Prediction
LASE improves local network structure visualization by targeting locally low-dimensional regions.
Sketch-GNN reduces GNN training time and memory usage to sublinear scales.
Complex textual information extraction tasks are often posed as sequence labeling or \emph{shallow parsing}, where fields are extracted using local labels made consistent through probabilistic inference in a graphical model with constrained transitions. Recently, it has become common to locally parametrize these models…
In this article, we study local holomorphic isometric embeddings from ${\BB}^n$ into ${\BB}^{N_1}\times... \times{\BB}^{N_m}$ with respect to the normalized Bergman metrics up to conformal factors. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic m…
Adaptive framework improves nonparametric dimensionality reduction.
We present ARU, an Adaptive Recurrent Unit for streaming adaptation of deep globally trained time-series forecasting models. The ARU combines the advantages of learning complex data transformations across multiple time series from deep global models, with per-series localization offered by closed-form linear models. Un…
We demonstrate new applications of the trace embedding lemma to the study of piecewise-linear surfaces and the detection of exotic phenomena in dimension four. We provide infinitely many pairs of homeomorphic 4-manifolds and homotopy equivalent to which have smooth structures distinguished by several for…
High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the observations into a lower dimensional latent space, estimating the latent dynami…
Researchers solve a complex equation to embed graphs with negative curvature.
Notes a flaw in a proof about embedding graphs.
Topological manifolds can be embedded flatly in high-dimensional Euclidean space and are locally retracts.