Study analyzes IMDB movie comments and Twitter data using machine learning and vector space techniques.
problem Sentiment analysis of IMDB movie comments and Twitter data.
method Created a vector space in KNIME Analytics platform, used Decision Trees, Naïve Bayes, and SVM algorithms for classification.
result SVM algorithm provided the best classification results for both IMDB movie comments and Twitter data sets.
We introduce several techniques for sampling and visualizing the latent spaces of generative models. Replacing linear interpolation with spherical linear interpolation prevents diverging from a model's prior distribution and produces sharper samples. J-Diagrams and MINE grids are introduced as visualizations of manifol…
Paper proposes efficient inner product approximation for hybrid sparse and dense vectors.
problem Efficient search in hybrid spaces with both sparse and dense components is challenging.
method Proposes a technique to approximate inner product computation in hybrid vectors.
result Achieves over 10x speedup and higher accuracy in search compared to baselines.
Paper develops techniques for singular metrics on vector bundles.
problem Developing techniques for singular metrics on vector bundles.
method Introducing non-pluripolar products and defining I-good singularities. result Derives a Chern--Weil type formula for Hermitian vector bundles with I-good singularities. In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of (α,β) spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of some classes of (α,β) spaces under certain c…
The Generator of a Generative Adversarial Network (GAN) is trained to transform latent vectors drawn from a prior distribution into realistic looking photos. These latent vectors have been shown to encode information about the content of their corresponding images. Projecting input images onto the latent space of a GAN…
We propose an algorithm to separate simultaneously speaking persons from each other, the "cocktail party problem", using a single microphone. Our approach involves a deep recurrent neural networks regression to a vector space that is descriptive of independent speakers. Such a vector space can embed empirically determi…
Stabilization technique applied to curve shortening flow in 3D space.
problem Stabilizing curve shortening flow in 3D space.
method Applying stabilization technique developed by T. Zelenyak to curve shortening flow in R3. result Derivation of several new monotonicity formulas for curve shortening flow.
The paper classifies vector fields on 5D nilpotent Lie groups.
problem Classifying left-invariant affine and projective vector fields on 5D nilpotent Lie groups.
method Algebraic characterization and case-by-case analysis of vector fields.
result All projective vector fields are affine, extending classical results.
New examples of solitons found using submersion techniques.
problem Finding new mean curvature solitons on manifolds.
method Riemannian submersion techniques to reduce PDE to ODE.
result New examples of rotators in hyperbolic space.
New method transfers emotions in facial images.
problem Transforming facial images to different emotions.
method Infinite task learning and vector-valued reproducing kernel Hilbert spaces.
result Achieves low reconstruction cost and high emotion classification accuracy.
In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (nor…
Novel proof technique for Gelfand-Fuks cohomology.
problem Comparing sheaf-like data over manifold Cartesian powers.
method Local-to-global analysis through generalized good covers and factorization algebras.
result Unified approach to Gelfand-Fuks cohomology.
Vectors of data are at the heart of machine learning and data mining. Recently, vector quantization methods have shown great promise in reducing both the time and space costs of operating on vectors. We introduce a vector quantization algorithm that can compress vectors over 12x faster than existing techniques while al…
The report analyzes infinite-dimensional output space regression.
problem Learning theory in vector-valued RKHS regression.
method Integral operator technique with spectral theory for non-compact operators.
result Results with minimal assumptions using Chebyshev's inequality.
New method uses weighting vectors for efficient boundary and outlier detection.
problem Boundary and outlier detection in machine learning.
method Recast metric space magnitude as weighting vector, solve kernelized SVM, apply nearest neighbor methods.
result Weighting vector can be efficiently approximated in linear time, outperforming state-of-the-art techniques.
We improve autoencoder image interpolation by shaping latent space.
problem Incongruities in autoencoder interpolation leading to artifacts or unrealistic results.
method Propose a regularization technique to shape latent space to follow a smooth, locally convex manifold consistent with training images.
result Faithful interpolation between data points achieved.
PersLay embeds graph topological signatures into neural networks for improved machine learning.
problem Embedding persistence diagrams from graph data into neural networks for machine learning.
method Extended persistence theory and heat kernel signature for encoding graphs into persistence diagrams. General framework for learning vectorizations of persistence diagrams.
result Achieved competitive scores on graph classification tasks.
Generative adversarial networks (GANs) transform latent vectors into visually plausible images. It is generally thought that the original GAN formulation gives no out-of-the-box method to reverse the mapping, projecting images back into latent space. We introduce a simple, gradient-based technique called stochastic cli…
Randomized algorithm solves vector-valued regression problems with low-rank operators.
problem Vector-valued regression problems involving infinite-dimensional spaces.
method Randomized Reduced Rank Regression (R4) using Gaussian sketching for optimization.
result R4 estimators are efficient and accurate, with empirical risk close to optimal.
This work learns shared word embeddings for acoustic and phonetic sequences.
problem Mapping variable-length acoustic and phonetic sequences to fixed-dimensional vectors.
method Weak supervision and binary classification task to predict word similarity.
result Best model achieves an F1 score of 0.95 for binary classification.
Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture non-linear structures within large data sets, and is a central tool in data analysis and learning. To allow for non-linear relations, typically a full n×n kernel matrix is constructed over n data points, but this…
Develops novel techniques for collaborative filtering and multi-label classification.
problem Information overload and categorization of data objects.
method Hierarchical bi-level maximum margin matrix factorization and piecewise-linear embedding method.
result Effective multi-label classification and collaborative filtering techniques developed.
This paper improves Koopman operator approximations by pruning subspaces in RKHS.
problem Improving predictive accuracy of Koopman operator approximations.
method Computes principal angles and vectors in RKHS to prune subspaces.
result Validated approach enhances Koopman operator approximations for large datasets.
In a finite-dimensional real vector space furnished with a rational structure with respect to a subfield of the field of real numbers, every (simplicial) rational semifan is contained in a complete (simplicial) rational semifan. In this paper this result is proved constructively on use of techniques from polyhedral geo…
We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to …
Screening is an effective technique for speeding up the training process of a sparse learning model by removing the features that are guaranteed to be inactive the process. In this paper, we present a efficient screening technique for sparse support vector machine based on variational inequality. The technique is both …
This paper explores autoencoders for estimating intrinsic dimensionality.
problem Estimating the intrinsic dimensionality of random vectors.
method Use of autoencoders for dimension estimation, focusing on architectural choices and regularization techniques.
result Autoencoders can be adapted for intrinsic dimension estimation, addressing questions beyond classic DR/DE techniques.
New algorithm improves topological stability in non-linear dimensionality reduction.
problem Topological instability in choosing nearest neighbors in Isomap.
method Uses point and its two nearest neighbors to find subspace and orthogonal complement, then adds new points based on distance and angle.
result Improves topological stability and reduces short-circuit errors.
Let X be a data matrix of rank ρ, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We pr…
FFM generates functions between Gaussian and data distributions.
problem Generating functions between Gaussian and data distributions.
method Define a path of measures, learn a vector field to generate this path.
result FFM outperforms other function-space generative models.
Paper transforms torse-forming vector fields into simpler forms.
problem Generalizing vector fields and their transformations.
method Present techniques to transform torse-forming vector fields into simpler cases.
result Concrete examples of transformations are provided.
Foliate systems are those which preserve some (possibly singular) foliation of phase space, such as systems with integrals, systems with continuous symmetries, and skew product systems. We study numerical integrators which also preserve the foliation. The case in which the foliation is given by the orbits of an action …
Paper proposes a new metric learning method for better class separability.
problem Class separability in metric spaces for improved classification.
method CLAS(M)K-ML, learning best kernel function for high class separability.
result Better flexibility and lower computational complexity achieved.
Solves numerical computation of Killing and conformal Killing vector fields on compact Riemannian manifolds.
problem Overdetermined systems of PDE make numerical computation difficult.
method Reduces to symmetric eigenvalue problem solved by finite element techniques.
result Valid in any dimension and for arbitrary compact Riemannian manifolds.
The study proves rationality of complex projective varieties with holomorphic vector fields.
problem Rationality of complex projective varieties with holomorphic vector fields.
method Key technique by Harvey-Lawson on finite volume flows.
result Uniform upper bound on Betti numbers for varieties with holomorphic vector fields.
The paper explores theories behind graph and relational data vector embeddings.
problem Understanding the foundations of vector embeddings for graphs and relational structures.
method Proposes two theoretical approaches to understand vector embeddings.
result Draws connections between various embedding techniques and suggests future research directions.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
Proves GAGA-style result for toric vector bundles.
problem None explicitly stated in the abstract.
method Algebraic construction of Frölicher approximating vector bundle.
result Proves GAGA-style result for toric vector bundles.
Einstein's non-symmetric geometry uses Bochner's technique to prove decomposition and vanishing results.
problem Analyzing Einstein's non-symmetric geometry with Bochner's technique.
method Defining concepts, proving decomposition formula, and showing vanishing results.
result Vanishing results about the null space of Bochner and Hodge type Laplacians.
Gaussian processes adapted for non-Euclidean spaces enhance decision-making.
problem Applying Gaussian processes in non-Euclidean spaces.
method Developed pathwise conditioning and Gaussian process models over non-Euclidean spaces.
result Efficient Gaussian process models for non-Euclidean spaces.
New integral estimates on substatic manifolds improve Alexandrov Theorem.
problem Improving integral estimates on substatic manifolds.
method Introducing a new vector field with nonnegative divergence.
result Generalization and improvement of integral estimates leading to Alexandrov Theorem.
Framework converts singer identity and vocal technique from non-parallel corpora.
problem Converts singer identity and vocal technique from non-parallel corpora.
method Uses variational autoencoders with separate encoders for singer identity and vocal technique.
result Successfully disentangles and converts singer identity and vocal technique.
A new method for stable vector representation of persistence diagrams.
problem Finding a stable vector representation of persistence diagrams for ML tasks.
method Persistence B-spline Grid (PBSG) based on data fitting.
result The PBSG method is stable with respect to the 1-Wasserstein distance metric.
ICQ improves high-dimensional similarity search without sacrificing precision.
problem High-dimensional similarity search is computationally expensive.
method Interleaved Composite Quantization (ICQ) reduces code length and quantization error.
result ICQ achieves fast similarity search without using shorter codes.
Develops mixed quantization for graph vector bundles.
problem Solving asymptotic spectral problems on graph vector bundles.
method Mixed quantization technique for graph vector bundles.
result Applications to various spectral problems.
New algorithms improve combinatorial linear semi-bandits for clustered feature vectors.
problem Poor performance of existing algorithms in clustered feature vector cases.
method Arm-wise randomization technique to address the shortcoming.
result Proposed algorithms (PC2UCB and TS) outperform existing algorithms in clustered feature vector cases. The paper extends Bochner's technique to singular distributions on manifolds.
problem Analyzing the curvature and null space of Hodge Laplacian on singular distributions.
method Defining modified statistical connection, exterior derivative, and Weitzenbock type curvature operator.
result Derivation of Bochner-Weitzenbock type formula leading to vanishing theorems.