Related papers: Frequent Knot Discovery

Irreducible frequent patters (IFPs) are introduced for transactional databases. An IFP is such a frequent pattern (FP),(x1,x2,...xn), the probability of which, P(x1,x2,...xn), cannot be represented as a product of the probabilities of two…

New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasetsstructured as graphs. We introduce a novel class of tree-shapedpatterns called tree queries, and present algorithms for…

Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…

Itemset mining has been an active area of research due to its successful application in various data mining scenarios including finding association rules. Though most of the past work has been on finding frequent itemsets, infrequent…

Data mining techniques have been widely used in various applications. Binary search tree based frequent items is an effective method for automatically recognize the most frequent items, least frequent items and average frequent items. This…

Mining frequent itemsets from a transaction database has emerged as a fundamental problem in data mining and committed itself as a building block for many pattern mining tasks. In this paper, we present a general technique to reduce support…

Given a class of objects, a pattern theorem is a powerful result describing their structure. We show that alternating knots exhibit a pattern theorem, and use this result to prove a long-standing conjecture that alternating knots grow rare.…

Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…

In this paper a new mining algorithm is defined based on frequent item set. Apriori Algorithm scans the database every time when it finds the frequent item set so it is very time consuming and at each step it generates candidate item set.…

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…

We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various objects, including prime alternating tangles with two connected components, up to order 18--22, and comment on…

In this paper, we propose a constraint-based modeling approach for the problem of discovering frequent gradual patterns in a numerical dataset. This SAT-based declarative approach offers an additional possibility to benefit from the recent…

We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to…

The development of novel platforms and techniques for emerging "Big Data" applications requires the availability of real-life datasets for data-driven experiments, which are however out of reach for academic research in most cases as they…

Nowadays, frequent pattern mining (FPM) on large graphs receives increasing attention, since it is crucial to a variety of applications, e.g., social analysis. Informally, the FPM problem is defined as finding all the patterns in a large…

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

Data mining is the task of discovering interesting, unexpected or valuable structures in large datasets and transforming them into an understandable structure for further use . Different approaches in the domain of data mining have been…

Clustering is an important data mining technique that groups similar data records, recently categorical transaction clustering is received more attention. In this research, we study the problem of categorical data clustering for…

The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of…