New model combines shape and feature-based measures for better time series classification.
problem Limited approaches in time series classification lead to poor results for some classes.
method Proposes a new model that automatically decides between shape and feature-based measures.
result Improves classification accuracy statistically significantly on real-world datasets.
Consumer Demand Response (DR) is an important research and industry problem, which seeks to categorize, predict and modify consumer's energy consumption. Unfortunately, traditional clustering methods have resulted in many hundreds of clusters, with a given consumer often associated with several clusters, making it diff…
Shapelet transform improves time series classification for earthquake, wind, and wave events.
problem Autonomous detection of specific events from large time series datasets in civil engineering.
method Shapelet transform for local similarity in time series subsequences, combined with machine learning.
result Shapelet transform yields a new feature representation for time series signals in civil engineering.
New algebraic rules for 5D shapes based on 3D cocycles.
problem Creating rules for 5D shapes.
method Using simplicial 3-cocycles to parameterize heptagon relations.
result Parameterized heptagon relations for 5D shapes.
Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and dynamic programming.
Benchmark study evaluates 8 clustering methods on 99 UCR time series datasets.
problem Assessing the performance of clustering methods on time series data.
method Examines 8 clustering methods across 3 categories and 3 distance measures on 99 UCR datasets.
result Provides a comprehensive dataset-level assessment of clustering methods.
Convolutional Neural Networks (CNNs) are commonly thought to recognise objects by learning increasingly complex representations of object shapes. Some recent studies suggest a more important role of image textures. We here put these conflicting hypotheses to a quantitative test by evaluating CNNs and human observers on…
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying …
EQShapelets detect earthquakes with high accuracy and interpretability.
problem Automated detection and cataloging of earthquakes.
method Time-series shape-based approach embedded in machine learning.
result EQShapelets detected all cataloged and 281 uncataloged events with lower false detection rate.
Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that integrating multiple input representations leads to state-of-the-art results. In p…
New method reconstructs 3D shapes from 2D images using Kendall's shape space.
problem Reconstruct 3D shapes from 2D images, especially for rare specimens.
method Kendall's shape space approach with prior information.
result More robust and plausible shapes compared to previous methods.
Efficient method for shape modeling invariant to rigid motion.
problem Statistical shape modeling for rigidly moving shapes.
method Non-Euclidean Lie group analysis of metric distortion and curvature.
result Outperforms state-of-the-art classifiers in sparse data.
Studying the impact of climate change on precipitation is constrained by finding a way to evaluate the evolution of precipitation variability over time. Classical approaches (feature-based) have shown their limitations for this issue due to the intermittent and irregular nature of precipitation. In this study, we prese…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right elements and geometrically composing them through basic set opera…
This paper proposes a new Nystrom-based clustering algorithm for large-scale data.
problem Spectral clustering's high computational complexity for large-scale data.
method Centroid Minimum Sum of Squared Similarities (CMS3) sampling procedure with eigen spectrum shape heuristic.
result Competitive low-rank approximations in test datasets compared to state-of-the-art methods.
The study optimizes cell membranes' shapes based on curvature and proves existence of minimizers.
problem Optimizing cell membranes' shapes with respect to curvature.
method Modeling cell membranes as optimal shapes with L2-deficit of mean curvature to spontaneous curvature, and proving lower semi-continuity and existence of minimizers. result Smoothly embedded minimizers and diameter bounds are obtained.
How is popularity gained online? Is being successful strictly related to rapidly becoming viral in an online platform or is it possible to acquire popularity in a steady and disciplined fashion? What are other temporal characteristics that can unveil the popularity of online content? To answer these questions, we lever…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determin…
Left atrium shape has been shown to be an independent predictor of recurrence after atrial fibrillation (AF) ablation. Shape-based representation is imperative to such an estimation process, where correspondence-based representation offers the most flexibility and ease-of-computation for population-level shape statisti…
We investigate the robustness properties of image recognition models equipped with two features inspired by human vision, an explicit episodic memory and a shape bias, at the ImageNet scale. As reported in previous work, we show that an explicit episodic memory improves the robustness of image recognition models agains…
We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end, we propose the stochastic wreath process, a fully generative probabilistic model…
Improves CNN robustness by reducing texture bias.
problem CNNs' reliance on local texture over global shape.
method Inspired by human vision, InfoDrop decorrelates model output from local texture.
result Enhanced robustness across various scenarios.
Data driven segmentation is an important initial step of shape prior-based segmentation methods since it is assumed that the data term brings a curve to a plausible level so that shape and data terms can then work together to produce better segmentations. When purely data driven segmentation produces poor results, the …
This research optimizes fluid-dynamic designs using deep learning and active learning.
problem Expensive and limited empirical design verification for fluid dynamics.
method Applied a deep learning architecture to predict and optimize fluid dynamics performance.
result Reduced the number of required simulation data points from ~8000 to 625.
Improves functional linear regression with shape transfer learning.
problem Data scarcity in functional linear models.
method Shape-based transfer learning from auxiliary to target domains.
result Enhances robustness and generalizability of functional linear models.
Short-term road traffic prediction (STTP) is one of the most important modules in Intelligent Transportation Systems (ITS). However, network-level STTP still remains challenging due to the difficulties both in modeling the diverse traffic patterns and tacking high-dimensional time series with low latency. Therefore, a …
Program synthesis struggles with complex spatial relationships in image classification.
problem Challenges in solving Synthetic Visual Reasoning Test problems.
method Quantitative reanalysis of human and machine performance, improved program synthesis classifier, categorization of SVRT problems.
result Program synthesis is constrained by spatial relationships in images, not just shape specification.
Study analyzes neural network models to understand generalization performance.
problem Understanding good generalization in neural networks.
method Analyzed a corpus of models from a public contest, breaking ALPHAHAT into scale and shape metrics.
result Identified a Simpson's paradox in metric performance across different model depths and regularization hyperparameters.
Study invariant measures on measured laminations for subgroups of mapping class group.
problem Classify invariant Radon measures on space of measured laminations for subgroups of mapping class group.
method Geometric approach, focusing on recurrent measured laminations, explicitly constructing ergodic measures.
result Show uniquely ergodic for divergence-type subgroups, generalize results for full mapping class group.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
The Bergman measure converges to the Zhang measure on a hybrid space.
problem Proving convergence of Bergman measures to Zhang measure.
method Analyzing convergence on a hybrid space and metrized curve complex.
result Bergman measure converges to Zhang measure on a hybrid space.
Bayesian approach to robust risk measures under model uncertainty.
problem Representing robust risk measures as a single probability measure.
method Introducing two types of risk measures and analyzing their relation to robust risk measures.
result Robust risk measures can be represented by a mixture probability measure, a Bayesian approach.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Introduces Star-Shaped deviation measures for risk analysis.
problem Risk measurement and analysis in finance.
method Characterizes Star-Shaped deviation measures through acceptance sets and convex deviation measures.
result Exposes the relationship between Star-Shaped risk measures and deviation measures.
Transformers can interpolate between arbitrary measures.
problem Understanding the expressive power of Transformers as measure-to-measure maps.
method Provided an explicit choice of parameters for a single Transformer to match N arbitrary input measures to N arbitrary target measures.
result A single Transformer can interpolate between arbitrary measures.
Classifies invariant measures on specific character varieties.
problem Classifying invariant probability measures on character varieties.
method Measure disintegration along transverse Lagrangian tori fibrations.
result Ergodic measures are either counting measures on finite orbits or Liouville measures.
Paper characterizes star-shaped risk measures and their properties.
problem Characterizing risk measures in the presence of liquidity risk and competitive delegation.
method Characterization of star-shaped risk measures, study of their properties.
result Star-shaped risk measures include all practically used risk measures.
Paper introduces quasi-logconvex risk measures and their properties.
problem Characterizing and understanding new risk measures.
method Characterization through dual representation and properties of acceptance sets.
result Established dual representation and taxonomy of quasi-logconvex risk measures.
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
New geometric measure simplifies complex analysis.
problem Complex geometric analysis challenges.
method Geometric integration and convergence methods.
result Smallest measure satisfying Area Formula.
The paper explores non-convex risk measures and their characterizations.
problem Characterizing non-convex risk measures without convexity or weak convexity.
method Characterizes monetary risk measures as lower envelopes of families of convex or coherent risk measures, considering law-invariance and SSD-consistency.
result Unified representation theorems for law-invariant risk measures, including VaR.
The paper calculates extreme measures in continuous time conic finance.
problem Determining valuation bounds for financial claims.
method Using dynamic spectral risk measures and estimating extreme measures from market data.
result Explicit formulas for extreme measures' Radon-Nykodim derivatives and estimation methods.
Paper characterizes monotonic mean-deviation risk measures.
problem Developing consistent risk measures from mean-deviation models.
method Applying a risk-weighting function to the deviation part of a mean-deviation model.
result Characterizes monotonic mean-deviation measures as consistent risk measures.
One often finds in the literature connections between measures of fairness and measures of feature importance employed to interpret trained classifiers. However, there seems to be no study that compares fairness measures and feature importance measures. In this paper we propose ways to evaluate and compare such measure…
Introduces factor risk measures to assess risk relative to multiple factors.
problem Measuring risk relative to multiple factors.
method Introduces a double-argument mapping as a risk measure to assess risk relative to a vector of factors.
result Characterizes various types of factor risk measures including distortion, quantile, linear, and coherent measures.
Dual representations for robust risk measures and uncertainty sets.
problem Characterizing continuity of robust risk measures and their uncertainty sets.
method Develop dual representations for robust risk measures and uncertainty sets based on distinct geometric assumptions.
result Two dual frameworks for consolidated uncertainty sets are complementary, not interchangeable.
A scalable approach to learning from probability measures using quantization.
problem Efficiently comparing and manipulating large sets of probability measures.
method Quantization of probability measures to a fixed support, followed by optimal transport computations.
result Consistency and convergence guarantees for quantized measures in various OT-based tasks.
Study on measurable pseudo-Anosov maps on surfaces.
problem Characterize dynamics of pseudo-Anosov maps on surfaces.
method Analyze measurable pseudo-Anosov homeomorphisms with specific properties.
result Prove transitivity, dense periodic points, sensitivity, and ergodicity.