arXiv research

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…

A new measure DCSI quantifies separability for density-based clustering.

New graph types help identify complex relationships.

We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.

New examples show some convex-cocompact subgroups are separable.

Criterion for subgroup separability in outer automorphism groups.

DSI measures dataset separability for neural networks.

Neural networks can separate non-separable data using feature maps.

This paper proposes a multichannel source separation technique called the multichannel variational autoencoder (MVAE) method, which uses a conditional VAE (CVAE) to model and estimate the power spectrograms of the sources in a mixture. By training the CVAE using the spectrograms of training examples with source-class l…

Constructs classifiers for neural networks with specific data configurations.

This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vec…

We consider the online multiclass linear classification under the bandit feedback setting. Beygelzimer, Pál, Szörényi, Thiruvenkatachari, Wei, and Zhang [ICML'19] considered two notions of linear separability, weak and strong linear separability. When examples are strongly linearly separable with margin $γ$, they prese…

Paper examines Dehn twists on non-orientable surfaces and their limitations.

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

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…

Fisher loss improves deep domain adaptation by learning discriminative within-class compact and between-class separable representations.

Paper optimizes hyperspherical prototypes for better class separation.

New approach for classification using trigonometric polynomial kernels from signal processing.

In this paper, a novel feature selection method is presented, which is based on Class-Separability (CS) strategy and Data Envelopment Analysis (DEA). To better capture the relationship between features and the class, class labels are separated into individual variables and relevance and redundancy are explicitly handle…

We consider Aubry-Mather theory for a subclass of class A spacetimes, i.e. compact vicious spacetimes with globally hyperbolic Abelian cover. In this subclass, called class A_1, we obtain improved results on timelike maximizers and Lipschitz continuity of the time separation of the Abelian cover on the i.g. optimal sub…

NullSpaceNet maps inputs to a joint-nullspace for clearer class separability.

Shallow nonlinear networks can separate classes linearly with polynomially scaling width.

We consider neural network training, in applications in which there are many possible classes, but at test-time, the task is a binary classification task of determining whether the given example belongs to a specific class, where the class of interest can be different each time the classifier is applied. For instance, …

We compute the Floer homology of mapping classes which do not have any pseudo-Anosov components in the sense of Thurston's theory of surface diffeomorphisms. The formula for the Floer homology is obtained from a topological separation of fixed points and a separation mechanism for Floer connecting orbits. As examples, …

We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and relevant homomorphisms are also calculable in quadratic time. The algorithm also dec…

In this paper, we focus on the separability of classes with the cross-entropy loss function for classification problems by theoretically analyzing the intra-class distance and inter-class distance (i.e. the distance between any two points belonging to the same class and different classes, respectively) in the feature s…

We quantify the separation between the numbers of labeled examples required to learn in two settings: Settings with and without the knowledge of the distribution of the unlabeled data. More specifically, we prove a separation by $Θ(\log n)$ multiplicative factor for the class of projections over the Boolean hypercube o…

We show that mapping class groups of surfaces of genus at least two contain elements of infinite order that are not conjugate to their inverses, but whose powers have bounded torsion lengths. In particular every homogeneous quasi-homomorphism vanishes on such an element, showing that elements of infinite order not conj…

New findings on robust learning with well-separated data.

The paper solves optimal bounds for separating data points in high dimensions.

We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. We also prove t…

In many situations, classes of data points of primary interest also happen to be those that are least numerous. A well-known example is detection of fraudulent transactions among the collection of all financial transactions, the vast majority of which are legitimate. These types of problems fall under the label of `rar…

Criteria for loop separability on surfaces using Goldman bracket.

This paper presents a new ensemble learning method for classification problems called projection pursuit random forest (PPF). PPF uses the PPtree algorithm introduced in Lee et al. (2013). In PPF, trees are constructed by splitting on linear combinations of randomly chosen variables. Projection pursuit is used to choos…

The article finds conditions for separating filling pairs on surfaces and constructs a Morse function.

New measures assess differences in causal graphs' separations.

We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\to\mathbb{R}$ and for every continuous function $ε:X\to\mathbb(0,+\infty)$ there exists a $C^1$ smooth function $g:X\to\mathbb{R}$ for which $|f(x)-g(x)|\leqε(x)$ and $g'(x)\neq 0$ for all $x\in X$ (that is, $g$ has no…

The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…

Separating the short jobs from the long is a known technique to improve scheduling performance. In this paper we describe a method we developed for accurately predicting the runtimes classes of the jobs to enable this separation. Our method uses the fact that the runtimes can be represented as a mixture of overlapping …

New kernels defined for various spaces, including measures.

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

Study on minimal surfaces in a 3D space with 2m-norm.

We show that for all but finitely many compact orientable surfaces, any superinjective map from the complex of separating curves into the Torelli complex is induced by an element of the extended mapping class group. As an application, we prove that any injective homomorphism from a finite index subgroup of the Johnson …

Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have …

According to [8] if the stationary Schroedinger equation on n-dim. Riemann space admits R-separation of variables (i.e. separation of variables with a factor R), then the underlying metric is necessarily isothermic. An important sub-class of isothermic metrics are the so called binary metrics. In this paper we study co…

We give new upper bounds on the stable commutator lengths of Dehn twists along separating curves in the mapping class group of a closed oriented surface. The estimates of these upper bounds are $O(1/g)$, where $g$ is the genus of the surface.

In this paper, we propose a two-step training procedure for source separation via a deep neural network. In the first step we learn a transform (and it's inverse) to a latent space where masking-based separation performance using oracles is optimal. For the second step, we train a separation module that operates on the…

Emission from a class of benzene-based molecules known as Polycyclic Aromatic Hydrocarbons (PAHs) dominates the infrared spectrum of star-forming regions. The observed emission appears to arise from the combined emission of numerous PAH species, each with its unique spectrum. Linear superposition of the PAH spectra ide…