This paper proposes a method to select project schedules with the lowest risk.
problem Selecting schedules that meet project deadlines while minimizing risk.
method Integrating aleatory uncertainty into project scheduling to quantify and compare risks.
result Proposes a method to select schedules with the lowest risk.
The paper explores properties of projections and gradient methods in hyperbolic space forms.
problem Optimization problems in hyperbolic space forms.
method Intrinsic κ-projection and gradient projection methods.
result Every accumulation point of the sequence generated by the gradient projection method is a stationary point.
Two new methods reduce OCO problem complexity without projections.
problem Efficiently solving smooth Online Convex Optimization problems without projections.
method ORGFW and MORGFW methods using recursive gradient estimation.
result Achieve optimal regret bounds with low computational costs.
New projection techniques reduce the frequency of projections in solving LCPs.
problem Solving linearly constrained problems efficiently with reduced projection frequency.
method Delayed projection technique to call a projection less frequently.
result Theoretical and practical improvements in convergence rates and efficiency.
We present an algorithm for converting an indoor spherical panorama into a photograph with a simulated overhead view. The resulting image will have an extremely wide field of view covering up to 4π steradians of the spherical panorama. We argue that our method complements the stereographic projection commonly used in t…
This paper surveys various methods for dimensionality reduction and nearest neighbor search.
problem Efficiently reducing high-dimensional data to lower dimensions while preserving essential information.
method Linear and nonlinear random projections, including sparse random projections, random Fourier Features, and Random Kitchen Sinks.
result Various methods for dimensionality reduction and nearest neighbor search are explained and compared.
A method for non-projective dependency parsing without fixed edge order.
problem Non-projective dependency parsing without fixed edge order.
method Incremental edge prediction, blending graph, transition, and easy-first parsing.
result Successfully parses near state-of-the-art on projective and non-projective languages.
Paper proposes a method to estimate project cost contingency reserves considering various types of uncertainty.
problem Inaccurate estimation of project cost contingency reserves due to ignoring different types of uncertainty.
method Quantitative determination of project cost contingency reserves using Monte Carlo Simulation considering aleatoric, stochastic, and epistemic uncertainties.
result The proposed method provides more accurate contingency reserves that align with actual project risks.
New algorithm reduces online learning iterations by a factor of T^2/3.
problem Efficiency in online learning with smooth cost functions.
method Follow-the-Perturbed-Leader method using online primal-dual framework.
result Guaranteed T^2/3 regret for general online convex optimization.
A new method sorts projects using Quicksort and Bradley-Terry model for uncertain long-term benefits.
problem Selecting projects with uncertain long-term benefits.
method Combining Quicksort and Bradley-Terry model for ranking projects based on uncertain long-term benefits.
result Proposed methods outperform existing aggregation methods and can be combined with sampling techniques.
Study on Gauduchon manifolds finds metrics for projectively flat bundles.
problem Existence of Hermitian-Poisson metrics on projectively flat bundles.
method Heat flow techniques and continuity methods.
result Established a correspondence between Hermitian-Poisson metrics and semi-simplicity.
A new framework for dimension reduction using ensemble of random projections.
problem High-dimensional regression problems with limited data.
method Aggregating an ensemble of carefully chosen random projections, retaining based on empirical performance, and selecting singular vectors.
result The proposed method stabilizes error as the number of projection groups increases.
Kernel methods with random projections improve least-squares regression efficiency.
problem Efficiently solving least-squares regression problems in high-dimensional spaces.
method Kernel conjugate gradient methods with randomized sketches and Nyström subsampling.
result Optimal generalization and computational advantages with proportional projection dimensions.
KL-LIME explains Bayesian models by projecting them locally to simpler models.
problem Explaining predictions of complex Bayesian models.
method Combines LIME with Bayesian projection methods.
result Demonstrates improved explanation of MNIST classifications.
A deep learning approach for efficient multidimensional projections.
problem Computational inefficiency and stability issues in existing projection methods.
method Train a deep neural network on sample projections to infer new ones.
result Generates projections similar to learned ones, faster and more stable.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.
Analyzes the moduli space of Higgs bundles to prove its quasi-projectivity.
problem Proving the quasi-projectivity of the moduli space of Higgs bundles.
method Uses analytic methods and the symplectic cut to construct a compactification.
result Proves the quasi-projectivity of the moduli space of Higgs bundles.
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
The paper studies conformal and projective structures using 2-frame bundles.
problem Understanding connections between conformal and projective structures.
method Using the dressing field method to obtain local, gauge invariant connections.
result A projective tractor bundle can be defined using the same construction as for conformal structures.
We consider stochastic strongly convex optimization with a complex inequality constraint. This complex inequality constraint may lead to computationally expensive projections in algorithmic iterations of the stochastic gradient descent~(SGD) methods. To reduce the computation costs pertaining to the projections, we pro…
New algorithm reduces adaptive regret without projections.
problem Computational expense of projections in online convex optimization.
method Lazy gradient-based algorithm with set-membership computations.
result Near-optimal adaptive regret bounds for general convex functions.
Optimizes reinsurance and investment strategies to minimize ruin probability.
problem Optimizing reinsurance and investment strategies to minimize ruin probability.
method Stochastic projected gradient method based on Malliavin calculus.
result Effectiveness of the proposed method demonstrated through numerical experiments.
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can "hear" the weights of a weighted projective space.
New framework uses elliptic operators to study projective maps.
problem Understanding projective structures on Riemannian manifolds.
method Develops two elliptic operators of second and fourth order.
result Establishes a natural correspondence between analytical and geometric properties.
Efficient methods for sparse random projections improve classification accuracy in very high-dimensional data.
problem Handling very high-dimensional sparse data efficiently.
method Non-iterative and iterative classification methods using sparse random projections and Jaccard kernel.
result Non-iterative methods yield larger, more accurate models than iterative methods.
A fast method for sparse PCA reduces computation time.
problem Time-consuming implementation of SPCA on high-dimensional data.
method Subspace projections using Household QR factorization for efficient deflation.
result Developed SPCA-SP method maintains good tradeoffs between various criteria.
Using sparse-inducing norms to learn robust models has received increasing attention from many fields for its attractive properties. Projection-based methods have been widely applied to learning tasks constrained by such norms. As a key building block of these methods, an efficient operator for Euclidean projection ont…
New method reduces computational cost for nonnegative low rank matrix approximation.
problem Efficiently compute nonnegative low rank matrix approximation for nonnegative matrices.
method Alternating projections onto tangent spaces of fixed rank matrices manifold and nonnegative matrix manifold.
result Sequence converges linearly to optimal solutions, showing better performance in terms of computational time and accuracy.
A dissertation on scalable projection-free optimization methods.
problem Efficient optimization algorithms for large-scale machine learning problems.
method Study of Frank-Wolfe variants and their extensions to distributed and derivative-free settings.
result Development of 1-SFW and QFW, achieving state-of-the-art complexity and efficiency.
The paper studies symplectic forms on projective limits of Banach bundles and their Darboux Theorem.
problem Conditions for weak symplectic forms on projective limits of Banach bundles.
method Analyzing projective sequences of Banach bundles and applying Darboux Theorem.
result Necessary and sufficient conditions for the Darboux Theorem on projective limits of Banach manifolds.
Study develops a cost model for field canals improvement projects in Egypt.
problem Accurately predict the preliminary costs of field canals improvement projects.
method Developed a parametric cost model using machine learning methods.
result Identified key cost drivers and developed a model for FCIPs.
Proves methods for creating convex projective 3-manifolds with cusps.
problem Creating convex projective 3-manifolds with generalized cusps.
method Properly convex deformations of hyperbolic structures, controlling cusp types.
result First known example of a 1-cusped hyperbolic 3-manifold with a type 2 cusp.
The paper sharpens the analysis of sketch-and-project methods using randomized singular value decomposition.
problem Improving convergence rates of sketch-and-project methods for solving linear systems and non-linear optimization problems.
method Developing a theoretical framework and new spectral bounds for the expected sketched projection matrix.
result The convergence rate improves linearly with sketch size and even faster with certain spectral decays.
Method recovers particle orientations from cryo-EM projections.
problem Unknown orientations in cryo-EM images.
method Two-step process: estimating distances and recovering orientations.
result Accurate orientation recovery from noisy projections.
The paper studies Jacobi fields and conjugate points in projective sprays.
problem Investigating Jacobi fields and conjugate points in projective sprays.
method Proved that conjugate points are preserved under projective changes and established conditions for the existence of conjugate points.
result Conditions for the existence of conjugate points in projectively deformed sprays.
A new ensemble method using random projections for kNN classification.
problem Improving kNN classification accuracy through ensemble methods.
method Random projection of bootstrap samples into lower dimensions, using extended neighbourhood rule for base learners.
result Enhanced classification accuracy compared to traditional kNN and other ensembles.
Paper proposes a method to reduce sensor drift in electronic noses.
problem Sensor drift in electronic noses.
method Discriminative subspace projection approach.
result The method minimizes within-class variance and maximizes between-class variance using label information.
We define a decomposition of link projections whose pieces we call atoroidal graphs. We describe a surgery operation on these graphs and show that all atoroidal graphs can be generated by performing surgery repeatedly on a family of well known link projections. This gives a method of enumerating atoroidal graphs and he…
Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.
problem Solving high-dimensional quadratic programming problems efficiently.
method Data-driven framework with a graph neural network generating projections tailored to each QP instance.
result Produces high-quality solutions with reduced computation time, outperforming existing methods.
Study minimal Lagrangian surfaces in complex projective plane, focusing on contractible cases.
problem Construct minimal Lagrangian surfaces in complex projective plane.
method Loop group method
result Presented new classes of minimal Lagrangian surfaces.
PPF uses projections to improve classification accuracy.
problem Improving classification accuracy in multi-class problems.
method PPF constructs trees using projections of variables, enhancing traditional random forest.
result PPF outperforms traditional random forest in multi-class problems.
Here, a non-linear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci tensor and its covariant derivatives.
Sharp-SSL uses random projections to identify important variables for semi-supervised learning.
problem High-dimensional semi-supervised learning problems.
method Careful aggregation of low-dimensional results from many axis-aligned random projections.
result Sharp-SSL algorithm can recover signal coordinates with high probability.
TTRP method preserves distances in high-dimensional data with reduced storage and speed.
problem Preserving distances in high-dimensional datasets efficiently and accurately.
method Tensor train random projection (TTRP) using TT-ranks of one.
result TTRP is an expected isometric projection with bounded variance.
New PG methods tackle nonconvex optimization with auto-conditioned stepsizes.
problem Optimizing nonconvex functions over convex sets.
method Auto-conditioned projected gradient (AC-PG) methods and stochastic variants.
result Achieved optimal iteration complexity for finding approximate stationary points.
Proposes TS-NMF for 2D clustering, preserving spatial info.
problem Loss of spatial information in 2D data.
method Semi-Nonnegative Matrix Factorization with manifold learning.
result Improves clustering performance compared to state-of-the-art.
A new method transfers parameters in ELM networks using projective model.
problem Parameter transfer in extreme learning machine networks.
method Projective model to bridge source and target model parameters, L2,1-norm penalty for joint feature selection and parameter transfer.
result Significantly outperforms non-transfer ELM networks and other methods.
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.