Paper uses random projection to preserve subspace structure for efficient data analysis.
problem Efficiently analyzing data with low-dimensional structure.
method Compressed Subspace Learning (CSL) framework based on Johnson-Lindenstrauss property.
result Random projection preserves the UoS structure of data, enabling efficient analysis.
PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust su…
Proposes a method to enforce nestedness in subspace learning methods.
problem Consistency between data representations when choosing different subspaces dimensions.
method Lifts Grassmannian optimization criteria to flag manifolds via nested projectors.
result Successfully addresses the nestedness issue in several machine learning methods.
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…
Due to the lack of enough generalization in the state-space, common methods in Reinforcement Learning (RL) suffer from slow learning speed especially in the early learning trials. This paper introduces a model-based method in discrete state-spaces for increasing learning speed in terms of required experience (but not r…
A new method learns multiple subspaces from data.
problem Learning discriminative representations for data on multiple subspaces.
method Sequential game using CTRL framework to solve linear subspaces.
result Equilibrium solutions provide correct representations.
The goal of subspace learning is to find a k-dimensional subspace of Rd, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe r≤d att…
Active learning improves subspace clustering with less labeled data.
problem Efficiently incorporating labeled data to improve subspace clustering models.
method Proposes an active learning framework for subspace clustering that queries informative points and updates the subspace model.
result Demonstrates the advantage of the proposed active strategy over state-of-the-art methods.
Transforms data into separable subspaces for clustering.
problem Data is not always separable into subspaces.
method Embeds subspace clustering techniques into transform learning.
result Improves upon state-of-the-art clustering techniques.
Study explores GAN dynamics for high-dimensional subspace learning.
problem Subspace learning in high-dimensional datasets.
method Single-layer GAN model with multi-feature discriminators.
result GANs outperform conventional methods in capturing informative subspace.
Study on robustness of subspace learning from adversarial modifications.
problem Adversarial robustness of subspace learning problems.
method Characterization of optimal rank-one attack strategies and generalization to non-rank-constrained scenarios.
result Optimal attack strategies depend on singular values and adversary's energy budget.
Paper develops a method to identify minimal sample subspaces from limited data.
problem Challenging task of subspace segmentation with minimal sample subspaces.
method Develops a theoretical framework and optimization algorithms for MSS.
result The MSS model can retrieve minimal sample subspaces even when they are heavily intersected.
Proposes Neural Random Subspace for deep learning.
problem Combining random subspace method with deep learning.
method Neural Random Subspace (NRS) integrating deep learning and random subspace.
result Achieves superior performance on 35 datasets and improves recognition tasks.
Kernel models learn low-dimensional predictive subspaces from input data.
problem Learning effective feature transformations in kernel models.
method Study of a compositional kernel ridge regression model.
result Global minimizers of the objective function identify the subspace with high probability.
Extracting the underlying low-dimensional space where high-dimensional signals often reside has long been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. At the same time, working with incomplete (partly observed) large scale datasets has recent…
Paper proposes a deep subspace clustering method using multi-level representations.
problem Deep subspace clustering of images.
method Convolutional autoencoders with multiple fully-connected layers for multi-level representations, loss minimization with iterative updates.
result The method outperforms state-of-the-art methods on real-world datasets.
New algorithm learns principal subspace from random samples.
problem Learning principal subspace from small random submatrices.
method Stochastic gradient descent algorithm for neural networks.
result Algorithm can handle infinite rows and columns.
Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subsp…
Paper reviews advances in solving sparsest vector problem in subspaces.
problem Finding the sparsest vector in a low-dimensional subspace.
method Geometric analysis of optimization landscapes and efficient nonconvex optimization algorithms.
result Recent advances in global nonconvex optimization for sparsest vector problem.
New method improves subspace iteration for eigenvectors in machine learning.
problem Computing eigenvectors for large-scale problems in machine learning.
method Subspace iteration with ℓ2o∞ norm convergence analysis. result Deterministic bounds and practical stopping criterion for improved performance.
A novel unsupervised feature selection method using subspace clustering and self-expressive model.
problem Feature selection for large datasets with minimal labeling effort.
method Subspace clustering with adaptive representation learning and regularized regression.
result The method effectively captures sample similarities and discriminative information.
Algorithm selects public datasets for private machine learning.
problem Choosing the most suitable public dataset for private machine learning.
method Measures gradient subspace distance between public and private datasets.
result Excess risk scales with the subspace distance between gradients.
A method for identifying joint and individual subspaces from multi-view data.
problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.
A hierarchical approach improves classification accuracy in large datasets.
problem Improving classification accuracy in large datasets with high dimensionality.
method Hierarchical subspace learning to scale manifold learning methods.
result Average 5% increase in classification accuracy.
New method disentangles hidden data structures using HSIC and supervision.
problem Tackles the challenge of interpreting high-dimensional data.
method Supervised Independent Subspace Principal Component Analysis (sisPCA) using HSIC.
result Identifies and separates hidden data structures effectively.
DCFSC uses a simple auto-encoder for subspace clustering without parameters.
problem Subspace clustering for large-scale high-dimensional datasets.
method Closed-form shallow auto-encoder for data-driven self-expressive layer, no parameters or optimization.
result Significant memory benefits over existing methods on large datasets.
New derivation shows how a three-factor learning rule is derived from Oja's rule.
problem Deriving a three-factor learning rule from Oja's rule.
method Using frame theory to systematically derive EGHR-PCA from Oja's rule.
result A principled derivation of a biologically plausible learning rule.
New method for active subspace analysis reduces gradient evaluations needed.
problem Efficiently perform subspace sensitivity analysis on expensive or noisy functions.
method Develops acquisition functions for sequential learning of active subspaces using Gaussian process surrogate models.
result ASM estimator can be computed in closed form for Gaussian process surrogates, reducing need for finite differencing.
Flow Matching models help generative models stay within the subspace of real data.
problem How do generative models stay within the subspace of real data?
method Flow Matching models using a learned velocity field to transform a simple prior into a complex target distribution.
result Generated samples memorize real data points and represent the sample data subspace exactly.
The paper simplifies Bayesian deep learning by reducing high-dimensional parameter space to lower dimensions.
problem Scaling Bayesian inference to deep neural networks is challenging due to high dimensionality.
method Construct low-dimensional subspaces using SGD trajectories and apply elliptical slice sampling and variational inference.
result Bayesian model averaging over induced posterior in subspaces produces accurate predictions and well-calibrated uncertainty.
Efficiently clusters millions of data points with learnable subspace clustering.
problem Large-scale subspace clustering with high-dimensional data.
method Develops a learnable subspace clustering paradigm using a parametric function and RPCM.
result Outperforms state-of-the-art methods in efficiency and effectiveness.
Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was recently proposed as a method for assessing the similarity of the representations …
We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of tr…
SAP learns efficient task-specific parameter subspaces for few-shot learning.
problem Efficient few-shot learning with limited data.
method Subspace Adaptation Prior (SAP) learns task-specific parameter subspaces for efficient few-shot learning.
result SAP yields superior or competitive performance in few-shot image classification.
Variational autoencoders (VAEs) are widely used deep generative models capable of learning unsupervised latent representations of data. Such representations are often difficult to interpret or control. We consider the problem of unsupervised learning of features correlated to specific labels in a dataset. We propose a …
RED-SC improves deep subspace clustering efficiency.
problem Slow convergence in training deep subspace clustering models.
method Residual Encoder-Decoder network with skip-layer connections and self-expressive layer.
result Training converges much faster with RED-SC.
Over the past decade a wide spectrum of machine learning models have been developed to model the neurodegenerative diseases, associating biomarkers, especially non-intrusive neuroimaging markers, with key clinical scores measuring the cognitive status of patients. Multi-task learning (MTL) has been commonly utilized by…
This work improves sample efficiency in meta-learning for nonlinear tasks.
problem Learning complex tasks efficiently with limited data.
method Subspace-based representations for nonlinear tasks.
result Subspace-based representations can be learned efficiently and improve future task performance.
Paper proves IRLS converges to subspace from any start, with practical benefits.
problem Robust subspace estimation in machine learning.
method Iteratively Reweighted Least Squares (IRLS) with dynamic smoothing regularization.
result IRLS converges linearly to the underlying subspace from any initialization under deterministic conditions.
Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subs…
The paper proposes a method to find interpretable subspaces in node embeddings using a knowledge base.
problem Finding interpretable subspaces in unsupervised node embeddings.
method Using a taxonomy of human-understandable concepts from a knowledge base to identify subspaces in node embeddings.
result Low error in finding fine-grained concepts.
IntroVAC learns interpretable latent subspaces for better image quality.
problem Difficulties in interpreting latent spaces and limitations in image generation.
method Introspective Variational Classifier (IntroVAC) using additional labels and adversarial training.
result Improved image quality and meaningful latent directions for fine-grained manipulation.
SGD updates align with a low-rank subspace but do not lead to further loss reduction.
problem Understanding the training dynamics of deep neural networks, particularly the role of the dominant subspace.
method Exploring whether neural networks can be trained within the dominant subspace of the loss Hessian.
result SGD updates, when projected onto the dominant subspace, do not decrease the training loss further, suggesting spurious alignment.
This work simplifies Bayesian inference for neural networks by identifying influential parameter directions.
problem High computational complexity in Bayesian inference for neural networks due to high-dimensional parameter space.
method Constructing an active subspace of influential parameter directions to reduce dimensionality.
result Effective and scalable Bayesian inference achieved via reduced active subspace.
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar features, while some others may have almost no cross-correlations with quite di…
A new method tackles bilevel optimization using Lanczos process for efficient hyper-gradient computation.
problem Efficiently solving large-scale bilevel optimization problems with gradient-based methods.
method Constructing low-dimensional approximate Krylov subspaces with the Lanczos process to approximate the Hessian inverse vector product.
result Demonstrates a O(ε−1) convergence rate and efficiency in synthetic and deep learning tasks. A new model classifies surface anomalies in 3D point cloud data.
problem Accurate classification of surface anomalies in manufacturing processes.
method Deep subspace learning approach for 3D point cloud data.
result The method effectively identifies new types of anomalies.
A parameter-free method clusters data points from multiple subspaces.
problem Subspace clustering with unknown number of clusters and parameters.
method Clusters data points based on angle differences between subspaces; merges clusters until final clustering is obtained.
result Parameter-free approach for clustering data points from multiple subspaces.