Paper proposes a new landmark selection method for kernel ridge regression.
problem Efficient landmark selection for scalable kernel methods.
method Two-step approach: first computes importance scores, then clusters them into landmarks.
result Proposed method provides better accuracy and efficiency trade-offs.
Proposes landmark selection for kernel methods.
problem Selecting important landmarks from large training sets.
method Deterministic and randomized adaptive algorithm for landmark selection.
result Landmarks are related to the minima of kernelized Christoffel functions.
Adaptive Nyström method improves Gaussian Process Regression scalability.
problem Scalability issue in Gaussian Process Regression due to cubic complexity.
method Adaptive Nyström approach that greedily selects landmarks to minimize kernel approximation error.
result Significantly outperforms random landmark selection in accuracy and stability.
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostl…
Landmark Diffusion Maps reduce manifold learning complexity for high-volume data streams.
problem Complexity of out-of-sample extensions in manifold learning techniques.
method Landmark Diffusion Maps (L-dMaps) using pruned spanning trees or k-medoids to select landmark points.
result Up to 50-fold speedups in out-of-sample extension with less than 4% errors in manifold reconstruction.
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcom…
Efficiently clusters large datasets with a subset of landmarks.
problem High computational complexity in subspace clustering for large-scale datasets.
method Selects a subset of landmarks to reduce the clustering problem to linear time.
result Subspace clustering method runs in linear time with respect to the size of the original data.
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we present a novel algori…
We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose algorithms that have guaranteed generalization properties when working with such good fu…
RULLS generates robust features for machine learning models.
problem Feature engineering for machine learning models.
method Randomized Union of Locally Linear Subspaces (RULLS) for unsupervised feature generation.
result RULLS provides high performance on classification and clustering tasks.
Method maps state space using landmarks for universal goal reaching.
problem Learning the Universal Value Function Approximator (UVFA) for long-range goals is challenging.
method Hierarchical modeling with a dynamic landmark-based map and a value network.
result The method enables agents to reach long-range goals at the early training stage.
For their ability to capture non-linearities in the data and to scale to large training sets, local Support Vector Machines (SVMs) have received a special attention during the past decade. In this paper, we introduce a new local SVM method, called L3-SVMs, which clusters the input space, carries out dimensionality r…
The study extends stochastic completeness to landmark spaces with any number of landmarks.
problem Stochastic completeness for landmark spaces with arbitrary numbers of landmarks.
method Volume growth criterion and eigenvalue bounds for geodesic balls.
result Stochastic completeness for landmark spaces with any number of landmarks is proven.
Diverse sampling improves kernel methods' performance in sparse regions.
problem Improving kernel methods' performance in sparse regions of datasets.
method Using Determinantal Point Processes (DPP) for sampling diverse landmarks in Nyström approximation.
result Nyström kernel regression with diverse landmarks increases accuracy in sparse regions of the dataset.
Landmark2Vec maps unknown landmarks without GPS.
problem Estimate positions of unknown landmarks without GPS.
method Unsupervised neural network trained on landmark signals.
result Maps landmarks up to scale, rotation, and shift.
RRN accurately identifies landmarks in CMF bones without segmentation.
problem Accurately identifying landmarks in craniomaxillofacial bones without segmentation.
method End-to-end RRN architecture using dense-block units for landmark imputation.
result RRN achieves <2 mm RMS error in landmarking.
Unified shape spaces with preserved invariances and regular metrics.
problem Combining shape invariances from Kendall's spaces with regular metrics.
method Defined a Sobolev-type operator to achieve the desired geometry, preserving invariances and regularity.
result Achieved a new landmark shape space with regular metrics and preserved invariances.
LA-VDM accelerates VDM using landmarks to improve data analysis.
problem Efficiently analyzing complex datasets with nonuniform sampling densities.
method Landmark-constrained two-stage normalization to accelerate VDM.
result LA-VDM accurately recovers parallel transport and converges to the connection Laplacian.
Landmark AD improves AD's efficiency without sacrificing performance.
problem Computational burden in diffusion-based sensor fusion.
method Inspired by landmark diffusion, proposes Landmark AD.
result Landmark AD offers superior computational efficiency.
Bayesian method learns optimal momentum for landmark matching.
problem Finding a diffeomorphism between two sets of landmarks.
method Ensemble Kalman filter for derivative-free Bayesian inverse method.
result Efficient algorithm for various target shapes.
DeepLocalization uses neural networks to localize vehicles from landmarks.
problem Vehicle self-localization from multi-modal sensor data and a reference map.
method Deep neural network that regresses vehicle pose from unordered landmarks.
result DeepLocalization achieves state-of-the-art accuracy and is faster than related work.
Researchers prove long-time existence for two landmark Brownian motion.
problem Proving long-time existence of Brownian motion on configurations of two landmarks.
method Classification and analysis of long-time existence for configurations of exactly two landmarks, using a radial kernel.
result For configurations of exactly two landmarks, long-time existence is possible for certain kernels, but not for others.
Landmark-based node embeddings approximate shortest path distances in random graphs.
problem Capturing global graph distances in node representations.
method Landmark-based node embeddings using shortest path distances from a subset of reference nodes (landmarks).
result Random graphs require lower dimensions in landmark-based embeddings compared to worst-case graphs.
Exact universal interpolation property for landmark configurations in Euclidean space.
problem Representing and deforming landmark configurations through flows of vector fields.
method Explicitly describe vector fields for exact universal interpolation property in all dimensions.
result Achieve controllability by combining constant and polynomial vector fields.
Paper evaluates CNN-based facial landmark detection methods.
problem Evaluate characteristics and performance of CNN-based facial landmark detection methods.
method Divided into regression and heatmap approaches, investigated using a hybrid loss function and discrimination network.
result Proposed model outperforms other models in all tested datasets.
Deep learning model detects landmarks in X-ray cephalograms.
problem Automatically detecting landmarks in cephalometric X-ray images.
method 2-stage U-Net with attention mechanism and Expansive Exploration strategy.
result State-of-the-art results in landmark detection.
Paper presents a more accurate method for nonparametric density estimation using FMMPL and SIR.
problem Improving nonparametric density estimation for complex datasets.
method Finite mixture model of nonparametric density estimation using sampling importance resampling.
result FMMPL provides more accurate results with less space complexity.
Learning automatically the structure of object categories remains an important open problem in computer vision. In this paper, we propose a novel unsupervised approach that can discover and learn landmarks in object categories, thus characterizing their structure. Our approach is based on factorizing image deformations…
Neumann eigenmaps improve landmark-based diffusion map embeddings.
problem Landmark-based diffusion map embeddings can be computationally inefficient and unstable.
method NeuMaps use a renormalized Neumann Laplacian for eigendecomposition, incorporating landmarks as a subgraph.
result NeuMaps offer a computationally efficient and stable embedding method.
Paper introduces conformal prediction for reliable uncertainty quantification in landmark localization.
problem Systematic underestimation of total predictive uncertainty in landmark localization.
method Conformal prediction framework for multi-output regression, generating flexible prediction regions.
result Methods outperform existing approaches in validity and efficiency across 2D and 3D datasets.
New landmark states improve transfer learning in multi-task RL.
problem Improving sample complexity and regret in new RL tasks.
method Topological landmark covering, landmark value functions, action pruning.
result Theoretical bounds on Q values at state-action pairs.
Novel deep learning framework for mandible segmentation and landmarking.
problem Challenging problem of mandible segmentation and anatomical landmarking from CBCT scans.
method Three-step approach: deep neural network for segmentation, geodesic space for landmarks, LSTM for closely spaced landmarks.
result Superior efficacy compared to state-of-the-art methods in craniofacial anomalies and diseased states.
The paper explores a new method for landmark matching using sub-Riemannian geometry and neural networks.
problem Finding a time-dependent vector field to warp points from an initial set to a target set.
method Sub-Riemannian geometry and residual neural networks.
result Demonstrates the importance of regularization in landmark matching.
Study uses stacked hourglass networks to improve facial landmark detection for medical diagnosis.
problem Improving accuracy of facial landmark detection for medical diagnosis.
method Conducted a study on landmark localisation methods using stacked hourglass networks.
result State-of-the-art stacked hourglass architecture outperforms traditional methods.
Characterizes geodesic completeness for landmark spaces.
problem Ensuring geodesics exist for all times in landmark spaces.
method Integrability criterion based on cometric kernel behavior.
result Full characterization of geodesic completeness for smooth Riemannian metrics.
Two active learning algorithms improve HSI classification using Fermat distances and harmonic label propagation.
problem Semi-supervised hyperspectral image classification with limited labeled data.
method Combines Fermat distances with Poisson-reweighted harmonic label propagation for active point selection.
result FALL and A-FALL algorithms enhance labeling accuracy and scalability for large HSI scenes.
Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In this paper we define a general class of kernels that can be easily approximated …
This work predicts and interpolates long-range videos using unsupervised landmarks.
problem Predicting and interpolating long-range video data with occlusions and appearance changes.
method Unsupervised latent structure inference followed by temporal prediction in a latent space.
result High-quality long-range video interpolation and extrapolation achieved through landmark representation.
Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular distortion. Conformal registrations are beneficial since it preserves the local ge…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To bui…
Landmark Ordinal Embedding improves scalability of ordinal embedding.
problem Learning low-dimensional Euclidean representations from ordinal constraints.
method Landmark-based strategy (LOE) that trades statistical efficiency for computational efficiency.
result LOE is significantly more efficient than conventional methods as the number of items grows.
Study reveals biases in facial landmark detection methods for dementia patients.
problem Challenges in facial landmark detection for older adults with dementia.
method Evaluation of seven facial landmark detection methods on frontal, profile, and various face regions.
result Significant performance differences between dementia patients and non-patients, and biases across face regions.
Improved Nyström approximation for kernel quadrature with theoretical guarantees.
problem Efficiently approximating positive definite kernels for large datasets.
method Refined sampling and subspace selection in Nyström approximation.
result Novel theoretical guarantees for non-i.i.d. landmark points in kernel quadrature.
Facial landmark localization and occlusion estimation for driver safety.
problem Robust facial landmark localization and occlusion estimation under harsh lighting and occlusion.
method Occluded Stacked Hourglass approach based on Stacked Hourglass network.
result State-of-the-art results in face detection, head pose, and occlusion estimation on various datasets.
Conditional modeling x \to y is a central problem in machine learning. A substantial research effort is devoted to such modeling when x is high dimensional. We consider, instead, the case of a high dimensional y, where x is either low dimensional or high dimensional. Our approach is based on selecting a small subset y_…
Survey of Locally Linear Embedding and its variants.
problem Representing high-dimensional data in a lower-dimensional space while preserving local structure.
method Explains various LLE and variant methods, including kernel LLE, inverse LLE, feature fusion, out-of-sample embedding, incremental LLE, landmark LLE, supervised LLE, robust LLE, fusion with other methods, and weighted LLE.
result Comprehensive overview of LLE and its variants.
Predict and classify brain image evolution trajectories from a single MRI timepoint.
problem Diagnosing early mild cognitive impairment (eMCI) from a single MRI scan.
method Supervised and unsupervised learning frameworks that predict and label intensity patch evolution trajectories from a baseline MRI.
result Classification accuracy increased by up to 10% points compared to single timepoint-based methods.
This paper deals with the computation of sectional curvature for the manifolds of N landmarks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the group action of diffeomorphisms. The inverse of the metric tensor for these manifolds (i.e. the cometric), when written in coordinates, i…