Data Mining and Knowledge Discovery Handbook, 2 Edition part 90 pdf

The geospatial visual analytics field has recently emerged as the discipline that combines automatic data mining approaches including spatio-temporal clustering with visual reasoning supp

44.4 Open Issues

Spatio-temporal properties of the data introduce additional complexity to the data mining pro-cess and to the clustering in particular We can differentiate between two types of issues that the analyst should deal with or take into consideration during analysis: general and appli-cation dependent The general issues involve such aspects as data quality, precision and un-certainty (Miller and Han(2009)) Scalability, spatial resolution and time granularity can be related to application dependent issues

Data quality (spatial and temporal) and precision depends on the way the data is generated Movement data is usually collected using GPS-enabled devices attached to an object For example, when a person enters a building a GPS signal can be lost or the positioning may be inaccurate due to a weak connection to satellites As in the general data preprocessing step, the analyst should decide how to handle missing or inaccurate parts of the data - should it be ignored, tolerated or interpolated

The computational power does not go in line with the pace at which large amounts of data are being generated and stored Thus, the scalability becomes a significant issue for the analysis and demand new algorithmic solutions or approaches to handle the data

Spatial resolution and time granularity can be regarded as most crucial in spatio-temporal clustering since change in the size of the area over which the attribute is distributed or change

in time interval can lead to discovery of completely different clusters and therefore, can lead

to the improper explanation of the phenomena under investigation There are still no gen-eral guidelines for proper selection of spatial and temporal resolution and it is rather unlikely that such guidelines will be proposed Instead, ad hoc approaches are proposed to handle the problem in specific domains (see for example (Nanni and Pedreschi(2006))) Due to this, the involvement of the domain expert in every step of spatio-temporal clustering becomes essen-tial The geospatial visual analytics field has recently emerged as the discipline that combines automatic data mining approaches including spatio-temporal clustering with visual reasoning supported by the knowledge of domain experts and has been successfully applied at differ-ent geographical spatio-temporal phenomena ( (Andrienko and Andrienko(2006), Andrienko

et al(2007)Andrienko, Andrienko, and Wrobel, Andrienko and Andrienko(2010)))

A class of application-dependent issues that is quickly emerging in the spatio-temporal clustering field is related to exploitation of available background knowledge Indeed, most

of the methods and solutions surveyed in this chapter work on an abstract space where loca-tions have no specific meanings and the analysis process extracts information from scratch, instead of starting from (and integrating to) possible a priori knowledge of the phenomena under consideration On the opposite, a priori knowledge about such phenomena and about the context they take place in is commonly available in real applications, and integrating them

in the mining process might improve the output quality (Alvares et al(2007)Alvares, Bogorny, Kuijpers, de Macedo, Moelans, and Vaisman, Baglioni et al(2009)Baglioni, Antonio Fernan-des de Macedo, Renso, Trasarti, and Wachowicz, Kisilevich et al(2010)Kisilevich, Keim, and Rokach) Examples of that include the very basic knowledge of the street network and land usage, that can help in understanding which aspects of the behavior of our objects (e.g., which parts of the trajectory of a moving object) are most discriminant and better suited to form ho-mogeneous clusters; or the existence of recurring events, such as rush hours and planned road maintenance in a urban mobility setting, that are known to interfere with our phenomena in predictable ways

Recently, the spatio-temporal data mining literature has also pointed out that the rele-vant context for the analysis mobile objects includes not only geographic features and other physical constraints, but also the population of objects themselves, since in most application

scenarios objects can interact and mutually interfere with each other’s activity Classical ex-amples include traffic jams – an entity that emerges from the interaction of vehicles and, in turn, dominates their behavior Considering interactions in the clustering process is expected

to improve the reliability of clusters, yet a systematic taxonomy of relevant interaction types is still not available (neither a general one, nor any application-specific one), it is still not known how to detect such interactions automatically, and understanding the most suitable way to integrate them in a clustering process is still an open problem

44.5 Conclusions

In this chapter we focused on geographical spatio-temporal clustering We presented a

classi-fication of main spatio-temporal types of data: ST events, Geo-referenced variables, Moving

objects and Trajectories We described in detail how spatio-temporal clustering is applied on

trajectories, provided an overview of recent research developments and presented possible sce-narios in several application domains such as movement, cellular networks and environmental studies

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Data Mining for Imbalanced Datasets: An Overview

Nitesh V Chawla

Department of Computer Science and Engineering

University of Notre Dame

IN 46530, USA

nchawla@cse.nd.edu

Summary A dataset is imbalanced if the classification categories are not approximately equally represented Recent years brought increased interest in applying machine learning techniques to difficult “real-world” problems, many of which are characterized by imbalanced data Additionally the distribution of the testing data may differ from that of the training data, and the true misclassification costs may be unknown at learning time Predictive accuracy, a popular choice for evaluating performance of a classifier, might not be appropriate when the data is imbalanced and/or the costs of different errors vary markedly In this Chapter, we dis-cuss some of the sampling techniques used for balancing the datasets, and the performance measures more appropriate for mining imbalanced datasets

Key words: imbalanced datasets, classification, sampling, ROC, cost-sensitive measures, pre-cision and recall

45.1 Introduction

The issue with imbalance in the class distribution became more pronounced with the appli-cations of the machine learning algorithms to the real world These appliappli-cations range from telecommunications management (Ezawa et al., 1996), bioinformatics (Radivojac et al., 2004), text classification (Lewis and Catlett, 1994, Dumais et al., 1998, Mladeni´c and Grobelnik,

1999, Cohen, 1995b), speech recognition (Liu et al., 2004), to detection of oil spills in satel-lite images (Kubat et al., 1998) The imbalance can be an artifact of class distribution and/or different costs of errors or examples It has received attention from machine learning and Data Mining community in form of Workshops (Japkowicz, 2000b, Chawla et al., 2003a, Dietterich

et al., 2003, Ferri et al., 2004) and Special Issues (Chawla et al., 2004a) The range of papers

in these venues exhibited the pervasive and ubiquitous nature of the class imbalance issues faced by the Data Mining community Sampling methodologies continue to be popular in the research work However, the research continues to evolve with different applications, as each application provides a compelling problem One focus of the initial workshops was primarily

O Maimon, L Rokach (eds.), Data Mining and Knowledge Discovery Handbook, 2nd ed.,

DOI 10.1007/978-0-387-09823-4_45, © Springer Science+Business Media, LLC 2010

the performance evaluation criteria for mining imbalanced datasets The limitation of the ac-curacy as the performance measure was quickly established ROC curves soon emerged as a popular choice (Ferri et al., 2004)

The compelling question, given the different class distributions is: What is the correct

distribution for a learning algorithm? Weiss and Provost presented a detailed analysis on the

effect of class distribution on classifier learning (Weiss and Provost, 2003) Our observations agree with their work that the natural distribution is often not the best distribution for learn-ing a classifier (Chawla, 2003) Also, the imbalance in the data can be more characteristic of

“sparseness” in feature space than the class imbalance Various re-sampling strategies have been used such as random oversampling with replacement, random undersampling, focused oversampling, focused undersampling, oversampling with synthetic generation of new sam-ples based on the known information, and combinations of the above techniques (Chawla

et al., 2004b)

In addition to the issue of inter-class distribution, another important probem arising due

to the sparsity in data is the distribution of data within each class (Japkowicz, 2001a) This problem was also linked to the issue of small disjuncts in the decision tree learning Yet an-other, school of thought is a recognition based approach in the form of a one-class learner The one-class learners provide an interesting alternative to the traditional discriminative approach, where in the classifier is learned on the target class alone (Japkowicz, 2001b, Juszczak and Duin, 2003, Raskutti and Kowalczyk, 2004, Tax, 2001)

In this chapter1, we present a liberal overview of the problem of mining imbalanced datasets with particular focus on performance measures and sampling methodologies We will present our novel oversampling technique, SMOTE, and its extension in the boosting proce-dure — SMOTEBoost

45.2 Performance Measure

A classifier is, typically, evaluated by a confusion matrix as illustrated in Figure 45.1 (Chawla

et al., 2002) The columns are the Predicted class and the rows are the Actual class In the

con-fusion matrix, T N is the number of negative examples correctly classified (True Negatives),

FP is the number of negative examples incorrectly classified as positive (False Positives), FN

is the number of positive examples incorrectly classified as negative (False Negatives) and T P

is the number of positive examples correctly classified (True Positives) Predictive accuracy is

defined as Accuracy = (TP + TN)/(TP + FP + TN + FN).

However, predictive accuracy might not be appropriate when the data is imbalanced and/or the costs of different errors vary markedly As an example, consider the classification of pixels

in mammogram images as possibly cancerous (Woods et al., 1993) A typical mammography dataset might contain 98% normal pixels and 2% abnormal pixels A simple default strategy

of guessing the majority class would give a predictive accuracy of 98% The nature of the application requires a fairly high rate of correct detection in the minority class and allows for

a small error rate in the majority class in order to achieve this (Chawla et al., 2002) Simple predictive accuracy is clearly not appropriate in such situations

1The chapter will utilize excerpts from our published work in various Journals and Confer-ences Please see the references for the original publications

Predicted Negative

Predicted Positive

Actual Negative Actual Positive Fig 45.1 Confusion Matrix

45.2.1 ROC Curves

The Receiver Operating Characteristic (ROC) curve is a standard technique for summarizing classifier performance over a range of tradeoffs between true positive and false positive error rates (Swets, 1988) The Area Under the Curve (AUC) is an accepted performance metric for

a ROC curve (Bradley, 1997)

Percent

True Positive

Percent False Positive

100

original data set

increased undersampling

of the majority class moves the operating point to the upper right

y = x

Ideal point

Fig 45.2 Illustration of Sweeping out an ROC Curve through under-sampling Increased under-sampling of the majority (negative) class will move the performance from the lower left point to the upper right

ROC curves can be thought of as representing the family of best decision boundaries for

relative costs of TP and FP On an ROC curve the X-axis represents %FP = FP/(TN + FP) and the Y-axis represents %T P = TP/(TP + FN) The ideal point on the ROC curve would

be (0,100), that is all positive examples are classified correctly and no negative examples are misclassified as positive One way an ROC curve can be swept out is by manipulating the balance of training samples for each class in the training set Figure 45.2 shows an illustra-tion (Chawla et al., 2002) The line y = x represents the scenario of randomly guessing the class A single operating point of a classifier can be chosen from the trade-off between the

%TP and %FP, that is, one can choose the classifier giving the best %TP for an acceptable

%FP (Neyman-Pearson method) (Egan, 1975) Area Under the ROC Curve (AUC) is a use-ful metric for classifier performance as it is independent of the decision criterion selected and prior probabilities The AUC comparison can establish a dominance relationship between clas-sifiers If the ROC curves are intersecting, the total AUC is an average comparison between models (Lee, 2000)

The ROC convex hull can also be used as a robust method of identifying potentially opti-mal classifiers (Provost and Fawcett, 2001) Given a family of ROC curves, the ROC convex hull can include points that are more towards the north-west frontier of the ROC space If a line passes through a point on the convex hull, then there is no other line with the same slope passing through another point with a larger true positive (TP) intercept Thus, the classifier

at that point is optimal under any distribution assumptions in tandem with that slope (Provost and Fawcett, 2001)

Moreover, distribution/cost sensitive applications can require a ranking or a probabilistic estimate of the instances For instance, revisiting our mammography data example, a proba-bilistic estimate or ranking of cancerous cases can be decisive for the practitioner (Chawla,

2003, Maloof, 2003) The cost of further tests can be decreased by thresholding the patients

at a particular rank Secondly, probabilistic estimates can allow one to threshold ranking for class membership at values< 0.5 The ROC methodology by (Hand, 1997) allows for

rank-ing of examples based on their class memberships — whether a randomly chosen majority class example has a higher majority class membership than a randomly chosen minority class example It is equivalent to the Wilcoxon test statistic

45.2.2 Precision and Recall

From the confusion matrix in Figure 45.1, we can derive the expression for precision and

recall (Buckland and Gey, 1994).

precision= T P

T P + FP

T P + FN The main goal for learning from imbalanced datasets is to improve the recall without hurting the precision However, recall and precision goals can be often conflicting, since when

increasing the true positive for the minority class, the number of false positives can also be

increased; this will reduce the precision The F-value metric is one measure that combines the trade-offs of precision and recall, and outputs a single number reflecting the “goodness” of a

classifier in the presence of rare classes While ROC curves represent the trade-off between

values of TP and FP, the F-value represents the trade-off among different values of TP, FP, and

FN (Buckland and Gey, 1994) The expression for the F-value is as follows:

F − value =(1 +β2) ∗ recall ∗ precision

β2∗ recall + precision

whereβ corresponds to the relative importance of precision vs recall It is usually set to

1

45.2.3 Cost-sensitive Measures

Cost Matrix

Cost-sensitive measures usually assume that the costs of making an error are known (Turney,

2000, Domingos, 1999, Elkan, 2001) That is one has a cost-matrix, which defines the costs

incurred in false positives and false negatives Each example, x, can be associated with a cost

C (i, j,x), which defines the cost of predicting class i for x when the “true” class is j The goal

is to take a decision to minimize the expected cost The optimal prediction for x can be defined

as

∑

j

The aforementioned equation requires a computation of conditional probablities of class j given feature vector or example x While the cost equation is straightforward, we don’t always

have a cost attached to making an error The costs can be different for every example and not

only for every type of error Thus, C(i, j) is not always ≡ to C(i, j,x).

Cost Curves

(Drummond and Holte, 2000) propose cost-curves, where the x-axis represents of the fraction

of the positive class in the training set, and the y-axis represents the expected error rate grown

on each of the training sets The training sets for a data set is generated by under (or over) sampling The error rates for class distributions not represented are construed by interpolation They define two cost-sensitive components for a machine learning algorithm: 1) producing

a variety of classifiers applicable for different distributions and 2) selecting the appropriate classifier for the right distribution However, when the misclassification costs are known, the

x-axis can represent the “probability cost function”, which is the normalized product of C(− | +) ∗ P(+); the y-axis represents the expected cost.

45.3 Sampling Strategies

Over and under-sampling methodologies have received significant attention to counter the effect of imbalanced data sets (Solberg and Solberg, 1996, Japkowicz, 2000a, Chawla et al.,

2002, Weiss and Provost, 2003, Kubat and Matwin, 1997, Jo and Japkowicz, 2004, Batista

et al., 2004, Phua and Alahakoon, 2004, Laurikkala, 2001, Ling and Li, 1998) Various stud-ies in imbalanced datasets have used different variants of over and under sampling, and have presented (sometimes conflicting) viewpoints on usefulness of oversampling versus under-sampling (Chawla, 2003, Maloof, 2003, Drummond and Holte, 2003, Batista et al., 2004) The random under and over sampling methods have their various short-comings The random undersampling method can potentially remove certain im-portant examples, and random oversampling can lead to overfitting However, there has been progression in both the under and over sampling methods (Kubat and Matwin, 1997) used one-sided selection to selectively undersample the original population They used Tomek Links (Tomek, 1976) to identify the noisy and borderline examples They also used the Condensed Nearest Neighbor (CNN) rule (Hart, 1968) to remove examples from the majority class that are far away from the decision border (Laurikkala, 2001) proposed Neighborhood