Related papers: Clustering with minimum spanning trees: How good c…
We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform…
We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations…
Tree ensembles such as random forests (RFs) and gradient boosting machines (GBMs) are among the most widely used supervised learners, yet their theoretical properties remain incompletely understood. We adopt a spectral perspective on these…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose…
The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this…
Online learning algorithms have become a ubiquitous tool in the machine learning toolbox and are frequently used in small, resource-constraint environments. Among the most successful online learning methods are Decision Tree (DT) ensembles.…
We seek to provide an interpretable framework for segmenting users in a population for personalized decision-making. We propose a general methodology, Market Segmentation Trees (MSTs), for learning market segmentations explicitly driven by…
We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned…
Categorical sequence clustering plays a crucial role in various fields, but the lack of interpretability in cluster assignments poses significant challenges. Sequences inherently lack explicit features, and existing sequence clustering…
Decision Trees are prominent prediction models for interpretable Machine Learning. They have been thoroughly researched, mostly in the batch setting with a fixed labelled dataset, leading to popular algorithms such as C4.5, ID3 and CART.…
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with $o(m)$ bits of communication, in a graph with $n$ nodes and $m$ edges. For decades, it was believed that $\Omega(m)$ bits of…
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…
In this paper, we address the problem of recovering arbitrary-shaped data clusters from datasets while facing \emph{high space constraints}, as this is for instance the case in many real-world applications when analysis algorithms are…
We consider two natural variants of the problem of minimum spanning tree (MST) of a graph in the parallel setting: MST verification (verifying if a given tree is an MST) and the sensitivity analysis of an MST (finding the lowest cost…
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…
Field level statistics, such as the minimum spanning tree (MST), have been shown to be a promising tool for parameter inference in cosmology. However, applications to real galaxy surveys are challenging, due to the presence of small scale…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…