Aggregating time-series and image data: functors and double functors
Aggregation of time-series or image data over subsets of the domain is a fundamental task in data science. We show that many known aggregation operations can be interpreted as (double) functors on appropriate (double) categories. Such functorial aggregations are amenable to parallel implementation via straightforward extensions of Blelloch's parallel scan algorithm. In addition to providing a unified viewpoint on existing operations, it allows us to propose new aggregation operations for time-series and image data.
Code (0)
등록된 구현이 없습니다.
Tasks
Time SeriesSimilar Papers 제목 키워드 기반
Learning Functors using Gradient Descent
Neural networks are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this paper we build a category-theoretic formalism around a neural networ…
Image-to-Image TranslationTranslationEffect Functors for Opinion Inference
Sentiment analysis has so far focused on the detection of explicit opinions. However, of late implicit opinions have received broader attention, the key idea being that the evaluation of an event type by a speaker depend…
Sentiment AnalysisFunctorial Clustering via Simplicial Complexes
We adapt previous research on topological unsupervised learning to characterize hierarchical overlapping clustering algorithms as functors that factor through a category of simplicial complexes. We first develop a pair o…
ClusteringThe Homunculus Brain and Categorical Logic
The interaction between syntax (formal language) and its semantics (meanings of language) is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the b…
Functorial Manifold Learning
We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning. We first characterize manifold learning algorithms as functors that map pseudo…
Clustering