arXiv research

Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high dimensions to any Euclidean space R^d manages to successfully separate the cluste…

We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.

Deep learning approaches have recently achieved impressive performance on both audio source separation and sound classification. Most audio source separation approaches focus only on separating sources belonging to a restricted domain of source classes, such as speech and music. However, recent work has demonstrated th…

Kernel embeddings separate distinct probability distributions, simplifying testing.

Isolating individual instruments in a musical mixture has a myriad of potential applications, and seems imminently achievable given the levels of performance reached by recent deep learning methods. While most musical source separation techniques learn an independent model for each instrument, we propose using a common…

Characterizes minor-minimal separating projective planar graphs and their generalizations.

The paper extends optimal transport for linear separability of sheared distributions in supervised learning.

Minimal simplicial complexes in high dimensions always contain complex links.

New proof shows no flat embedding for Petersen family graphs.

We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two handlebody. In the orientable case the embedding can be either separating or non-…

In this paper, we present a novel system that separates the voice of a target speaker from multi-speaker signals, by making use of a reference signal from the target speaker. We achieve this by training two separate neural networks: (1) A speaker recognition network that produces speaker-discriminative embeddings; (2) …

Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We combine these two active but independent lines of research and propose a new parad…

Sep-SpectralNet improves SE for broader applicability and scalability.

Many successful methods have been proposed for learning low dimensional representations on large-scale networks, while almost all existing methods are designed in inseparable processes, learning embeddings for entire networks even when only a small proportion of nodes are of interest. This leads to great inconvenience,…

Deep clustering is the first method to handle general audio separation scenarios with multiple sources of the same type and an arbitrary number of sources, performing impressively in speaker-independent speech separation tasks. However, little is known about its effectiveness in other challenging situations such as mus…

For n >2, we shall show that the group Aut(NS(M)) of simplicial automorphisms of the complex NS(M) of non-separating embedded spheres in the manifold M,connected sum of n copies of S^2 X S^1, isomorphic to the group Out(F_n) of outer automorphisms of the free group F_n, where $F_n$ is identified with the fundamental gr…

A new method improves graph node embeddings by considering both nearby and distant node similarities.

This research evaluates the quality of unsupervised embeddings using linear separability metrics.

Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respe…

Let S be an immersed horizontal surface in a 3-dimensional graph manifold. We show that the fundamental group of the surface S is quadratically distorted whenever the surface is virtually embedded (i.e., separable) and is exponentially distorted when the surface is not virtually embedded.

Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …

We analyze the spectral clustering procedure for identifying coarse structure in a data set $x_1, \dots, x_n$, and in particular study the geometry of graph Laplacian embeddings which form the basis for spectral clustering algorithms. More precisely, we assume that the data is sampled from a mixture model supported on …

In the curve complex for a surface, a handlebody set is the set of loops that bound properly embedded disks in a given handlebody bounded by the surface. A boundary set is the set of non-separating loops in the curve complex that bound two-sided, properly embedded surfaces. For a Heegaard splitting, the distance betwee…

Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation o…

We address the problem of acoustic source separation in a deep learning framework we call "deep clustering." Rather than directly estimating signals or masking functions, we train a deep network to produce spectrogram embeddings that are discriminative for partition labels given in training data. Previous deep network …

Faster, context-aware topic modeling approach unveiled.

Speech separation has been very successful with deep learning techniques. Substantial effort has been reported based on approaches over spectrogram, which is well known as the standard time-and-frequency cross-domain representation for speech signals. It is highly correlated to the phonetic structure of speech, or "how…

The unknot U in S^4 has non-unique smooth spanning 3-balls up to isotopy fixing U. Equivalently there are properly embedded non-separating 3-balls in S^1xB^3 not properly isotopic to 1xB^3. More generally there exist non-separating 3-spheres in S^1xS^3 not isotopic to 1xS^3 and non trivial elements of π_0 Diff_0(S^1xS^…

Heterophily affects GNN robustness; separating ego- and neighbor-embeddings improves defense.

This paper is devoted to the study of the embeddings of a complex submanifold $S$ inside a larger complex manifold $M$; in particular, we are interested in comparing the embedding of $S$ in $M$ with the embedding of $S$ as the zero section in the total space of the normal bundle $N_S$ of $S$ in $M$. We explicitely desc…

The paper extends graph embedding models to handle multiple relations.

Study the space of embeddings of split links in 3D and 4D.

New algorithm quantifies uncertainty in regression models for complex data types.

A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. …

There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…

Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in the fundamental group of M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a "sufficient" collection of surfaces in M, then the fundamental group of M is…

New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.

Learning a good speaker embedding is important for many automatic speaker recognition tasks, including verification, identification and diarization. The embeddings learned by softmax are not discriminative enough for open-set verification tasks. Angular based embedding learning target can achieve such discriminativenes…

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in time, the embedding vectors are inferred from a probabilistic version of word2ve…

X-DC improves speech separation by making DNNs more interpretable.

GCNs distinguish graph models based on embeddings, but depth matters.

SPIRE enables efficient federated learning for diffusion models by separating client-specific embeddings from a shared backbone.

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable $X$ lead to consistent estimators of the mean embedding of $f(X)$. For Matérn ke…

Improves visualization of high-dimensional data by correcting misleading artifacts in neighbor embedding methods.

Simple framework decouples word alignment and multilingual embedding mapping.

Learning product representations that reflect complementary relationship plays a central role in e-commerce recommender system. In the absence of the product relationships graph, which existing methods rely on, there is a need to detect the complementary relationships directly from noisy and sparse customer purchase ac…

Evaluating data separation in a geometrical space is fundamental for pattern recognition. A plethora of dimensionality reduction (DR) algorithms have been developed in order to reveal the emergence of geometrical patterns in a low dimensional visible representation space, in which high-dimensional samples similarities …

We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for manifolds commensurable with these groups, immersed incompressible surfaces lift to embe…