On clustering procedures and nonparametric mixture estimation

This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the additional covariates to guess the mixture component of each observation. Conditional densities of the mixture model are then estimated using kernel density estimates ap-plied separately to each cluster. We investigate the expected L 1 -error of the resulting estimates and derive optimal rates of convergence over classical nonparametric density classes provided the clustering method is accurate. Performances of clustering algorithms are measured by the maximal misclassification error. We obtain upper bounds of this quantity for a single linkage hierarchical clustering algorithm. Lastly, applications of the proposed method to mixture models involving elec-tricity distribution data and simulated data are presented

Online Tool Condition Monitoring Based on Parsimonious Ensemble+

Accurate diagnosis of tool wear in metal turning process remains an open challenge for both scientists and industrial practitioners because of inhomogeneities in workpiece material, nonstationary machining settings to suit production requirements, and nonlinear relations between measured variables and tool wear. Common methodologies for tool condition monitoring still rely on batch approaches which cannot cope with a fast sampling rate of metal cutting process. Furthermore they require a retraining process to be completed from scratch when dealing with a new set of machining parameters. This paper presents an online tool condition monitoring approach based on Parsimonious Ensemble+, pENsemble+. The unique feature of pENsemble+ lies in its highly flexible principle where both ensemble structure and base-classifier structure can automatically grow and shrink on the fly based on the characteristics of data streams. Moreover, the online feature selection scenario is integrated to actively sample relevant input attributes. The paper presents advancement of a newly developed ensemble learning algorithm, pENsemble+, where online active learning scenario is incorporated to reduce operator labelling effort. The ensemble merging scenario is proposed which allows reduction of ensemble complexity while retaining its diversity. Experimental studies utilising real-world manufacturing data streams and comparisons with well known algorithms were carried out. Furthermore, the efficacy of pENsemble was examined using benchmark concept drift data streams. It has been found that pENsemble+ incurs low structural complexity and results in a significant reduction of operator labelling effort.Comment: this paper has been published by IEEE Transactions on Cybernetic

Dimension-adaptive bounds on compressive FLD Classification

Efficient dimensionality reduction by random projections (RP) gains popularity, hence the learning guarantees achievable in RP spaces are of great interest. In finite dimensional setting, it has been shown for the compressive Fisher Linear Discriminant (FLD) classifier that forgood generalisation the required target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data points. However these bounds depend on the dimensionality d of the original data space. In this paper we give further guarantees that remove d from the bounds under certain conditions of regularity on the data density structure. In particular, if the data density does not fill the ambient space then the error of compressive FLD is independent of the ambient dimension and depends only on a notion of ‘intrinsic dimension'