arXiv research

Proposes a hierarchical clustering method for positive and negative dissimilarities.

DTE uses tree leaf means to embed data, balancing accuracy and speed.

We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, $G$ admits quasi-isometric group embeddings into a pure braid group and into the area-preserving diffeomorphism groups of the 2--disk an…

Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram $L$, there is an associated ribbon graph whose quasi-trees correspond bijectively to …

The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that enables to build ultra-sparse NN (u-NN) graphs with guaranteed preservation of the or…

Interpretable surrogates of black-box predictors trained on high-dimensional tabular datasets can struggle to generate comprehensible explanations in the presence of correlated variables. We propose a model-agnostic interpretable surrogate that provides global and local explanations of black-box classifiers to address …

Protein Thoughts interprets protein interactions with clear reasoning, improving prediction accuracy.

Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior work, we first advocate for using hyperbolic spaces which provably model tree-li…

Study on embedding tree products into groups, distinguishing them.

Paper presents a new method for learning hyperbolic representations using tree structures.

New method embeds phylogenetic trees for clustering, recovering evolutionary relationships.

The Farey tree helps embed rational balls and lens spaces into complex projective space.

New Lie-group methods preserve geometric divergence-free features on manifolds.

Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront the so-called "crowding problem" that clusters tend to overlap with each other i…

Spaces of circle embeddings in curved surfaces indexed by trees.

We show that for each n\ge 2 there is a quasi-isometric embedding of the hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding H^2 --> TxR^m for any metric tree T and any m\ge 0.

The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and prediction tractable by assuming that the training label matrix is low-rank and hen…

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…

We prove the equivalence between a relative bottleneck property and being quasi-isometric to a tree-graded space. As a consequence, we deduce that the quasi-trees of spaces defined axiomatically by Bestvina-Bromberg-Fujiwara are quasi-isometric to tree-graded spaces. Using this we prove that mapping class groups quasi-…

Paper introduces algorithms for private decision tree learning.

We prove that every visual Gromov hyperbolic space X whose boundary at infinity has the finite capacity dimension n admits a quasi-isometric embedding into (n+1)-fold product of metric trees.

Curvature regularization prevents distortion in graph embeddings.

It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…

A new method for hierarchical clustering using continuous embeddings and optimization.

Maximal representations are studied using tree embeddings and geodesic currents.

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…

Federated Extra-Trees protects privacy while improving machine learning performance.

Rectified decision trees improve machine learning interpretability and effectiveness.

We study isometric actions of tree automorphism groups on the infinite-dimensional hyperbolic spaces. On the one hand, we exhibit a general one-parameter family of such representations and analyse the corresponding equivariant embeddings of the trees, showing that they are convex-cocompact and asymptotically isometric.…

Study on inflection points of plane curve shadows with fixed embedded shapes.

Sparse oblique decision tree improves security rules for renewable power systems.

Graph regularized autoencoder improves anomaly detection performance.

SX-GeoTree improves spatially coherent explanations in geospatial regression trees.

Various standard texts on differential topology maintain that the level-preserving map defined by the track of an isotopy of embeddings is itself an embedding. This note describes a simple counterexample to this assertion.

EmDT generates synthetic fraud data to improve detection accuracy.

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., $A_n$, $D_n$, $E_6$, $E_7$ and $E_8$…

A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.

Proposes a deep tree-ensemble model for multi-output prediction.

Enhances binomial model with machine learning for microstructure effects.

This paper develops embeddings that preserve likelihood-based statistical inference.

We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms preserving the set of elliptic subgroups).

This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.

A new method, tree-SNE, solves the scale problem in t-SNE.

Let ${\mathcal H}$ be the group of isotopy classes of orientation preserving homeomorphisms of $S^3$ that preserve a Heegaard splitting of genus two. In this paper, we use a tree in the barycentric subdivision of the disk complex of a handlebody of the splitting to obtain a finite presentation of ${\mathcal H}$.

Smooth fractal trees via analytic generators, preserving combinatorial and geometric properties.

Develops a binary tree model for option pricing with skew dynamics.

Higher-order proximity preserved network embedding has attracted increasing attention. In particular, due to the superior scalability, random-walk-based network embedding has also been well developed, which could efficiently explore higher-order neighborhoods via multi-hop random walks. However, despite the success of …

Paper develops a new method for game options in local volatility models.