Finite Set Of Classes Research Articles

An open‐set method for automatic recognition of low probability of intercept radar waveforms based on reciprocity points learning

AbstractDeep learning‐based methods for Low Probability of Intercept radar waveform recognition typically assume that the signal to be recognized belongs to a known and finite set of classes. However, in practical scenarios, the electromagnetic signal environment is open and there may be a large number of unknown signals, making such methods difficult to apply. To address this issue, a novel open‐set recognition method based on reciprocal points is proposed. This approach uses a neural network to extract a high‐dimensional time‐frequency feature map of the signal, and measures the difference between the known and unknown signals by computing the distance between the feature vector and the reciprocal points. This allows the model to correctly identify known class signals while simultaneously detecting unknown signals. Experimental results show that the proposed method achieves open‐set recognition of Low Probibability of Intercept radar signals. On test signals with signal‐to‐noise ratios ranging from 6 dB to 15 dB, the model achieves nearly 100% accuracy in identifying known class signals and more than 90% accuracy in detecting unknown signals.

An integrated explicit and implicit offensive language taxonomy

Abstract The current study represents an integrated model of explicit and implicit offensive language taxonomy. First, it focuses on a definitional revision and enrichment of the explicit offensive language taxonomy by reviewing the collection of available corpora and comparing tagging schemas applied there. The study relies mainly on the categories originally proposed by Zampieri et al. (2019) in terms of offensive language categorization schemata. After the explanation of semantic differences between particular concepts used in the tagging systems and the analysis of theoretical frameworks, a finite set of classes is presented, which cover aspects of offensive language representation along with linguistically sound explanations (Lewandowska-Tomaszczyk et al. 2021). In the analytic procedure, offensive from non-offensive discourse is first distinguished, with the question of offence Target and the following categorization levels and sublevels. Based on the relevant data generated from Sketch Engine (https://www.sketchengine.eu/ententen-english-corpus/), we propose the concept of offensive language as a superordinate category in our system with a number of hierarchically arranged 17 subcategories. The categories are taxonomically structured into 4 levels and verified with the use of neural-based (lexical) embeddings. Together with a taxonomy of implicit offensive language and its subcategorization levels which has received little scholarly attention until now, the categorization is exemplified in samples of offensive discourses in selected English social media materials, i.e., publicly available 25 web-based hate speech datasets (consult Appendix 1 for a complete list). The offensive category levels (types of offence, targets, etc.) and aspects (offensive language property clusters) as well as the categories of explicitness and implicitness are discussed in the study and the computationally verified integrated explicit and implicit offensive language taxonomy proposed in the study.

On the security of deep learning novelty detection

Deep learning is a type of machine learning that adapts a deep hierarchy of concepts. Deep learning classifiers link the most basic version of concepts at the input layer to the most abstract version of concepts at the output layer, also known as a class or label. However, once trained over a finite set of classes, some deep learning models do not have the power to say that a given input does not belong to any of the classes and simply cannot be linked. Correctly invalidating the prediction of unrelated classes is a challenging problem that has been tackled in many ways in the literature. Novelty detection gives deep learning the ability to output “do not know” for novel/unseen classes. Still, no attention has been given to the security aspects of novelty detection. In this paper, we consider the case study of abstraction-based novelty detection and show its weakness against adversarial samples. We show the feasibility of crafting adversarial samples that bypass the novelty detection monitoring and fool the deep learning classifier at the same time. In other words, novelty detection itself ends up as an attack surface. Moreover, we call for further research from a defender’s point of view. We investigate auto-encoders as a plausible defense mechanism and assess its performance.

Stability of the stochastic matching model

Abstract We introduce and study a new model that we call the matching model. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be matched. There is a finite set of classes 𝒱 for the items, and the allowed matchings depend on the classes, according to a matching graph on 𝒱. Upon arrival, an item may find several possible matches in the buffer. This indeterminacy is resolved by a matching policy. When the sequence of classes of the arriving items is independent and identically distributed, the sequence of buffer-content is a Markov chain, whose stability is investigated. In particular, we prove that the model may be stable if and only if the matching graph is nonbipartite.

Control systems of interacting objects modeled as a game against nature under a mean field approach

This paper deals with discrete-time stochastic systems composed of a large number of N interacting objects (a.k.a. agents or particles). There is a central controller whose decisions, at each stage, affect the system behavior. Each object evolves randomly among a finite set of classes, according to a transition law which depends on an unknown parameter. Such a parameter is possibly non observable and may change from stage to stage. Due to the lack of information and to the large number of agents, the control problem under study is rewritten as a game against nature according to the mean field theory; that is, we introduce a game model associated to the proportions of the objects in each class, whereas the values of the unknown parameter are now considered as actions selected by an opponent to the controller (the nature). Then, letting \begin{document} $N \to \infty $ \end{document} (the mean field limit) and considering a discounted optimality criterion, the objective for the controller is to minimize the maximum cost, where the maximum is taken over all possible strategies of the nature.

Unsupervised classification using hidden Markov chain with unknown noise copulas and margins

We consider the problem of unsupervised classification of hidden Markov models (HMC) with dependent noise. Time is discrete, the hidden process takes its values in a finite set of classes, while the observed process is continuous. We adopt an extended HMC model in which the rich possibilities of different kinds of dependence in the noise are modelled via copulas. A general model identification algorithm, in which different noise margins and copulas corresponding to different classes are selected in given families and estimated in an automated way, from the sole observed process, is proposed. The interest of the whole procedure is shown via experiments on simulated data and on a real SAR image.

Multi-class Markovian arrival processes and their parameter fitting

Markovian arrival processes are a powerful class of stochastic processes to represent stochastic workloads that include autocorrelation in performance or dependability modeling. However, fitting the parameters of a Markovian arrival process to given measurement data is non-trivial and most known methods focus on a single class case, where all events are of the same type and only the sequence of interarrival times is of interest. In this paper, we propose a method to fit data to a multi-class Markovian arrival process, where arrivals can be partitioned into a finite set of classes. This allows us to use a Markovian arrival process to represent workloads where interarrival times are correlated across customer classes and to achieve models of greater accuracy. The fitting approach performs in several consecutive steps and applies a single non-linear optimization step and several non-negative least squares computations.

On a problem from the Kourovka Notebook

In this article, it is proved that if a group G coincides with its commutator subgroup, is generated by a finite set of classes of conjugate elements, and contains a proper minimal normal subgroup A such that the factor group G/A coincides with the normal closure of one element, then G coincides with the normal closure of an element. From this a positive answer to question 5.52 from the Kourovka Notebook for the group with the condition of minimality on normal subgroups follows. We have found a necessary and sufficient condition for a group coinciding with its commutator subgroup and generated by a finite set of classes of conjugate elements not to coincide with the normal closure of any element.

Static typing for object-oriented programming

We develop a theory of statically typed object-oriented languages. It represents classes as labeled, regular trees, types as finite sets of classes, and subclassing as a partial order on trees. We show that our subclassing order strictly generalizes inheritance, and that a novel genericity mechanism arises as an order-theoretic complement. This mechanism, called class substitution, is pragmatically useful and can be implemented efficiently.

Object-oriented type inference

We present a new approach to inferring types in untyped object-oriented programs with inheritance, assignments, and late binding. It guarantees that all messages are understood, annotates the program with type information, allows polymorphic methods, and can be used as the basis of an optimizing compiler. Types are finite sets of classes and subtyping is set inclusion. Using a trace graph, our algorithm constructs a set of conditional type constraints and computes the least solution by least fixed-point derivation.

Static Typing for Object-Oriented Programming

We develop a theory of statically typed object-oriented languages. It represents classes as labeled, regular trees, types as finite sets of classes, and subclassing as a partial order on trees. We show that our subclassing order strictly generalizes inheritance, and that a novel genericity mechanism arises as an order-theoretic complement. This mechanism, called class substitution, is pragmatically useful and can be implemented efficiently.

Object-Oriented Type Inference

We present a new approach to inferring types in untyped object-oriented programs with inheritance, assignments, and late binding. It guarantees that all messages are understood, annotates the program with type information, allows polymorphic methods, and can be used as the basis of an optimizing compiler. Types are finite sets of classes and subtyping is set inclusion. Using a trace graph, our algorithm constructs a set of conditional type constraints and computes the least solution by least fixed-point derivation.

Definable equivalence relations on algebraically closed fields

This article was inspired by the question: is there a definable equivalence relation on the field of complex numbers, each of whose equivalence classes has exactly two elements? The answer turned out to be no, as we now explain in greater detail.Let Κ be an algebraically closed field and let E be a definable equivalence relation on Κ. [Note: By “definable” we will always mean “definable with parameters”.] Either E has one cofinite class, or all classes are finite and there is a number d such that all but a finite set of classes have cardinality d. In the latter case let B be the finite set of elements of Κ which are not in a class of size d. We prove the following result.Theorem 1. a) If char(Κ) = 0 or char(Κ) = p > d, then ∣B∣ ≡ 1 (mod d).b) If char(Κ) = 2 and d = 2, then ∣B∣ ≡ 0 (mod 2).c) If char(Κ) = p > 2 and d = p + s, where 1 ≤ s ≤ p/2, then ∣B∣ ≡ p + 1 (mod d).Furthermore, a)−c) are the only restrictions on ≡B≡.If one is in the right mood, one can view this theorem as saying that the “algebraic cardinality” of the complex numbers is congruent to 1 (mod n) for every n.§1 contains a reduction of the problem to the special case where E is induced by a rational function in one variable. §2 contains the main calculations and the proofs of a)−c). §3 contains eight families of examples showing that all else is possible. In §4 we prove an analogous result for real closed fields.