Deep learning method clusters multi-view data matrices.
problem Clustering heterogeneous relational data matrices.
method Deep collective matrix tri-factorization (DCMTF).
result Discover latent clusters across input matrices and their associations.
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48 results for “collective matrix factorization”
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank structure, wherein each component matrix is low rank and the latent space of th…
Multi-way Clustering and Discordance Analysis through Deep Collective Matrix Tri-Factorizationstat.ML
Advances neural tri-factorization for clustering and discordance analysis of multi-typed data.
problem Challenges in analyzing heterogeneous, multimodal relational data.
method Deep collective matrix tri-factorization for spectral clustering and cluster association learning.
result Demonstrates efficacy over previous non-neural approaches in clustering and discordance analysis.
dCMF learns shared latent representations from multiple matrices, improving predictive modeling.
problem Learning from multiple heterogeneous data sources, especially non-linear interactions.
method Develops a deep-learning based method (dCMF) for unsupervised learning of multiple shared representations.
result dCMF significantly outperforms previous CMF algorithms in integrating heterogeneous data.
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), -means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. W…
This paper analyzes privacy threats in federated matrix factorization.
problem Privacy threats in federated matrix factorization models.
method Categorizes federated matrix factorization into three types and analyzes privacy threats.
result This is the first study of privacy threats in federated matrix factorization.
A Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizationsmath.OC
An algorithm for computing positive semidefinite factorizations of matrices.
problem Computing positive semidefinite factorizations of matrices.
method Non-commutative extension of Lee-Seung's algorithm (Matrix Multiplicative Update, MMU).
result The MMU algorithm ensures PSD updates and achieves critical points.
This work explores the ability of collective matrix factorization models in recommender systems to make predictions about users and items for which there is side information available but no feedback or interactions data, and proposes a new formulation with a faster cold-start prediction formula that can be used in rea…
Optimal model selection for forecasting large collections of short time series using latent space.
problem Challenges in choosing among multiple forecasting methods for large, high-dimensional time series with limited data.
method Combining low-rank temporal matrix factorization with optimal model selection using cross-validation.
result Forecasting latent factors leads to significant performance gains compared to direct uni-variate model application.
Proposes CC-NMDF for analyzing manifold-valued data.
problem Nonlinear structure in manifold-valued data requires new analysis methods.
method Curvature-corrected nonnegative manifold data factorization (CC-NMDF) with an iterative algorithm.
result Demonstrates CC-NMDF on real-world diffusion tensor MRI data.
Paper introduces SMM for forecasting multiple time series with missing values.
problem Forecasting multiple time series with missing and noisy values.
method Sliding Mask Method (SMM) using Non-negative Matrix Factorization (NMF).
result The method outperforms state-of-the-art methods in time series forecasting.
A new multi-view clustering method using deep matrix decomposition and partition alignment.
problem Improving multi-view clustering methods to better utilize data representations and view-specific structures.
method Deep matrix decomposition for partition representations, joint use of partition representations, and alternating optimization.
result Demonstrated effectiveness on six benchmark datasets compared to state-of-the-art methods.
NoTMF forecasts sparse urban road movement speeds with nonstationary temporal matrix factorization.
problem Sparse and nonstationary movement speed data from urban roads.
method Nonstationary Temporal Matrix Factorization (NoTMF) model.
result NoTMF outperforms baseline models in forecasting urban road movement speeds.
Study active learning for multi-level user preferences in recommendation systems.
problem Efficiently learning user preferences through active querying in recommendation systems.
method Proposes a theoretically optimal active learning strategy based on Fisher information matrix for collective matrix factorization.
result Demonstrates strong improvements over active learning methods in personalized, cold-start, and noisy data settings.
Modeling dynamic user interests using neural matrix factorization.
problem Challenging extraction of valuable insights from unstructured, high-dimensional, and dynamic online content data.
method Combines matrix factorization with neural networks to model nonlinear user and content factors.
result Accurately identifies nuanced and coherent consumption patterns of Boston Globe readers over five years.
Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matricescond-mat.stat-mech
Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite fraction of all pairs of elements. The coexistence of an eigenvalue spectrum predic…
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the collection. Recently, "self expression", the idea of using a small subset of data vect…
Nonnegative matrix factorization (NMF) has attracted much attention in the last decade as a dimension reduction method in many applications. Due to the explosion in the size of data, naturally the samples are collected and stored distributively in local computational nodes. Thus, there is a growing need to develop algo…
For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data fusion. Fusion can focus on a specific target relation and exploit directly ass…
Regular medical records are useful for medical practitioners to analyze and monitor patient health status especially for those with chronic disease, but such records are usually incomplete due to unpunctuality and absence of patients. In order to resolve the missing data problem over time, tensor-based model is suggest…
Emergency Department (ED) crowding is a worldwide issue that affects the efficiency of hospital management and the quality of patient care. This occurs when the request for an admit ward-bed to receive a patient is delayed until an admission decision is made by a doctor. To reduce the overcrowding and waiting time of E…
New PSDMF algorithms derived from PR and ARM methods.
problem Positive semidefinite matrix factorization (PSDMF) challenges.
method Design PSDMF algorithms based on phase retrieval (PR) and affine rank minimization (ARM) methods.
result New PSDMF algorithms inherit numerical properties from PR and ARM methods.
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new cha…
NMF identifies hidden component processes from thermal manufacturing data.
problem Thermal manufacturing processes with many interacting parameters are hard to diagnose.
method Non-negative matrix factorization guided by a knowledge-based initialization strategy.
result Identifies physical meaningful sources from temperature time series.
A network-based approach identifies financial factors from asset interactions, explaining market dynamics.
problem Characterizing joint financial asset behavior through underlying drivers.
method Modeling market as coupled iterated maps, where asset returns depend on past returns and interactions.
result Stable patterns of co-movement (financial factors) emerge from asset interactions, explaining asset variance.
The paper develops new algorithms for KL-divergence NMF, proving convergence and performance.
problem Improving NMF for nonnegative data with KL divergence.
method Collect and analyze properties of KL objective function, propose and test new algorithms.
result Guaranteed non-increasing objective function for one proposed algorithm, global convergence.
DaConA improves recommendation accuracy with auxiliary data by adapting to different data contexts.
problem Improving recommendation accuracy with auxiliary data considering different data contexts.
method Data context adaptation layer, latent interaction vector, latent independence vector, non-linear function.
result DaConA achieves state-of-the-art accuracy on real-world datasets.
Study discovers patterns in insulin needs for T1D patients.
problem Finding the right insulin dose and time for T1D patients is challenging.
method Used OpenAPS Data Commons dataset and time series techniques like matrix profile and multi-variate clustering.
result Identified temporal patterns in insulin needs driven by factors like carbohydrates and possibly others.
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…
The task of dialog management is commonly decomposed into two sequential subtasks: dialog state tracking and dialog policy learning. In an end-to-end dialog system, the aim of dialog state tracking is to accurately estimate the true dialog state from noisy observations produced by the speech recognition and the natural…
dCMF models evolving patterns in multiway data with temporal dynamics.
problem Capturing evolving patterns in multiway datasets with temporal dependencies.
method Time-aware coupled factorization model constrained by LDS structure.
result dCMF outperforms alternatives in capturing complex dynamics.
Proposes MVMC for multi-view clustering, enhancing diversity and quality.
problem Leveraging multi-view data for diverse clustering.
method Adapts multi-view self-representation learning, HSIC for redundancy reduction, matrix factorization.
result Generates multiple high-quality and diverse clusterings from multi-view data.
D-GCCA improves multi-view data analysis by separating common and distinctive components.
problem Analyzing multi-view high-dimensional data with latent factors.
method Decomposes each view's data matrix into common and distinctive sources with orthogonality constraints.
result Consistent estimators with good performance and efficient computation.
Develops deep NMF models using β-divergences for feature extraction.
problem Inadequate evaluation metrics for deep NMF on diverse datasets.
method Introduces new deep NMF models using Kullback-Leibler divergence.
result Improves feature extraction quality across different types of data.
Collective Matrix Completionstat.ML
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources whic…
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing a class of nonparametric covariance regression models, which allow an unknown p …
Sparse NMF with archetypal regularization aims to robustly represent data points.
problem Representing data points as sparse linear combinations of archetypes.
method Sparse NMF with archetypal regularization, introducing strong and weak robustness.
result Theoretical robustness guarantees hold under minimal assumptions.
New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.
Efficient Discrete Supervised Hashing improves cross-modal retrieval by preserving semantic correlations and reducing quantization error.
problem Challenges in preserving semantic correlations and reducing quantization error in cross-modal hashing for large-scale retrieval.
method Collective matrix factorization on heterogenous features and semantic embedding with class labels to learn hash codes efficiently.
result EDSH produces superior performance in both accuracy and scalability over existing methods.
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country took action toward country at time "---known as dyadic events---in order to form an…
Muon optimizer simplifies matrix optimization with spectral orthogonalization.
problem Matrix optimization challenges, especially with large condition numbers.
method Simplified Muon optimizer using spectral orthogonalization of gradients.
result Simplified Muon converges linearly with independent scalar sequences, outperforming gradient descent and Adam.
Gradient descent proves global convergence for 4-layer matrix factorization.
problem Global convergence of gradient descent on four-layer matrix factorization under random initialization.
method New techniques to show saddle-avoidance properties and extend eigenvalue theories.
result Polynomial-time global convergence guarantee for randomly initialized gradient descent on four-layer matrix factorization.
Unified framework for nonconvex matrix completion with linearly parameterized factors.
problem Matrix completion with improved accuracy using linearly parameterized factors.
method Unified nonconvex optimization framework with Correlated Parametric Factorization condition.
result Uniform upper bounds for low-rank estimation at any local minimum.
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…
Proposes a robust factor analysis for matrix data.
problem Robust factor analysis for matrix data with heavy-tailed or contaminated data.
method Bilinear factor analysis based on the matrix-variate distribution.
result Significantly higher breakdown point than traditional methods.
In this work, we empirically explore the question: how can we assess the quality of samples from some target distribution? We assume that the samples are provided by some valid Monte Carlo procedure, so we are guaranteed that the collection of samples will asymptotically approximate the true distribution. Most current …
Cluster analysis is a field of data analysis that extracts underlying patterns in data. One application of cluster analysis is in text-mining, the analysis of large collections of text to find similarities between documents. We used a collection of about 30,000 tweets extracted from Twitter just before the World Cup st…
Federated multi-view matrix factorization learns from multiple data sources without centralizing user data.
problem Cold-start federated recommendations and multi-view data structure.
method Federated learning framework extended to multi-view matrix factorization.
result Federated multi-view matrix factorization outperforms simpler methods in cold-start federated recommendations.