A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Survey on decorated marked surfaces for Calabi-Yau categories.
Unified clustering model handles both pairwise and cardinality constraints for better performance.
We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of as intersection numbers of ta…
This paper proposes a method to reduce complexity in GLMs with categorical predictors.
This paper provides an embedding perspective to consensus clustering.
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Mémoli to par…
Constructs exotic Lagrangian tori in Grassmannians using cluster algebra.
This paper introduces PM and PMLP to enhance SSL by considering probability density and cluster assumptions.
This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations…
An unsupervised method clusters patient incident reports for content analysis.
Quantum annealing speeds up extreme clustering.
We consider the problem of learning to play first-person shooter (FPS) video games using raw screen images as observations and keyboard inputs as actions. The high-dimensionality of the observations in this type of applications leads to prohibitive needs of training data for model-free methods, such as the deep Q-netwo…
We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable objects in terms of negative geometric intersection numbers between correspondin…
In this paper, we focus on finding clusters in partially categorized data sets. We propose a semi-supervised version of Gaussian mixture model, called C3L, which retrieves natural subgroups of given categories. In contrast to other semi-supervised models, C3L is parametrized by user-defined leakage level, which control…
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi--Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We show that, in the case where the category is the generalised cluster category associated to a surface, the coloured quivers coincide. We also …
We use statistically validated networks, a recently introduced method to validate links in a bipartite system, to identify clusters of investors trading in a financial market. Specifically, we investigate a special database allowing to track the trading activity of individual investors of the stock Nokia. We find that …
Adapts category theory to manifold learning for better understanding and stability.
New algorithm clusters sparse, high-dimensional texts efficiently.
We formalize the arithmetic topology, i.e. a relationship between knots and primes. Namely, using the notion of a cluster C*-algebra we construct a functor from the category of 3-dimensional manifolds M to a category of algebraic number fields K, such that the prime ideals (ideals, resp.) in the ring of integers of K c…
Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection in GANs to cluster, we demonstrate that the cluster structure is not re…
HCRL learns hierarchical embeddings from deep embeddings of hierarchy components.
This paper explains spectral clustering and its equivalence to PCA, breaking it into fully connected and multi-connected cases.
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…
In acoustic scene classification researches, audio segment is usually split into multiple samples. Majority voting is then utilized to ensemble the results of the samples. In this paper, we propose a punishment voting algorithm based on the super categories construction method for acoustic scene classification. Specifi…
Proposes CRG_IMSC for better clustering of multi-view data.
Following widely used in visual recognition concept of relative attributes, the article establishes definition of the relative PCA attributes for a class of objects defined by vectors of their parameters. A new rating model (RELARM) is built using relative PCA attribute ranking functions for rating object description a…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic approaches. Since the most of clustering methods depend on their input parameters, it i…
Benchmark study evaluates 8 clustering methods on 99 UCR time series datasets.
The study finds that the export shares of machinery and food/crude materials are significantly correlated with GDP.
Adversarial MoE learns category-specific models for product search.
A new clustering algorithm inspired by Wittgenstein's philosophy.
Kan extensions help in data science extrapolation and learning.
A new algorithm identifies outliers in Gaussian clustering models.
We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approach to analyzing biological networks yields results that are as good as or better than state of the art existing approaches.
Nowadays, financial data analysis is becoming increasingly important in the business market. As companies collect more and more data from daily operations, they expect to extract useful knowledge from existing collected data to help make reasonable decisions for new customer requests, e.g. user credit category, confide…
We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface with marked points and non-empty boundary, which generalizes Brüstle-Zhang's result for the puncture free case. As an application, we show that the intersection of the shi…
Solves complex clustering and rotation synchronization problem.
In this study, we establish a network structure of the Korean stock market, one of the emerging markets, with its minimum spanning tree through the correlation matrix. Base on this analysis, it is found that the Korean stock market doesn't form the clusters of the business sectors or of the industry categories. When th…
Study evaluates clustering methods for Google Trends data.
The paper constructs tilting modules for knots using algebraic structures.
The contraction inequality for Rademacher averages is extended to Lipschitz functions with vector-valued domains, and it is also shown that in the bounding expression the Rademacher variables can be replaced by arbitrary iid symmetric and sub-gaussian variables. Example applications are given for multi-category learnin…
Spectral clustering adapted for mixed data types without preprocessing.
In many applications that involve processing high-dimensional data, it is important to identify a small set of entities that account for a significant fraction of detections. Rather than formalize this as a clustering problem, in which all detections must be grouped into hard or soft categories, we formalize it as an i…
Develops a measure for checking cluster quality using multinomial distribution.
PAM models generate dependent random distributions across groups with overlapping clusters.
New clustering method for uncertain data using Wasserstein barycenters.
New method tackles instance segmentation on 3D point clouds with improved metrics.
Deep learning improves community detection in graph datasets.