arXiv research

This paper presents a new insight into improving the performance of Stochastic Neighbour Embedding (t-SNE) by using Isolation kernel instead of Gaussian kernel. Isolation kernel outperforms Gaussian kernel in two aspects. First, the use of Isolation kernel in t-SNE overcomes the drawback of misrepresenting some structu…

Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. A current key approach focuses on ways to produce an approximate finite-dimensional feature map, assuming that the kernel used has a feature map wit…

MIK improves t-SNE's local structure preservation in biological sequence data.

IDK improves anomaly detection for points and groups without explicit learning.

Develops a machine learning method for parameter estimation in branching processes models.

Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the…

A recent proposal of data dependent similarity called Isolation Kernel/Similarity has enabled SVM to produce better classification accuracy. We identify shortcomings of using a tree method to implement Isolation Similarity; and propose a nearest neighbour method instead. We formally prove the characteristic of Isolatio…

Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced directly from the residue theorem of Jeffrey and Kirwan. A characterization of the ke…

In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for…

TIME network simplifies complex physical processes with interpretable models.

The analysis of holomorphic sections of high powers $L^N$ of holomorphic ample line bundles $L\to M$ over compact Kähler manifolds has been widely applied in complex geometry and mathematical physics. The Tian-Yau-Zelditch's asymptotic expansion of the Szegö kernel of a circle bundle plays an important role in Kähler-E…

Assume that the circle group acts holomorphically on a compact Kähler manifold with isolated fixed points and that the action can be lifted holomorphically to a holomorphic Hermitian vector bundle. We give a heat kernel proof of the equivariant holomorphic Morse inequalities. We use some techniques developed by Bismut …

From a fibered link in the 3-sphere may be constructed a field of not everywhere tangent 2-planes; when the fibered link is the link of an isolated critical point of a map from 4-space to the plane, the plane field is essentially the field of kernels of the derivative of the map. Homotopically, such a plane field deter…

Given an associative 3-fold in R^7 which is asymptotically conical with generic rate less than 1, we show that its moduli space of deformations is locally homeomorphic to the kernel of a smooth map between smooth manifolds. Moreover, the virtual dimension of the moduli space is computed and shown to be non-negative for…

We prove that the half-integer valued local index of an isolated umbilic point on a $C^{3+α}$-smooth convex surface in Euclidean 3-space is less than two. The approach is to study the co-kernel of an associated Riemann-Hilbert boundary value problem. The link between the local and global is a semi-local technique that …

Study local convergence of GDA for training GANs with kernel-based discriminators.

DKMD is a fast signed statistic for comparing univariate distributions.

We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that …

The paper identifies all link projections with isolate-region number one.

New method controls false discoveries in structured hypothesis spaces.

Efficiently computes sparse signature coefficients using kernels.

In this paper we define a new convergence called "asymptotically conic convergence" in which a smooth family of Riemannian metrics on a fixed compact manifold degenerate to a metric with isolated conic singularity. Our results are: convergence of the spectrum of the geometric Laplacians and uniform convergence of the c…

Study irrational pencils on complex manifolds, finding non-finitely generated homology.

The paper develops CI tests for causal discovery in SDEs.

Study of $G_2$-structures with isolated singularities and bounded torsion.

Framework isolates causal effects from time series data, improving accuracy under non-stationarity and autocorrelation.

New stability and isolation results for Einstein manifolds.

Map quandle orders to actions, characterize isolated orders, and prove no isolated right orders.

Improved spectral clustering via Gromov-Wasserstein Learning.

A new DML method for continuous treatments uncovers causal mediation effects.

STRIDE improves explainable AI by efficiently decomposing feature interactions without subset enumeration.

Study of singular solutions to a fourth order system in a ball with a singularity.

Defines Perelman's functionals on manifolds with non-isolated conical singularities.

iMondrian forest combines isolation forest and Mondrian forest for better anomaly detection.

We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower bound theorems when the singularities are also homological…

We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces. We prove that the geometric boundary of the space is an invariant of the group up to equivariant homeomorphism. We also prove that…

In this paper, we discuss the general existence theory of Dirac-harmonic maps from closed surfaces via the heat flow for $α$-Dirac-harmonic maps and blow-up analysis. More precisely, given any initial map along which the Dirac operator has nontrivial minimal kernel, we first prove the short time existence of the heat f…

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Quantifies how geodesic planes isolate in hyperbolic 3-manifolds.

We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.

Study reveals GAGA phenomenon in Poisson cohomology for plane structures with isolated singularities.

Proves conditions for positive scalar curvature on certain manifolds with conical singularities.

The paper presents a method to reduce computational and storage costs in PCA and spectral clustering.

We study the Euler obstruction of essentially isolated determinantal singularities (EIDS). The EIDS were defined by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity. We obtain some formulas to calculate the Euler obstruction for the determinantal varieties with singular set an ICIS.

The paper builds complex hyperbolic 2-manifolds with isolated singularities.

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Robert Bryant (Theorie des varietes minimales et applications, 1988, 154: 321-347) proved that an isolated singularity of a conformal metric of positive constant curvature on a Riemann surface is a conical one. Using Complex Analysis, we find all of the local models for an isolated singularity of a flat metric whose ar…

Study on solutions near isolated singularities in 6D Yamabe equation.