k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours to determine the class of the query. This approach to classification is of particular importance because issues of poor run-time performance is not such a problem these days with the computational power that is available. This paper presents an overview of techniques for Nearest Neighbour classification focusing on; mechanisms for assessing similarity (distance), computational issues in identifying nearest neighbours and mechanisms for reducing the dimension of the data. This paper is the second edition of a paper previously published as a technical report. Sections on similarity measures for time-series, retrieval speed-up and intrinsic dimensionality have been added. An Appendix is included providing access to Python code for the key methods.Comment: 22 pages, 15 figures: An updated edition of an older tutorial on kN

Case-based maintenance : Structuring and incrementing the Case.

International audienceTo avoid performance degradation and maintain the quality of results obtained by the case-based reasoning (CBR) systems, maintenance becomes necessary, especially for those systems designed to operate over long periods and which must handle large numbers of cases. CBR systems cannot be preserved without scanning the case base. For this reason, the latter must undergo maintenance operations.The techniques of case base’s dimension optimization is the analog of instance reduction size methodology (in the machine learning community). This study links these techniques by presenting case-based maintenance in the framework of instance based reduction, and provides: first an overview of CBM studies, second, a novel method of structuring and updating the case base and finally an application of industrial case is presented.The structuring combines a categorization algorithm with a measure of competence CM based on competence and performance criteria. Since the case base must progress over time through the addition of new cases, an auto-increment algorithm is installed in order to dynamically ensure the structuring and the quality of a case base. The proposed method was evaluated through a case base from an industrial plant. In addition, an experimental study of the competence and the performance was undertaken on reference benchmarks. This study showed that the proposed method gives better results than the best methods currently found in the literature

Connectivity Preservation and Coverage Schemes for Wireless Sensor Networks

International audienceIn this paper, we consider the self-deployment of wireless sensor networks. We present a mechanism which allows to preserve network connectivity during the deployment of mobile wireless sensors. Our algorithm is localized and is based on a subset of neighbors for motion decision. Our algorithm maintains a connected topology regardless of the direction chosen by each sensor. To preserve connectivity, the distance covered by the mobile nodes is constrained by the connectivity of the node to its neighbors in a connected subgraph like the relative neighborhood graph (RNG). We show the connectivity preservation property of our algorithm through analysis and present some simulation results on different deployment schemes such as full coverage, point of interest coverage or barrier coverage

Reliable fault-tolerant model predictive control of drinking water transport networks

This paper proposes a reliable fault-tolerant model predictive control applied to drinking water transport networks. After a fault has occurred, the predictive controller should be redesigned to cope with the fault effect. Before starting to apply the fault-tolerant control strategy, it should be evaluated whether the predictive controller will be able to continue operating after the fault appearance. This is done by means of a structural analysis to determine loss of controllability after the fault complemented with feasibility analysis of the optimization problem related to the predictive controller design, so as to consider the fault effect in actuator constraints. Moreover, by evaluating the admissibility of the different actuator-fault configurations, critical actuators regarding fault tolerance can be identified considering structural, feasibility, performance and reliability analyses. On the other hand, the proposed approach allows a degradation analysis of the system to be performed. As a result of these analyses, the predictive controller design can be modified by adapting constraints such that the best achievable performance with some pre-established level of reliability will be achieved. The proposed approach is tested on the Barcelona drinking water transport network.Postprint (author's final draft

A concept drift-tolerant case-base editing technique

© 2015 Elsevier B.V. All rights reserved. The evolving nature and accumulating volume of real-world data inevitably give rise to the so-called "concept drift" issue, causing many deployed Case-Based Reasoning (CBR) systems to require additional maintenance procedures. In Case-base Maintenance (CBM), case-base editing strategies to revise the case-base have proven to be effective instance selection approaches for handling concept drift. Motivated by current issues related to CBR techniques in handling concept drift, we present a two-stage case-base editing technique. In Stage 1, we propose a Noise-Enhanced Fast Context Switch (NEFCS) algorithm, which targets the removal of noise in a dynamic environment, and in Stage 2, we develop an innovative Stepwise Redundancy Removal (SRR) algorithm, which reduces the size of the case-base by eliminating redundancies while preserving the case-base coverage. Experimental evaluations on several public real-world datasets show that our case-base editing technique significantly improves accuracy compared to other case-base editing approaches on concept drift tasks, while preserving its effectiveness on static tasks

Functional sets with typed symbols: Framework and mixed Polynotopes for hybrid nonlinear reachability and filtering

Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, an original framework with mixed sets defined as function images of symbol type domains is first proposed. Syntax and semantics are explicitly distinguished. Then, both continuous (interval) and discrete (signed, boolean) symbol types are used to model dependencies through linear and polynomial functions, so leading to mixed zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes with typed symbols. Polynotopes can both propagate a mixed encoding of intervals and describe the behavior of logic gates. A functional completeness result is given, as well as an inclusion method for elementary nonlinear and switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a stochastic uncertainty paradigm are outlined. Finally, several discrete, continuous and hybrid numerical examples including comparisons illustrate the effectiveness of the theoretical results.Comment: 21 pages, 8 figure

Reachability in Restricted Chemical Reaction Networks

The popularity of molecular computation has given rise to several models of abstraction, one of the more recent ones being Chemical Reaction Networks (CRNs). These are equivalent to other popular computational models, such as Vector Addition Systems and Petri-Nets, and restricted versions are equivalent to Population Protocols. This paper continues the work on core reachability questions related to Chemical Reaction Networks; given two configurations, can one reach the other according to the system's rules? With no restrictions, reachability was recently shown to be Ackermann-complete, this resolving a decades-old problem. Here, we fully characterize monotone reachability problems based on various restrictions such as the rule size, the number of rules that may create a species (k-source) or consume a species (k-consuming), the volume, and whether the rules have an acyclic production order (feed-forward). We show PSPACE-completeness of reachability with only bimolecular reactions with two-source and two-consuming rules. This proves hardness of reachability in Population Protocols, which was unknown. Further, this shows reachability in CRNs is PSPACE-complete with size-2 rules, which was previously only known with size-5 rules. This is achieved using techniques within the motion planning framework. We provide many important results for feed-forward CRNs where rules are single-source or single-consuming. We show that reachability is solvable in polynomial time if the system does not contain special void or autogenesis rules. We then fully characterize all systems of this type and show that if you allow void/autogenesis rules, or have more than one source and one consuming, the problems become NP-complete. Finally, we show several interesting special cases of CRNs based on these restrictions or slight relaxations and note future significant open questions related to this taxonomy.Comment: This research was supported in part by National Science Foundation Grant CCF-181760

Reachability in Restricted Chemical Reaction Networks

The popularity of molecular computation has given rise to several models of abstraction, one of the more recent ones being Chemical Reaction Networks (CRNs). These are equivalent to other popular computational models, such as Vector Addition Systems and Petri-Nets, and restricted versions are equivalent to Population Protocols. This paper continues the work on core reachability questions related to Chemical Reaction Networks; given two configurations, can one reach the other according to the system\u27s rules? With no restrictions, reachability was recently shown to be Ackermann-complete, this resolving a decades-old problem.Here, we fully characterize monotone reachability problems based on various restrictions such as the rule size, the number of rules that may create a species (k-source) or consume a species (k-consuming), the volume, and whether the rules have an acyclic production order (feed-forward). We show PSPACE-completeness of reachability with only bimolecular reactions with two-source and two-consuming rules. This proves hardness of reachability in Population Protocols, which was unknown. Further, this shows reachability in CRNs is PSPACE-complete with size-2 rules, which was previously only known with size-5 rules. This is achieved using techniques within the motion planning framework.We provide many important results for feed-forward CRNs where rules are single-source or single-consuming. We show that reachability is solvable in polynomial time if the system does not contain special void or autogenesis rules. We then fully characterize all systems of this type and show that if you allow void/autogenesis rules, or have more than one source and one consuming, the problems become NP-complete. Finally, we show several interesting special cases of CRNs based on these restrictions or slight relaxations and note future significant open questions related to this taxonomy