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.
The paper generalizes Thurston's earthquake map to cluster algebras of finite type.
The paper provides presentations for mapping class groups and cluster automorphism groups of surfaces.
Global optimization approach for MAP clustering under Gaussian mixtures.
A new clustering framework using fixed points for data analysis.
Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Cl…
We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix repres…
DPSOM combines self-organizing maps with deep learning for better data clustering.
Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.
Develops TCD maps to relate discrete differential geometry and cluster algebras.
Paper translates train track concepts to cluster algebras for pseudo-Anosov mapping classes.
A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial ti…
Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront the so-called "crowding problem" that clusters tend to overlap with each other i…
DCMAP optimizes clustering in Bayesian Networks with dependent costs.
Integrable dynamics explained via geometric maps and cluster algebras.
Characterizes pseudo-Anosov mapping classes on general marked surfaces.
Interpolates mean shift and spectral clustering on graphs.
Proposes variational Wasserstein barycenters for geometric clustering.
This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance structures of time series which are related directly to modes in those tim…
We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction is based on the "quantum trace" map introduced by Bonahon …
Improved spectral clustering algorithm for better performance.
Unified framework for various geometric constructions.
We advocate the use of cluster algebras and their y-variables in the study of hyperbolic 3-manifolds. We study hyperbolic structures on the mapping tori of pseudo-Anosov mapping classes of punctured surfaces, and show that cluster y-variables naturally give the solutions of the edge-gluing conditions of ideal tetrahedr…
DBS uses swarm intelligence to cluster data without needing a global objective function.
Bayesian methods detect clusters in noisy data more reliably.
Efficiently clusters data on manifolds using Fréchet maps.
iCVI-ARTMAP accelerates clustering with adaptive resonance theory and validity indices.
Quantum trace maps for surfaces are shown to be compatible under triangulations.
Time series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However, these approaches do not take the similarity of the different subsequences of each …
NN-EVCLUS uses neural networks to cluster data with uncertainty.
We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we descr…
We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by …
Adaptive orthogonalization of data for clustering and visualization.
We present a framework for clustering with cluster-specific feature selection. The framework, CRAFT, is derived from asymptotic log posterior formulations of nonparametric MAP-based clustering models. CRAFT handles assorted data, i.e., both numeric and categorical data, and the underlying objective functions are intuit…
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
Algorithm maps trade-off between clustering fidelity and representation size.
We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping …
aweSOM accelerates SOM clustering for large datasets.
Previously, we proposed a physically-inspired method to construct data points into an effective in-tree (IT) structure, in which the underlying cluster structure in the dataset is well revealed. Although there are some edges in the IT structure requiring to be removed, such undesired edges are generally distinguishable…
Smile-GANs clusters brain MRI scans to reveal disease subtypes and progression.
Survey of robust clustering methods for hotspot detection.
Fixed points found in cluster modular groups under specific conditions.
We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed, symmetry-invariant representations of cluster arrangements into conditional probabilities. Th…
A neural-network model clusters subjects based on their lifetime distributions.
Proposes a new K-means method for efficient clustering of nonlinear data.
There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work with both types of data, combining them to obtain better performance for both c…
NOs can learn any finite collection of classes in functional data.
Functional neuroimaging can measure the brain?s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised learning task where the neuroimaging data are used as predictors for the stimulus. Brai…
This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topog…