Instance Ranking and Numerosity Reduction Using Matrix Decomposition and Subspace Learning
One way to deal with the ever increasing amount of available data for processing is to rank data instances by usefulness and reduce the dataset size. In this work, we introduce a framework to achieve this using matrix decomposition and subspace learning. Our central contribution is a novel similarity measure for data instances that uses the basis obtained from matrix decomposition of the dataset. Using this similarity measure, we propose several related algorithms for ranking data instances and performing numerosity reduction. We then validate the effectiveness of these algorithms for data reduction on several datasets for classification, regression, and clustering tasks.
Code (1)
Tasks
ClusteringDimensionality ReductionMatrix Factorization / DecompositionPrototype SelectionregressionSimilar Papers 제목 키워드 기반
Perception of visual numerosity in humans and machines
Numerosity perception is foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representa…
Deep Spectral Improvement for Unsupervised Image Instance Segmentation
Deep spectral methods reframe the image decomposition process as a graph partitioning task by extracting features using self-supervised learning and utilizing the Laplacian of the affinity matrix to obtain eigensegments.…
graph partitioningInstance SegmentationSegmentationSelf-Supervised Learning+1Program-Synthesis-Driven Autodesign of Universal Unitary Operators
We demonstrate that AI-driven program synthesis can autonomously discover fundamental strategies for decomposing unitary matrices in photonic networks. By extending DreamCoder to complex-valued linear algebra, the system…
Program SynthesisNumber detectors spontaneously emerge in a deep neural network designed for visual object recognition
Humans and animals have a “number sense,” an innate capability to intuitively assess the number of visual items in a set, its numerosity. This capability implies that mechanisms to extract numerosity indwell the brain’…
ObjectObject RecognitionEstimating the distribution of numerosity and non-numerical visual magnitudes in natural scenes using computer vision
Humans share with many animal species the ability to perceive and approximately represent the number of objects in visual scenes. This ability improves throughout childhood, suggesting that learning and development play …