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Hidden Markov Models (HMMs) are powerful tools for modeling sequential data, where the underlying states evolve in a stochastic manner and are only indirectly observable. Traditional HMM approaches are well-established for linear sequences,…
In this paper, we propose the Ordered Median Tree Location Problem (OMT). The OMT is a single-allocation facility location problem where p facilities must be placed on a network connected by a non-directed tree. The objective is to minimize…
Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…
Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree…
Cartesian tree matching is a form of generalized pattern matching where a substring of the text matches with the pattern if they share the same Cartesian tree. This form of matching finds application for time series of stock prices and can…
This paper presents a batch-parallel 2-3 tree T in an asynchronous dynamic multithreading model that supports searches, insertions and deletions in sorted batches and has essentially optimal parallelism, even under the restrictive QRMW…
It is widely known that there is a lot of useful information hidden in big data, leading to a new saying that "data is money." Thus, it is prevalent for individuals to mine crucial information for utilization in many real-world…
We face a need of discovering a pattern in locations of a great number of points in a high-dimensional space. Goal is to group the close points together. We are interested in a hierarchical structure, like a B-tree. B-Trees are…
A consensus tree is a phylogenetic tree that synthesizes a given collection of phylogenetic trees, all of which share the same leaf labels but may have different topologies, typically obtained through bootstrapping. Our research focuses on…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Frequent pattern mining is a key area of study that gives insights into the structure and dynamics of evolving networks, such as social or road networks. However, not only does a network evolve, but often the way that it evolves, itself…
In this paper we describe an algorithm that embeds a graph metric $(V,d_G)$ on an undirected weighted graph $G=(V,E)$ into a distribution of tree metrics $(T,D_T)$ such that for every pair $u,v\in V$, $d_G(u,v)\leq d_T(u,v)$ and…
Tucker decomposition has been widely used in a variety of applications to obtain latent factors of tensor data. In these applications, a common need is to compute Tucker decomposition for a given time range. Furthermore, real-world tensor…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…
Decision trees are one of the most widely used nonparametric methods for regression and classification. In existing literature, decision tree-based methods have been used for estimating continuous functions or piecewise-constant functions.…
The main purpose of data mining and analytics is to find novel, potentially useful patterns that can be utilized in real-world applications to derive beneficial knowledge. For identifying and evaluating the usefulness of different kinds of…
We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…
This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…
Constraint-based pattern discovery is at the core of numerous data mining tasks. Patterns are extracted with respect to a given set of constraints (frequency, closedness, size, etc). In the context of sequential pattern mining, a large…