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.
HiPart offers an efficient, interactive tool for hierarchical clustering.
funLOCI identifies clusters in functional data.
In this short communication we introduce the quick clustering algorithm (QUIST), an efficient hierarchical clustering algorithm based on sorting. QUIST is a poly-logarithmic divisive clustering algorithm that does not assume the number of clusters, and/or the cluster size to be known ahead of time. It is also insensiti…
Nowadays, data are generated massively and rapidly from scientific fields as bioinformatics, neuroscience and astronomy to business and engineering fields. Cluster analysis, as one of the major data analysis tools, is therefore more significant than ever. We propose in this work an effective Semi-supervised Divisive Cl…
Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.
In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic Feature Clustering model in probabilistic space with Kullbac…
We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which takes into account natural gaps in the data between clusters. Geometric features …
A clustering algorithm for natural hierarchical clusters with near-linear time complexity.
With pressure to increase graduation rates and reduce time to degree in higher education, it is important to identify at-risk students early. Automated early warning systems are therefore highly desirable. In this paper, we use unsupervised clustering techniques to predict the graduation status of declared majors in fi…
Empty core found in max-loss non-centroid clustering.
The precise diagnosis is of great significance in developing precise treatment plans to restore neck function and reduce the burden posed by the cervical spondylosis (CS). However, the current available neck function assessment method are subjective and coarse-grained. In this paper, based on the relationship among CS,…
Improved accuracy in machine learning with Cross-Cluster Weighted Forests.
Two algorithms improve K-means clustering speed without sacrificing quality.
A new proof of an extension theorem with bounded generators.
Solves division problem for L. Hörmander's systems.
Paper develops a new objective for hierarchical clustering in Euclidean space.
Proves divisibility relations for symplectic curve polynomials.
Uniform convexity in divisible domains leads to hyperbolic geometry.
New algorithm for clustering data streams with no substitutions.
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by the set of features available to the algorithm. This gives rise to the problem …
This paper converts ADMM to proximal gradient for efficient sparse estimation.
Paper tackles division difficulty, proposing new methods to improve accuracy.
New mixture models for clustering and density estimation of unknown distributions.
In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of -planes in when . Moreover, this convex divisible domain is a model of the symmetric space associ…
Division algorithm for surface group rings yields standard complexes and cohomological dimensions.
Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …
Divide-and-conquer is a general strategy to deal with large scale problems. It is typically applied to generate ensemble instances, which potentially limits the problem size it can handle. Additionally, the data are often divided by random sampling which may be suboptimal. To address these concerns, we propose the $DC^…
Understanding how spatial configurations of economic activity emerge is important when formulating spatial planning and economic policy. A simple model was proposed by Simon, who assumed that firms grow at a rate proportional to their size, and that new divisions of firms with certain probabilities relocate to other fi…
New proof of divisibility property for certain algebraic varieties.
The paper sets lower bounds on envy-free divisions in cake-cutting problems.
The paper revisits Rokhlin's divisibility theorem and its significance.
Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
In recent years, the majority of works on deep-learning-based image colorization have focused on how to make a good use of the enormous datasets currently available. What about when the data at disposal are scarce? The main objective of this work is to prove that a network can be trained and can provide excellent color…
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical cha…
Algorithm learns fair division from noisy feedback in uncertain markets.
Study of characteristic numbers in 24-dimensional String manifolds.
We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which minimise the second eigenvalue of the graph Laplacian of the projected data, whic…
An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have boundary, and have word hyperbolic divid…
In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.
Study shows non-symmetric convex sets have full boundary limits.
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic quantities as test statistics, that is, as quantities obtained from empirical data, p…
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…
Study of congestion in negative curvature manifolds using fair-division algorithms.
Research shows how certain flat structures behave in specific convex domains.