Related papers: Configuration space of intervals with partially su…
For a path-connected space X, a well-known theorem of Segal, May and Milgram asserts that the configuration space of finite points in R^n with labels in X is weakly homotopy equivalent to the n-th loop-suspension of X. In this paper, we…
Let M be an n-manifold, and let A be a space with a partial sum behaving as an n-fold loop sum. We define the space C(M;A) of configurations in M with summable labels in A via operad theory. Some examples are symmetric products, labelled…
In this note we provide a characterization, in terms of additional algebraic structure, of those intervals (certain cocategory objects) in a symmetric monoidal closed category E that are representable in the sense of inducing on E the…
The cost and scarcity of fully supervised labels in statistical machine learning encourage using partially labeled data for model validation as a cheaper and more accessible alternative. Effectively collecting and leveraging weakly…
A characterization of simplicial objects in categories with finite products obtained by the reduced bar construction is given. The condition that characterizes such simplicial objects is a strictification of Segal's condition guaranteeing…
The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product…
The purpose of partial multi-label feature selection is to select the most representative feature subset, where the data comes from partial multi-label datasets that have label ambiguity issues. For label disambiguation, previous methods…
Annotating datasets is one of the main costs in nowadays supervised learning. The goal of weak supervision is to enable models to learn using only forms of labelling which are cheaper to collect, as partial labelling. This is a type of…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
By considering labeled configurations of ``bounded multiplicity'', one can construct a functor that fits between homology and stable homotopy. Based on previous work, we are able to give an equivalent description of this labeled…
Let $M$ be a subset of vector space or projective space. The authors define the \emph{generalized configuration space} of $M$ which is formed by $n$-tuples of elements of $M$ where any $k$ elements of each $n$-tuple are linearly…
We describe the problem of aggregating the label predictions of diverse classifiers using a class taxonomy. Such a taxonomy may not have been available or referenced when the individual classifiers were designed and trained, yet mapping the…
Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label…
Due to the expensive costs of collecting labels in multi-label classification datasets, partially annotated multi-label classification has become an emerging field in computer vision. One baseline approach to this task is to assume…
This paper aims to find the most general combinatorial conditions under which a moment-angle complex $(D^2,S^1)^K$ is a co-$H$-space, thus splitting unstably in terms of its full subcomplexes. In this way we study to which extent the…
In contrast to conventional (single-label) classification, the setting of multilabel classification (MLC) allows an instance to belong to several classes simultaneously. Thus, instead of selecting a single class label, predictions take the…
This paper introduces and studies a categorical analogue of the familiar monoid semiring construction. By introducing an axiomatisation of summation that unifies notions of summation from algebraic program semantics with various notions of…
In this article, we construct a cofibrantly generated model structure on the category of spaces stratified over a fixed poset, and show that it is Quillen-equivalent to a category of diagrams of simplicial sets. Then, considering all those…
Multi-label classification is a widely encountered problem in daily life, where an instance can be associated with multiple classes. In theory, this is a supervised learning method that requires a large amount of labeling. However,…
A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras…