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.
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48 results for “subspace transformation”
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…
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.
LOFT separates subspace rotation and transformation for orthogonal fine-tuning.
problem Conflating subspace rotation and transformation in orthogonal fine-tuning.
method LOFT explicitly separates subspace rotation and transformation, using task-aware support selection.
result LOFT recovers principal-subspace orthogonal adaptation and improves efficiency-performance trade-off.
Research explores flat subspaces in complex projective manifolds using Okounkov bodies.
problem Existence of flat subspaces in complex projective manifolds.
method Utilizes the generalised Legendre transform to the Okounkov body and a result by Schwer--Lytchak.
result Sufficient conditions for the existence of flat subspaces are identified.
A new method for projecting multimodal data to a common subspace for one-class classification.
problem Classifying data from multiple sources with varying features.
method Iterative transformation to a common subspace, separate transformations for each modality, regularization strategies.
result Outperforms competing methods across multiple datasets.
We develop embeddings for nonlinear subspaces preserving vector norms.
problem Preserving vector norms in nonlinear subspaces.
method Low-distortion embeddings for subspaces under nonlinear transformations.
result First low-distortion embeddings for a wide class of nonlinear functions.
New model learns symmetry transformations from complex data.
problem Learning symmetry transformations in complex domains like chemical space.
method Two latent subspaces, deep information bottleneck, continuous mutual information regularizer.
result Model outperforms state-of-the-art methods on artificial and molecular datasets.
A multi-step framework tackles online unsupervised domain adaptation with novel mean-target subspace computation.
problem Online unsupervised domain adaptation with unlabelled target data arriving sequentially.
method Multi-step framework with a novel mean-target subspace computation and temporal coherency consideration.
result Improved performance over previous approaches on four datasets.
A new method for one-class classification using ellipsoidal encapsulation.
problem One-class classification for data optimization.
method Iterative transformation into an optimized subspace with regularization terms.
result Better results in one-class classification compared to existing methods.
The paper studies the Poisson transform of differential forms on hyperbolic spaces.
problem Analyzing the Poisson transform of differential forms on real hyperbolic spaces.
method Proving the Poisson transform is a topological isomorphism between boundary forms and eigenforms.
result The Poisson transform is a topological isomorphism for -differential forms on the boundary of hyperbolic spaces.
A method to visualize multidimensional local subspaces using implicit differentiation.
problem Understanding the effect of multidimensional projection on local subspaces.
method Implicit function differentiation to analyze local subspaces shaped by multidimensional ellipses.
result Visualization of local subspaces provides insights into the global structure of data.
Subspace models play an important role in a wide range of signal processing tasks, and this paper explores how the pairwise geometry of subspaces influences the probability of misclassification. When the mismatch between the signal and the model is vanishingly small, the probability of misclassification is determined b…
BERT captures linguistic features in separate semantic and syntactic subspaces.
problem Understanding how transformer models like BERT represent linguistic features internally.
method Qualitative and quantitative investigations of BERT's internal representations.
result Evidence of a fine-grained geometric representation of word senses and syntactic representations.
Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspectivestat.ML
Paper provides a mathematical model for transformer ICL out-of-distribution generalization.
problem Understanding when transformer in-context learning can generalize beyond pre-training data.
method Minimal mathematical model of linear regression tasks with low-rank covariance matrices, analyzing distribution shifts as varying angles between subspaces.
result Transformers can generalize to all angle shifts if pre-training tasks are drawn from a union of subspaces, but not from a single Gaussian.
3S-SC framework improves SC accuracy by optimizing affinity matrices.
problem Inaccurate clustering results due to flawed affinity matrices.
method 3S-SC framework with GBTO to optimize affinity matrices.
result Improves connectivity and accuracy in SC methods.
In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes finite transformation law highly complicated, both technically and conceptually. In…
WPCA improves subspace recovery robustness to outliers.
problem Improving subspace recovery in the presence of outliers.
method Winsorized PCA (WPCA) with theoretical analysis of accuracy and robustness.
result WPCA provides consistent subspace recovery from contaminated data.
It is known since 40 years old paper by M. Keane that minimality is a generic (i.e. holding with probability one) property of an irreducible interval exchange transformation. If one puts some integral linear restrictions on the parameters of the interval exchange transformation, then minimality may become an "exotic" p…
Proposes -PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
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.
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.
We consider differential operators on a supermanifold of dimension . We define non-degenerate operators as those with an invertible top coefficient in the expansion in the "superderivative" (which is the square root of the shift generator, the partial derivative in an even variable, with the help of an odd ind…
A new geometry-preserving method for interpreting compositional data.
problem Statistical challenges in high-dimensional compositional data.
method Geometry-preserving framework for dimension reduction of compositional data.
result Identification of a central compositional subspace for compositional predictors.
SIG model identifies invariant variables for MSDA with fewer domain constraints.
problem Challenges in enforcing minimal changes across domains for MSDA.
method Subspace identification theory and variational inference.
result SIG model outperforms existing techniques on various benchmark datasets.
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces are known in advance, but the particular set of subspaces that are active (i.e., …
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.
PixelHop++: A Small Successive-Subspace-Learning-Based (SSL-based) Model for Image Classificationeess.IV
PixelHop++ improves image classification with a smaller model size.
problem Improving image classification models with smaller sizes.
method Decomposing input tensor, channel-wise Saab transform, successive subspace learning, feature ranking.
result PixelHop++ offers a flexible tradeoff between model size and performance.
New analysis shows how attention masks and LayerNorm prevent rank collapse in transformers.
problem Rank collapse in transformer models with increasing depth.
method General analysis of rank collapse under self-attention, considering attention masks and LayerNorm.
result Self-attention with LayerNorm can prevent rank collapse and maintain a rich set of equilibria.
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 …
This work introduces a transformation-based learner model for classification forests. The weak learner at each split node plays a crucial role in a classification tree. We propose to optimize the splitting objective by learning a linear transformation on subspaces using nuclear norm as the optimization criteria. The le…
The paper explores properties of the Radon transform in relation to neural networks and ridges.
problem Understanding the Radon transform and its application to neural networks and ridges.
method Investigates properties of the Radon transform, introduces new subspaces, and characterizes ridges for any distributional profile.
result Clarifies and simplifies results on the optimality of ReLU networks using the Radon transform.
Quantum Fourier Transform aids machine learning inference.
problem Generalizing from finite data samples to ground truth.
method Inspired by quantum algorithms, uses Quantum Fourier Transform to expose invariant subspace for data comparison.
result Proposes a concrete implementation for machine learning applications leveraging symmetries.
In this article we study an exact analogue of the cross-ratio for the algebra of quaternions H and use it to derive several interesting properties of quaternionic fractional linear transformations. In particular, we show that there exists a fractional linear transformation T on H mapping four distinct quaternions q_1, …
A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirr…
Transformers infer tasks from context via two modes, geometrically shaped task vectors explain their behavior.
problem Understanding how transformers infer tasks from context and the geometric properties of task vectors.
method Synthetic setting to train small transformers, mathematical characterization of task-vector geometry and inference modes.
result Task-vector geometry shapes in-distribution and out-of-distribution behavior of transformers.
New method improves reliability of depth estimation models.
problem Uncertainty quantification in large-scale vision models.
method Parameter-efficient Bayesian neural networks with PEFT methods.
result Combining PEFT methods with Bayesian inference enhances predictive performance.
We develop a method of extending actions of compact transformation groups which is then applied to the problem of preservation of equivariant extensor property by passing to a subspace of given orbit types.
We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient piecewise linear structure.
Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found applicati…
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data non-linearly while learning temporal relationships within the data. We then perform corre…
Out-of-distribution generalization via composition: a lens through induction heads in Transformerscs.CL
Transformers learn to generalize unseen tasks by composing self-attention layers.
problem How Transformers generalize to unseen, out-of-distribution tasks.
method Examined synthetic examples and pretrained LLMs, focusing on induction heads and latent subspace.
result Transformers can learn hidden rules for unseen tasks by composing self-attention layers, achieving OOD generalization.
QFDA combines machine learning and information theory for image classification.
problem Lack of literature on combining machine learning and information theory.
method Quantized Fisher Discriminant Analysis (QFDA) using a cost function for rate-distortion optimization.
result QFDA achieves at least as good classification accuracy as FDA on quantized images.
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the intrinsic non-linear structure of the underlying manifold and the absence of a canonical…
Paper extends ICA to ISA with auxiliary variables for better speech representation learning.
problem Learning unsupervised speech representations with independent subspaces.
method Theoretical framework of nonlinear ISA with auxiliary variables.
result Proposes an algorithm to learn speech representations with independent subspaces.
Paper proposes distributed sparse multicategory discriminant analysis for classification.
problem Sparse multicategory classification with distributed data.
method Convex formulation, distributed setting, invariant discriminant subspace recovery.
result Distributed sparse multicategory linear discriminant analysis performs as good as centralized version after a few rounds of communications.
In this thesis, we study a class of special Lagrangian submanifolds of toric Calabi-Yau manifolds and construct their mirrors using some techniques developed in the SYZ programme. We present a justification on the conjecture on the mirror construction of D- branes in Aganagic-Vafa [2]. We apply the techniques employed …
TrIM improves gradient-based dimension reduction and regression.
problem Efficiently identifying relevant feature subspace for high-dimensional regression.
method Introduced TrIM forest, an iterative approach using Mondrian forest and EGOP estimate.
result Consistency guarantees and convergence rates for EGOP matrix and random forest estimator.