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Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…
Taxonomy construction is not only a fundamental task for semantic analysis of text corpora, but also an important step for applications such as information filtering, recommendation, and Web search. Existing pattern-based methods extract…
We analyze the combinatorics behind the operation of taking the logarithm of the generating function $G_k$ for $k^\text{th}$ generalized Catalan numbers. We provide combinatorial interpretations in terms of lattice paths and in terms of…
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
Clustering mechanisms are essential in certain multiuser networks for achieving efficient resource utilization. This lecture note presents the theory of coalition formation as a useful tool for distributed clustering problems. We reveal the…
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…
This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…
We present a new theoretical framework for modelling the fusion process of Lennard-Jones (LJ) clusters. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we…
Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$ have the structure of…
With the huge upsurge of information in day-to-days life, it has become difficult to assemble relevant information in nick of time. But people, always are in dearth of time, they need everything quick. Hence clustering was introduced to…
We describe an algorithm for the Rosenbluth Monte Carlo enumeration of clusters and lattice animals. The method may also be used to calculate associated properties such as moments or perimeter multiplicities of the clusters. The new scheme…
Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation…
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions…
When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a…
Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…
Randomly generating structured objects is important in testing and optimizing functional programs, whereas generating random $'l$-terms is more specifically needed for testing and optimizing compilers. For that a tool called QuickCheck has…
We review some basic methodologies from pattern recognition that can be applied to helping solve combinatorial problems in free group theory. We illustrate how this works with recognizing Whitehead minimal words in free groups of rank 2.…
High dimensional Gaussian graphical models provide a rigorous framework to describe a network of statistical dependencies between entities, such as genes in genomic regulation studies or species in ecology. Penalized methods, including the…