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.
Novel PairNet speeds up ANN training with fast hyperparameter optimization.
Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance. Basically, it integrates multi-view information into graphs, which are then fed into sp…
A method for identifying joint and individual subspaces from multi-view data.
The study explores continuous noncrossing partitions and their relation to weighted circular factorizations.
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that…
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different p…
A new method for state space partitioning in block particle filtering reduces bias and variance.
Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the dimensionality of data points to be clustered are compressed due to constraints of measuremen…
Paper provides a performance guarantee for spectral clustering.
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the lit…
Efficiently clusters millions of data points with learnable subspace clustering.
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star, Lie derivative, pullback and interior product. Partitions of unity exist in thi…
A new model reduces noise and speeds up subspace segmentation.
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and conditional uniqueness of MSS are discussed with conditions generally satisfied…
We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds with boundary. We emphasize var…
It is proved that the isometry classes of pointed connected complete Riemannian -manifolds form a Polish space, , with the topology described by the convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifo…
We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces. While there is vast literature on heuristics for this kind of problem, such approaches are known to be susceptible to poor initializations and getting…
Abstract Morse index theorem applied to various optimization problems.
Sparse subspace clustering (SSC) is one of the current state-of-the-art methods for partitioning data points into the union of subspaces, with strong theoretical guarantees. However, it is not practical for large data sets as it requires solving a LASSO problem for each data point, where the number of variables in each…
Paper perfect clusters sparse, diverse multilayer networks.
New tree and forest methods use oblique splits for better risk bounds.
uMoE trains NNs with uncertain data by embedding uncertainty into training.
We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying (weak) symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions we defi…
Extreme multi-label classification aims to learn a classifier that annotates an instance with a relevant subset of labels from an extremely large label set. Many existing solutions embed the label matrix to a low-dimensional linear subspace, or examine the relevance of a test instance to every label via a linear scan. …
New basis for permutation equivariant layers reduces computation costs.
Paper uses SSC for identifying layers with identical community structures in DIMPLE networks.
Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there are many other applications in which only \emph{multi}-way similarity measures ar…
TrIM improves gradient-based dimension reduction and regression.
Proposes PredVAR model for reduced-dimensional dynamics from noisy data.
This paper improves spectral embedding for multipartite networks, revealing latent subspaces and providing consistent node representations.
CLSVAE repairs systematic errors in images with minimal labeled data.
Batching stabilizes risk in high-dimensional linear regression models.
Paper improves classification rates for private data.
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired behaviour through the \textit{Principle of Constant Correlations} (PCC), which constrai…
Designs an MLP from LDA for multi-Gaussian class classification.
New integrators for Lagrangian systems on homogeneous spaces derived from nonholonomic mechanics.
We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which minimise the second eigenvalue of the graph Laplacian of the projected data, whic…
In this paper, we propose a design methodology for one-class classifiers using an ensemble-of-classifiers approach. The objective is to select the best structures created during the training phase using an ensemble of spanning trees. It takes the best classifier, partitioning the area near a pattern into sub-…
We consider a continuous curve of self-adjoint Fredholm extensions of a curve of closed symmetric operators with fixed minimal domain and fixed {\it intermediate} domain . Our main example is a family of symmetric generalized operators of Dirac type on a compact manifold with boundary with varying well-posed…
The meridian maps of the full Homfly skein of the annulus are linear endomorphisms induced by the insertion of a meridian loop, with either orientation, around a diagram in the annulus. The eigenvalues of the meridian maps are known to be distinct, and are indexed by pairs of partitions of integers p and n into k and k…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…
Proposes methods for local clustering in attributed graphs.
PairNets optimize AI models for fast IoT applications.
The paper challenges the validity of cluster validity measures in unsupervised learning.
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
The study limits how many parts regular simplicial partitions can overlap.
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …