Related papers: Cluster Algebras: Network Science and Machine Lear…
While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We…
Patchwork learning arises as a new and challenging data collection paradigm where both samples and features are observed in fragmented subsets. Due to technological limits, measurement expense, or multimodal data integration, such patchwork…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
We give a precise definition of folded quivers and folded cluster algebras. We give many examples of including some with finite mutation structure that do not have analogues in the unfolded cases. We relate these examples to the finite…
Big Data processing systems handle huge unstructured and structured data to store, process, and analyze through cluster analysis which helps in identifying unseen patterns to find the relationships between them. Clustering analysis over the…
Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.
In this paper, we show that, for skew-symmetric cluster algebras, the c-vectors of any seed with respect to an acyclic initial seed define a quasi-Cartan companion of the corresponding exchange matrix. As an application, we show that any…
Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set $X$ of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization, that cannot be captured by trees. A variety of…
We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
The proposal is to use clusters, graphs and networks as models in order to analyse the Web structure. Clusters, graphs and networks provide knowledge representation and organization. Clusters were generated by co-site analysis. The sample…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…