We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by p…
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48 results for “Feature Matrix”
PSMM method optimizes matrix sufficient dimension reduction.
problem Feature matrices with row- and column-wise interpretations require efficient dimension reduction.
method PSMM method converts matrix problem into classification problems using rank-1 normal matrix.
result PSMM outperforms existing methods and provides strong interpretability.
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…
DeepTMR reorders matrices without prior knowledge of structural patterns.
problem Matrix reordering without prior structural knowledge.
method DeepTMR uses a neural network to automatically extract features and reorder matrices.
result Trained network produces denoised mean matrix for visualization.
The paper introduces a statistical distance matrix for better feature representation and clustering.
problem Lack of detailed distance representation between feature elements.
method Extended traditional statistical distance to a matrix form (statistical distance matrix) and applied hierarchical clustering.
result The statistical distance matrix with clustering (Information Mandala) provides clearer and geometrically arranged feature representations.
Random matrix theory explains how neural networks adapt to data.
problem Understanding how neural networks learn and generalize from data.
method Random matrix analysis of two-layer neural networks.
result Sharp characterization of feature spectrum and generalization error.
SC-InfoNCE improves InfoNCE for feature clustering in contrastive learning.
problem Lack of theoretical understanding of InfoNCE's feature clustering mechanism.
method Introduced a transition probability matrix to model data augmentation dynamics and optimize feature similarity.
result SC-InfoNCE achieves strong performance across diverse domains, aligning feature similarity with downstream data.
Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function-…
The paper identifies redundant columns in matrices for feature selection and clustering.
problem Identifying redundant columns in matrices for feature selection and clustering.
method Proves that after re-ordering columns, a matrix can be block-diagonalized revealing linearly dependent columns.
result Identifies redundant columns in matrices, aiding in feature selection and clustering.
Proposes a transductive matrix completion method with calibration for multi-task learning.
problem Improving multi-task learning with multiple related data sources.
method Transductive matrix completion with calibration constraint.
result The proposed algorithm recovers incomplete feature and target matrices with improved results.
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm…
A clustering algorithm uses the left Gram matrix for high dimensional data.
problem Clustering high dimensional data with many features and few objects.
method The algorithm uses the normalized left Gram matrix G = XX'/P to cluster objects based on row means.
result The algorithm provides the most accurate cluster configuration more than twice as often as competitors.
Deep MF extracts hierarchical features from large data sets.
problem Mining complex, interleaved features in large data sets.
method Deep matrix factorization models and algorithms.
result Deep MF achieves outstanding performance on unsupervised tasks.
New method normalizes matrix features for robust low-rank approximation.
problem Robust feature normalization for low-rank matrix approximation.
method Learn quantile normalization operators jointly with matrix factorization.
result Improves quality of low-rank representation of data.
Unified framework for graph coarsening using node features and graph matrices.
problem Dimensionality reduction of large graphs while preserving node features.
method Optimization-based framework that unifies graph learning and dimensionality reduction.
result The learned coarsened graph is ε-similar to the original graph, where ε is a small positive number.
New method enforces encoder sparsity in HPF for more interpretable feature selection.
problem Lack of encoder sparsity in HPF leads to lack of column-clustering property.
method Enforces encoder sparsity using a generalized additive model (GAM).
result Gains ability to perform feature selection and relates each representation to original features.
Production recommendation systems rely on embedding methods to represent various features. An impeding challenge in practice is that the large embedding matrix incurs substantial memory footprint in serving as the number of features grows over time. We propose a similarity-aware embedding matrix compression method call…
Feature missing is a serious problem in many applications, which may lead to low quality of training data and further significantly degrade the learning performance. While feature acquisition usually involves special devices or complex process, it is expensive to acquire all feature values for the whole dataset. On the…
A new method for feature selection in high-dimensional data.
problem Dealing with noise and high-dimensional data in unsupervised feature selection.
method Sparse PCA via -norm regularization, combined with an efficient optimization algorithm.
result The proposed method effectively selects features from real-world data sets.
We revisit the inductive matrix completion problem that aims to recover a rank- matrix with ambient dimension given features as the side prior information. The goal is to make use of the known features to reduce sample and computational complexities. We present and analyze a new gradient-based non-convex…
Covariance pooling is a feature pooling method with good classification accuracy. Because covariance features consist of second-order statistics, the scale of the feature elements are varied. Therefore, normalizing covariance features using a matrix square root affects the performance improvement. When pooling methods …
DMFAW improves multi-view clustering with adaptive weights and feature selection.
problem Lack of effective feature selection and empirical hyperparameter selection in existing deep matrix factorization methods.
method Introduces Deep Matrix Factorization with Adaptive Weights (DMFAW) for multi-view clustering, incorporating feature selection and dynamically updating weights using Control Theory.
result DMFAW outperforms state-of-the-art methods in clustering performance.
A new imputation method considers feature importance for missing value completion.
problem Missing values in datasets reduce accuracy and increase processing difficulty.
method Iterative matrix completion with feature importance learning.
result The method outperforms existing imputation algorithms on various datasets.
Exponentially fast SMF algorithm for multi-class classification.
problem Learning interpretable features from high-dimensional data.
method Novel framework that 'lifts' SMF as a low-rank matrix estimation problem.
result Provable exponential convergence to global minimizer under mild assumptions.
Interpretable Kernelsstat.ML
This paper makes kernels interpretable for wide feature matrices.
problem Loss of interpretability in kernel methods for wide feature matrices.
method Re-express kernel solution as a linear combination of original features with a special metric.
result Interpretable kernel solutions for wide feature matrices are possible.
Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices using the floating point Intel Pentium SIMD (Single Instruction Multiple Data) a…
Recommender systems (RS), which have been an essential part in a wide range of applications, can be formulated as a matrix completion (MC) problem. To boost the performance of MC, matrix completion with side information, called inductive matrix completion (IMC), was further proposed. In real applications, the factorize…
New model for high rank matrix completion with online and batch methods.
problem Matrix completion for high rank matrices with latent structure.
method Kernel trick to map data into a high dimensional feature space, explicit parametrization of low dimensional subspace, online fitting procedure.
result Online method can handle streaming data and adapt to non-stationary latent structure.
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired …
We analyze the condition number of random feature matrices and prove their well-conditioned nature.
problem Understanding the condition number of random feature matrices and its impact on generalization error.
method Established concentration bounds and derived risk bounds for regression problems using random feature matrices.
result The risk associated with random feature matrices exhibits the double descent phenomenon, improving even with noise.
DPERC efficiently estimates covariance matrices for mixed data with missing values.
problem Estimating covariance matrices for datasets with missing values and mixed features.
method Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC).
result DPERC outperforms other methods in estimating covariance matrices for mixed data with missing values.
AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.
problem Finding optimal node order in adjacency matrices without predefined features.
method Developed AutoLL-D and AutoLL-U neural network models for one-mode reordering of directed and undirected graphs.
result Demonstrated effectiveness of AutoLL through qualitative and quantitative evaluations.
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral analysis on the Gr…
New regularization scheme for FMs improves feature interaction selection.
problem Feature selection in FMs leads to loss of feature interactions.
method Proposes a new regularization scheme for FMs with upper bound of regularizer.
result Improves feature interaction selection without restricting sparsity patterns.
Robust method learns nonlinear structures robustly to noise.
problem Learning nonlinear structures in noisy data.
method Robust Non-Linear Matrix Factorization (RNLMF).
result RNLMF achieves noticeable improvements in denoising and clustering.
A new framework for deep matrix factorizations improves model consistency and flexibility.
problem Inconsistent loss functions in deep matrix factorizations.
method Introduces two new loss functions and a generic optimization framework.
result Demonstrates improved model performance on synthetic and real data.
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the most important factors in predicting outcomes. However, the economic importance of …
Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlationscs.LG
Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the wei…
2L-FUSE enhances feature sparsity through kernel learning.
problem Sparsity and feature selection in regression tasks.
method 2-Layered kernel machines for learning a shape matrix and feature direction identification.
result Minimal yet informative feature sets are identified without losing predictive performance.
Polytopic Matrix Factorization models data as latent vectors from a polytope, maximizing determinant for identifiability.
problem Data decomposition with semi-structured latent vectors and polytope constraints.
method Model input data as latent vectors from a polytope, using determinant maximization for identifiability.
result Identifiability condition for polytopes with specific symmetry restrictions.
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analys…
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a g…
Joint Learning of Graph Representation and Node Features in Graph Convolutional Neural Networkscs.LG
Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graph data domain, such as brain networks, social networks and 3D point clouds. It is critical to identify an appropriate graph for the subsequent graph convolution. Existing methods manually construct or learn one fixed graph for all the layers of a …
Improves sparse recovery with non-linear Fourier features.
problem Sparse recovery challenges with non-linear Fourier features.
method Characterizes sufficient data points for perfect recovery.
result Sufficient data points depend on kernel matrix.
Conventional machine learning algorithms cannot be applied until a data matrix is available to process. When the data matrix needs to be obtained from a relational database via a feature extraction query, the computation cost can be prohibitive, as the data matrix may be (much) larger than the total input relation size…
NGRC shows numerical instabilities with short lags and high-degree polynomials.
problem Numerical instabilities in NGRC feature matrix.
method Combining numerical linear algebra and dynamical systems theory, we study feature matrix conditioning. We evaluate different numerical algorithms for solving the regularized least-squares problem.
result SVD-based training achieves accurate forecasts without regularization, preferable for short lags and high-degree polynomials.
Study analyzes feedback complexity for sparse feature retrieval in deep networks.
problem Learning sparse superposed features with feedback.
method Analysis of feedback complexity in sparse settings, including triplet comparisons.
result Establishes tight bounds and strong upper bounds for feature recovery.
RFM reduces feature space for linear models, improving sparse recovery.
problem Sparse linear regression and low-rank matrix recovery.
method Recursive Feature Machines (RFM) that alternates between reweighting feature vectors by AGOP and learning prediction function.
result RFM generalizes IRLS and outperforms deep linear networks.