Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. …
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48 results for “matrix pairs”
Explicit matrix presentations of Blanchfield pairings and twisted pairings for torus knots.
problem Computing explicit matrix presentations of Blanchfield and twisted Blanchfield pairings for torus knots.
method Using a taut identity to construct a chain complex with few generators, and describing the twisted Alexander module.
result Explicit matrix presentations of the Blanchfield pairing and twisted pairings for -torus knots.
Study of twisted Alexander matrices for certain quandles and their invariants.
problem Investigate -twisted Alexander matrices for quandles associated with Alexander pairs.
method Define and analyze -twisted Alexander matrices of certain quandles, relate to Carter-Saito-Satoh's invariant, and discuss connections to quandle homology groups.
result 0-th elementary ideal of -twisted Alexander matrix can be described using Carter-Saito-Satoh's invariant.
A new tool, matrix profile, finds all pair similarities in time series data.
problem Finding all pair similarities in time series data.
method Near universal time series data mining tool called matrix profile.
result Matrix profile solves the all-pairs-similarity-search problem for time series subsequences.
Calculates Blanchfield pairings for 3-manifolds and knots.
problem Calculating Blanchfield pairings for 3-manifolds and knots.
method Formula derivation for fibred 3-manifolds and proof using Seifert matrices.
result New proof and formula for knot Blanchfield pairings.
Study on Gaussian ensemble of matrix products with mixed moments computed.
problem Understanding the statistical properties of matrix products of Gaussian matrices.
method Analysis of a multi-Wishart ensemble and enumeration of non-crossing pairings.
result Mixed moments of the product matrix are computed and found to be weighted by Fuss-Catalan numbers at large .
SL2MF predicts synthetic lethality using logistic matrix factorization.
problem Predicting synthetic lethality in human cancers from limited experimental data.
method Logistic matrix factorization incorporating biological knowledge.
result SL2MF effectively predicts known and unknown SL interactions.
Study Alexander matrices for link quandles and their relation to knot invariants.
problem Understanding Alexander matrices for link quandles and their applications to knot invariants.
method Investigate -twisted Alexander matrices and their connection to quandle cocycle invariants.
result Show that -twisted Alexander invariants of knot quandles are stronger than those of knot groups.
Recently Kearton showed that any Seifert matrix of a knot is S--equivalent to the Seifert matrix of a prime knot. We show in this note that such a matrix is in fact S--equivalent to the Seifert matrix of a hyperbolic knot. This result follows from reinterpreting this problem in terms of Blanchfield pairings and by appl…
Paper solves NP-hard haplotyping problem using matrix completion.
problem Reconstructing inherited genetic variations from DNA sequencing data.
method Binary matrix factorization and alternating minimization.
result The proposed technique achieves lower haplotype reconstruction error.
Study symplectic spinors and Frobenius structures on manifolds.
problem Understanding Frobenius structures and symplectic spectral invariants.
method Analyzing Hamiltonian mappings and metaplectic structures on symplectic manifolds.
result Derives Hopf-algebra-type structures and matrix factorizations for Frobenius structures.
The paper defines matrices related to cluster transformations and proves certain quivers have no maximal sequences.
problem Proving quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.
method Defining matrices related to cluster transformations and showing their relationships to the Jacobian and C-matrix.
result Quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.
Preconditioned SGD accelerates convergence for ill-conditioned huge-scale matrix completion.
problem Recovering a low-rank matrix from incomplete data with high condition number.
method Preconditioned Stochastic Gradient Descent (SGD) for huge-scale online optimization.
result Preconditioned SGD converges to ε-accuracy in O(log(1/ε)) iterations, compared to O(κlog(1/ε)) for unpreconditioned SGD.
CDP reduces point cloud dimensions by preserving detour-induced local non-convexity.
problem Preserving local non-convexity in point cloud dimensionality reduction.
method CDP builds a k-NN graph, identifies admissible pairs, aggregates normalized directions, and uses top-k eigenvectors for projection.
result CDP provides verifiable guarantees on post-projection distortion and direction energy.
A Summary Of The Kernel Matrix, And How To Learn It Effectively Using Semidefinite Programmingstat.ML
This study simplifies learning kernel matrices for SVMs.
problem Learning distances between unlabeled pairs in partially labeled datasets.
method Semidefinite programming to optimize kernel matrices.
result Improved understanding of kernel matrix learning.
Characterizes the OU matrix for up to 5 strands in braids.
problem Understanding the structure of braid diagrams through their matrices.
method Characterization of the OU matrix for up to 5 strands in braids.
result Standard form of the OU matrix for general braids of up to 5 strands is given and characterized.
Innovates rotation index for matrix pairs, solving group action problems.
problem Solving group actions problems, especially Nielsen realization and higher-rank Anosov actions.
method Rotation index and Milnor--Munkres--Novikov pairing applied to group actions.
result Solved specific group action problems using new matrix pair invariant.
Calculates Gordian distances using algebraic methods.
problem Determining when Alexander polynomials can't be realized by matrices with Gordian distance one.
method Using Blanchfield pairings and quadratic equations with integer solutions.
result Shows that certain Alexander polynomials cannot be realized by matrices with Gordian distance one.
Characterizes conjugacy classes of pairs in SU(3,1) using symmetry.
problem Classifying conjugacy classes of pairs of matrices in SU(3,1).
method Minimal global coordinate system on SL(4,C)-character variety, symmetry analysis.
result 22 coordinates subject to 5 relations determine conjugacy classes.
Bonnet surfaces' equations link to Painlevé sixth equation.
problem Understanding Bonnet surfaces and Painlevé equations.
method Moving frame equations of Bonnet surfaces and Lax pair construction.
result Moving frame equations of Bonnet surfaces lead to a Lax pair for the sixth Painlevé equation.
Abstract: New invariants for links and three-manifolds from finite groups.
problem Creating invariants for links and three-manifolds.
method Using finite groups to define matrices and extended matrices, constructing invariants through colored tangle categories.
result Invariants for links and three-manifolds are group invariants.
New algorithms for efficient matrix profile computation using various Euclidean distances.
problem Efficiently computing matrix profile for all-pairs-similarity search on time series.
method Proposed AAMP, ACAMP, and extended algorithms for p-norm distance.
result AAMP and ACAMP algorithms outperform existing methods for specific Euclidean distances.
Paper defines a new braid invariant and shows it's commutative.
problem Understanding the structure of braids and their invariants.
method Defining purified determinant and analyzing crossing matrices.
result The purified determinant is commutative for any pair of braids.
Cobordism of disk knotsmath.GT
We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots $D^{n-2}\into D^n$. Cobordisms of disk knots that do not fix the boundary sphere knots are easily classified by the cobordism properties of these boundaries, and any two even-dimensional disk knots with isotopic boundary knots are cobordant r…
This article investigates the correlation structure of the global crude oil market using the daily returns of 71 oil price time series across the world from 1992 to 2012. We identify from the correlation matrix six clusters of time series exhibiting evident geographical traits, which supports Weiner's (1991) regionaliz…
New method clusters tasks for deep learning to improve multi-task and few-shot learning.
problem Uncertainty and asymmetry in task similarity matrices affect clustering accuracy.
method Proposes a matrix completion technique to overcome limitations of task similarity matrices.
result The proposed algorithm can accurately recover task clusters with high probability.
New approach speeds up DNA sequence alignment.
problem Efficiently estimating alignment scores for large sets of reads.
method Rank-one crowdsourcing models and multi-armed bandit algorithm.
result Adaptive algorithm identifies pairs with large alignment scores.
We show that the Lawrence--Krammer representation is unitary. We explicitly present the non-singular matrix representing the sesquilinear pairing invariant under the action. We show that reversing the orientation of a braid is equivalent to the transposition of its Lawrence--Krammer matrix followed by a certain conjuga…
IGMC learns inductive matrix completion without side info.
problem Inductive matrix completion without side information.
method Graph Neural Network (GNN) trained on 1-hop subgraphs of the rating matrix.
result Achieves competitive performance with state-of-the-art transductive baselines.
E2Efold predicts RNA secondary structures better than previous methods.
problem RNA secondary structure prediction with constraints.
method End-to-end deep learning model using unrolled algorithms to enforce constraints.
result E2Efold predicts significantly better structures, especially for pseudoknotted structures.
Efficiently trains large corpora models without sampling.
problem Training neural network embedding models on very large corpora using SGD is expensive.
method Proposes new methods to train models without sampling unobserved pairs, using Gramian estimation and variance reduction schemes.
result Significant improvement in training time and generalization quality compared to traditional methods.
We define a notion of facets-pairing structure and its seal space on a nice manifold with corners. We will study facets-pairing structures on any cube in detail and investigate when the seal space of a facets-pairing structure on a cube is a closed manifold. In particular, for any binary square matrix with zero dia…
In this paper we consider the Poisson algebraic structure associated with a classical -matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the -matrix type Poisson orbits. Then we describe the -matrix Poisson pencil (i.e the pair o…
Proposes a method to classify with matrix-valued predictors using penalized likelihood.
problem Classification with matrix-valued predictors.
method Penalized likelihood method with Kronecker product decomposition for precision matrix estimation.
result Outperforms competitors in classification accuracy, even when assumptions are violated.
In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and we also decompose the Chern character of the index bundle for a fi…
New model predicts drug effects across various cell types using causal imputation.
problem Predict drug effects across different cell types given limited data.
method Introduces a novel SCM-based model class with latent factor structure and uses Synthetic Interventions estimator.
result Method outperforms other matrix completion approaches in drug repurposing dataset.
Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, an…
The paper proposes a model to learn motion perception in V1 using vector and matrix representations.
problem Motion perception in primary visual cortex (V1).
method Coupling vector representations of local contents and matrix representations of local pixel displacements.
result The model can learn Gabor-like filter pairs and infer local motions.
New model for clustering dependent community Hawkes processes in temporal networks.
problem Modeling strong dependence and community structure in temporal networks.
method Dependent Community Hawkes (DCH) models combining stochastic block models and Hawkes processes.
result Spectral clustering error bound derived for DCH models.
This paper studies the minimum number of queries needed to cluster elements with side information.
problem Query complexity of interactive clustering with side information.
method Information-theoretic lower bounds and nearly matching upper bounds.
result Side information reduces query complexity from to $O(\frac{k^2\log{n}}{\cH^2(f_+\|f_-)})$.
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix map…
Paper proposes neural networks for fundamental matrix estimation without key-point correspondences.
problem Estimating fundamental matrices from noisy and unreliable key-point correspondences.
method End-to-end neural network architectures preserving fundamental matrix properties.
result Neural networks achieve competitive performance on the KITTI dataset without correspondences.
New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
problem Discount regularization leads to poor performance in unevenly sampled data.
method Equivalence theorem showing discount regularization as a strong prior, setting regularization parameters locally for individual state-action pairs.
result Discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
A new metric for uncertainty quantification using class collisions.
problem Fine-grained uncertainty quantification in classification problems.
method Introducing the collision matrix and estimating it from one-hot labeled data.
result The collision matrix uniquely recovers the posterior class probability distribution.
Learning Embedded Representation of the Stock Correlation Matrix using Graph Machine Learningq-fin.CP
Algorithm learns stock correlation matrix embedding using graph machine learning.
problem Understanding complex relationships among stocks based on their correlation matrix.
method Proposes a graph machine learning approach called Node2Vec to compress the correlation network into an embedding.
result The algorithm can learn an embedding from the correlation network of S&P 500 stock data.
MoDeGPT compresses large language models without accuracy loss, saving 98% compute costs.
problem Compression of large language models for resource-constrained devices.
method Structured compression framework using modular decomposition and matrix pair reduction.
result MoDeGPT achieves 90-95% zero-shot performance with 25-30% compression rates.
Let be a vector space and be a pair of Lie brackets on . By definition they are compatible if is again a Lie bracket. Such pairs play important role in bihamiltonian and -matrix formalisms in the theory of integrable systems. We propose an approach to a long standin…
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
problem Community recovery in multilayer hypergraphs using aggregated similarity matrices.
method Semidefinite programming (SDP) approach.
result Information-theoretic conditions for exact recovery in both assortative and disassortative cases.