Related papers: Efficient Algorithms for Finding Tucker Patterns
In this paper a novel biclustering algorithm based on artificial intelligence (AI) is introduced. The method called EBIC aims to detect biologically meaningful, order-preserving patterns in complex data. The proposed algorithm is probably…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our…
The Aho, Hopcroft and Ullman (AHU) algorithm has been the state of the art since the 1970s for determining in linear time whether two unordered rooted trees are isomorphic or not. However, it has been criticized (by Campbell and Radford)…
Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems…
We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…
A time series is a collection of measurements in chronological order. Discovering patterns from time series is useful in many domains, such as stock analysis, disease detection, and weather forecast. To discover patterns, existing methods…
Given some binary matrix $M$, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the unique original orderings and matrix? We present an…
Boolean matrix factorization is a natural and a popular technique for summarizing binary matrices. In this paper, we study a problem of Boolean matrix factorization where we additionally require that the factor matrices have consecutive…
Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential…
Given a log and a specification, timed pattern matching aims at exhibiting for which start and end dates a specification holds on that log. For example, "a given action is always followed by another action before a given deadline". This…
The classic exact pattern matching problem, given two strings -- a pattern $P$ of length $m$ and a text $T$ of length $n$ -- asks whether $P$ occurs as a substring of $T$. A property tester for the problem needs to distinguish (with high…
A Transaction database contains a set of transactions along with items and their associated timestamps. Transitional patterns are the patterns which specify the dynamic behavior of frequent patterns in a transaction database. To discover…
In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group $G$ satisfying the Triple Product Property (TPP) as a means to bound the exponent $\omega$ of matrix…
Discovering frequent trends in time series is a critical task in data mining. Recently, order-preserving matching was proposed to find all occurrences of a pattern in a time series, where the pattern is a relative order (regarded as a…
We have found that known community identification algorithms produce inconsistent communities when the node ordering changes at input. We propose two metrics to quantify the level of consistency across multiple runs of an algorithm:…
A new condition, the strong inner product property, is introduced and used to construct sign patterns of row orthogonal matrices. Using this property, infinite families of sign patterns allowing row orthogonality are found. These provide…
A matrix is called totally negative (totally non-positive) of order $k$, if all its minors of size at most $k$ are negative (non-positive). The objective of this article is to provide several novel characterizations of total negativity via…