arXiv research

Detect anomalies in complex networks using topological subspace detectors.

Adversarial attacks have always been a serious threat for any data-driven model. In this paper, we explore subspaces of adversarial examples in unitary vector domain, and we propose a novel detector for defending our models trained for environmental sound classification. We measure chordal distance between legitimate a…

In unsupervised outlier ensembles, the absence of ground truth makes the combination of base outlier detectors a challenging task. Specifically, existing parallel outlier ensembles lack a reliable way of selecting competent base detectors, affecting accuracy and stability, during model combination. In this paper, we pr…

A new method detects outliers using ensembles of Dirichlet process mixtures.

New algebraic structures for topological pairs.

Interactive art piece shows braid groups and plane motions.

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a …

Finite group action on a surface yields a special homology subspace.

Study the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds.

In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the last decade, researchers proposed many new (non-linear) techniques for dimensio…

Morse neural networks improve uncertainty quantification and detection.

Stability result for nearly isometric subspaces and Finsler surfaces.

Adversarial perturbations fool deepfake detectors with high accuracy.

This paper studies concept drift detectors for financial time series.

Classifies big mapping classes on infinite type surfaces.

The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-…

We explore the use of graph networks to deal with irregular-geometry detectors in the context of particle reconstruction. Thanks to their representation-learning capabilities, graph networks can exploit the full detector granularity, while natively managing the event sparsity and arbitrarily complex detector geometries…

In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces de…

We obtain two in a sense dual to each other results: First, that the capacity dimension of every compact, locally self-similar metric space coincides with the topological dimension, and second, that the asymptotic dimension of a metric space, which is asymptotically similar to its compact subspace coincides with the to…

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

In this paper, deep neural network (DNN) is utilized to improve the belief propagation (BP) detection for massive multiple-input multiple-output (MIMO) systems. A neural network architecture suitable for detection task is firstly introduced by unfolding BP algorithms. DNN MIMO detectors are then proposed based on two m…

New method uses neural networks to estimate parameters without needing detector simulations.

The anomaly detection of time series is a hotspot of time series data mining. The own characteristics of different anomaly detectors determine the abnormal data that they are good at. There is no detector can be optimizing in all types of anomalies. Moreover, it still has difficulties in industrial production due to pr…

KPCA improves OoD detection by separating InD and OoD data.

For an infinite cardinal $κ$ let $\ell_2(κ)$ be the linear hull of the standard othonormal base of the Hilbert space $\ell_2(κ)$ of density $κ$. We prove that a non-separable convex subset $X$ of density $κ$ in a locally convex linear metric space if homeomorphic to the space (i) $\ell_2^f(κ)$ if and only if $X$ can be…

We introduce a Bayesian defect detector to facilitate the defect detection on the motion blurred images on rough texture surfaces. To enhance the accuracy of Bayesian detection on removing non-defect pixels, we develop a class of reflected non-local prior distributions, which is constructed by using the mode of a distr…

Modern smart grids rely on advanced metering infrastructure (AMI) networks for monitoring and billing purposes. However, such an approach suffers from electricity theft cyberattacks. Different from the existing research that utilizes shallow, static, and customer-specific-based electricity theft detectors, this paper p…

TomOpt optimizes muon detector designs using differentiable programming.

In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact …

ImageNet pre-training has been regarded as essential for training accurate object detectors for a long time. Recently, it has been shown that object detectors trained from randomly initialized weights can be on par with those fine-tuned from ImageNet pre-trained models. However, the effects of pre-training and the diff…

Improves relevancy of black-box anomaly detectors with user feedback.

The paper studies the Poisson transform of differential forms on hyperbolic spaces.

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full r…

For Riem(M) the space of Riemannian metrics over a compact 3-manifold without boundary $M$, we study topological properties of the dense open subspace Riem'(M) of metrics which possess no Killing vectors. Given the stratification of Riem(M), we work under the condition that, in a sense defined in the text, the connecte…

Selecting and combining the outlier scores of different base detectors used within outlier ensembles can be quite challenging in the absence of ground truth. In this paper, an unsupervised outlier detector combination framework called DCSO is proposed, demonstrated and assessed for the dynamic selection of most compete…

New non-semisimple Ising anyons enable robust universal quantum computation.

In this paper, we consider signal detection algorithms in a multiple-input multiple-output (MIMO) decode-forward (DF) relay channel with one source, one relay, and one destination. The existing suboptimal near maximum likelihood (NML) detector and the NML with two-level pair-wise error probability (NMLw2PEP) detector a…

Novel unsupervised MIG detectors improve signal detection in cluttered environments.

Unified detector calibration and simulation using MLE from generative models.

We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the group-compact coarse structure generalizing several familiar results for discrete group…

This paper proposes a generic classification system designed to detect security threats based on the behavior of malware samples. The system relies on statistical features computed from proxy log fields to train detectors using a database of malware samples. The behavior detectors serve as basic reusable building block…

The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show that, like the Grassmannian, the affine Grassmannian has rich geometrical and topolo…

The paper studies affine manifolds with linear foliations and their topological properties.

In this paper we study the real time deployment of deep learning algorithms in low resource computational environments. As the use case, we compare the accuracy and speed of neural networks for smile detection using different neural network architectures and their system level implementation on NVidia Jetson embedded p…

Autoencoders misidentify anomalies due to data topology.

Study geodesics in 3-torus, determining complements' topology.

DALC customizes LSTM models for detectors in large-scale traffic networks.

Spectrum sensing is of critical importance in any cognitive radio system. When the primary user's signal has uncertain parameters, the likelihood ratio test, which is the theoretically optimal detector, generally has no closed-form expression. As a result, spectrum sensing under parameter uncertainty remains an open qu…