arXiv research

Paper proposes a new method to improve clustering ensemble performance.

In this paper, we solve a semi-supervised regression problem. Due to the lack of knowledge about the data structure and the presence of random noise, the considered data model is uncertain. We propose a method which combines graph Laplacian regularization and cluster ensemble methodologies. The co-association matrix of…

We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.

Solves weakly supervised regression using low-rank approximations and manifold regularization.

Study $SO(3)$-invariant $G_2$-cobordisms on 6-manifolds.

We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds. As a TQFT, in relative situations, we have the Fukaya-Floer category of Lagrangians intersection in the moduli space of special Lagrangian submanifolds in CY threefo…

By analogy with associative and co-associative cases we introduce a class of three-dimensional non-orientable submanifolds, of almost $\mathrm{G}_2-$manifolds, modelled on planes lying in a special $\mathrm{G}_2-$orbit. An application of the Cartan-Kähler theory shows that some three-manifold can be presented in this w…

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees, or depend heavily on their initialization. We present a novel …

Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of the existing algorithms tend to investigate the ensemble information at the obje…

This article studies the geometry of moduli spaces of G2-manifolds, associative cycles, coassociative cycles and deformed Donaldson-Thomas bundles. We introduce natural symmetric cubic tensors and differential forms on these moduli spaces. They correspond to Yukawa couplings and correlation functions in M-theory. We ex…

Given a parallel calibration $φ\in Ω^p(M)$ on a Riemannian manifold $M$, I prove that the $φ$--critical submanifolds with nonzero critical value are minimal submanifolds. I also show that the $φ$--critical submanifolds are precisely the integral manifolds of a $\mathscr{C}^\infty(M)$--linear subspace $\sP \subset Ω^p(M…

We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an orientation with respect to the corresponding normed algebra A. For example, special Riema…

Imaging genetic research has essentially focused on discovering unique and co-association effects, but typically ignoring to identify outliers or atypical objects in genetic as well as non-genetics variables. Identifying significant outliers is an essential and challenging issue for imaging genetics and multiple source…

The paper examines properties of deformed Donaldson-Thomas connections on G2-manifolds.

The paper studies deformations of calibrated subbundles in special holonomy manifolds.

The paper studies deformations of Hermitian Yang-Mills and Donaldson-Thomas connections on $G_2$-manifolds.

Defines a volume functional for Hermitian connections on manifolds, proving its properties and connections.

DeepTMR reorders matrices without prior knowledge of structural patterns.

Paper speeds up matrix multiplication on Intel PIII using SIMD.

The paper constructs Goeritz matrices from Dehn colorings.

New matrix reveals cluster info in sparse directed graphs.

The CN matrix of a pure braid projection is characterized and applied.

Characterizes the OU matrix for up to 5 strands in braids.

Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.

Unified approach for robust low rank matrix estimation with adversaries.

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the…

A new algorithm speeds up matrix operations in Neural Networks.

New NMF algorithm uses Toeplitz matrix for facial recognition.

Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of rati…

The paper defines the OU matrix for braid diagrams and finds determinant relationships.

New method improves robust low-rank matrix completion for computer vision.

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study ma…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…

Unified framework for nonconvex matrix completion with linearly parameterized factors.

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a W…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…

Proposes a robust factor analysis for matrix data.

3-manifold triangulation can be reconstructed from its intersection matrix.

We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix. To the best of our knowledge, all previous algorithms either incurred a quadrat…

Paper presents a new framework for covariance matrix estimation with geometric insights.

Study improves fractional posterior for 1-bit matrix completion.

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…

Incorporates matrix exponential into generative flows for improved performance.

In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective funct…

Matrix SMD converges to unique solution minimizing Bregman divergence.

Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.

Proposes a new matrix factorization model for interval-valued matrices.

Gradient descent proves global convergence for 4-layer matrix factorization.