Statistical Analysis with Missing Data

An Introduction to MultiAgent Systems.

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

This chapter introduces the subject of statistical pattern recognition (SPR). It starts by considering how features are defined and emphasizes that the nearest neighbor algorithm achieves error rates comparable with those of an ideal Bayes’ classifier. The concepts of an optimal number of features, representativeness of the training data, and the need to avoid overfitting to the training data are stressed. The chapter shows that methods such as the support vector machine and artificial neural networks are subject to these same training limitations, although each has its advantages. For neural networks, the multilayer perceptron architecture and back-propagation algorithm are described. The chapter distinguishes between supervised and unsupervised learning, demonstrating the advantages of the latter and showing how methods such as clustering and principal components analysis fit into the SPR framework. The chapter also defines the receiver operating characteristic, which allows an optimum balance between false positives and false negatives to be achieved.

Statistical Pattern Recognition

Hyperspectral imaging involves large amounts of information. This paper presents a technique for dimensionality reduction to deal with hyperspectral images. The proposed method is based on a hierarchical clustering structure to group bands to minimize the intracluster variance and maximize the intercluster variance. This aim is pursued using information measures, such as distances based on mutual information or Kullback-Leibler divergence, in order to reduce data redundancy and non useful information among image bands. Experimental results include a comparison among some relevant and recent methods for hyperspectral band selection using no labeled information, showing their performance with regard to pixel image classification tasks. The technique that is presented has a stable behavior for different image data sets and a noticeable accuracy, mainly when selecting small sets of bands.

/pdf/clustering-based-hyperspectral-band-selection-using-73nc955ok0.pdf

Clustering-Based Hyperspectral Band Selection Using Information Measures

Supervised feature selection by clustering using conditional mutual information-based distances

The k-nearest neighbors (k-NN) classifier is one of the most popular supervised classification methods. It is very simple, intuitive and accurate in a great variety of real-world domains. Nonetheless, despite its simplicity and effectiveness, practical use of this rule has been historically limited due to its high storage requirements and the computational costs involved. On the other hand, the performance of this classifier appears strongly sensitive to training data complexity. In this context, by means of several problem difficulty measures, we try to characterize the behavior of the k-NN rule when working under certain situations. More specifically, the present analysis focuses on the use of some data complexity measures to describe class overlapping, feature space dimensionality and class density, and discover their relation with the practical accuracy of this classifier.

https://link.springer.com/content/pdf/10.1007%2Fs10044-007-0061-2.pdf

An analysis of how training data complexity affects the nearest neighbor classifiers

http://homepage.tudelft.nl/a9p19/papers/pr_06_protopt.pdf

Experimental study on prototype optimisation algorithms for prototype-based classification in vector spaces

The Nearest Neighbor classifier is one of the most popular supervised classification methods It is very simple, intuitive and accurate in a great variety of real-world applications Despite its simplicity and effectiveness, practical use of this rule has been historically limited due to its high storage requirements and the computational costs involved, as well as the presence of outliers In order to overcome these drawbacks, it is possible to employ a suitable prototype selection scheme, as a way of storage and computing time reduction and it usually provides some increase in classification accuracy Nevertheless, in some practical cases prototype selection may even produce a degradation of the classifier effectiveness From an empirical point of view, it is still difficult to know a priori when this method will provide an appropriate behavior The present paper tries to predict how appropriate a prototype selection algorithm will result when applied to a particular problem, by characterizing data with a set of complexity measures

/pdf/data-characterization-for-effective-prototype-selection-3mhvu71zhk.pdf

José Martínez Sotoca

Papers

Clustering-Based Hyperspectral Band Selection Using Information Measures

Supervised feature selection by clustering using conditional mutual information-based distances

An analysis of how training data complexity affects the nearest neighbor classifiers

Experimental study on prototype optimisation algorithms for prototype-based classification in vector spaces

Data characterization for effective prototype selection