A Review on Concept Drift

Abstract

The concept changes in continuously evolving data streams are termed as concept drifts. It is required to address the problems caused due to concept drift and adapt according to the concept changes. This can be achieved by designing supervised or unsupervised techniques in such a way, that concept changes are considered, and useful knowledge is extracted. This paper discusses various techniques to manage concept drifts. The synthetic and real datasets with different concept drifts and the applications are discussed.

Full text

IOSR Journal of Computer Engineering (IOSR-JCE)
e-ISSN: 2278-0661,p-ISSN: 2278-8727, Volume 17, Issue 1, Ver. II (Jan – Feb. 2015), PP 20-26
www.iosrjournals.org
DOI: 10.9790/0661-17122026 www.iosrjournals.org 20 | Page
A Review on Concept Drift
Yamini Kadwe1, Vaishali Suryawanshi2
1,2 (Department of IT, M.I.T. College Of Engineering, Pune, India)
Abstract: The concept changes in continuously evolving data streams are termed as concept drifts. It is
required to address the problems caused due to concept drift and adapt according to the concept changes. This
can be achieved by designing supervised or unsupervised techniques in such a way, that concept changes are
considered, and useful knowledge is extracted. This paper discusses various techniques to manage concept
drifts. The synthetic and real datasets with different concept drifts and the applications are discussed.
Keywords: Drift detectors, ensemble classifiers, data stream mining, and bagging.
I. Introduction
Today, is a world of advanced technologies, every field is automated. Due to advances in technology,
plenty of data is generated every second. Examples of such applications include network monitoring, web
mining, sensor networks, telecommunications data management, and financial applications [14]. The data needs
to be gathered and processed, to extract unknown, useful and interesting knowledge. But it is impossible to
manually extract that knowledge due to the volume and speed of the data gathered.
Concept drift occurs when the concept about which data is being collected shifts from time to time after
a minimum stability period. This problem of concept drift needs to be considered to mine data with acceptable
accuracy level. Some examples of concept drift include spam detection, financial fraud detection, climate
change prediction, customer preferences for online shopping.
This paper is organized as follows, Section II gives the overview of concept drift, involving problem,
need to adapt concept drift and types of concept drift. Section III explains various methods of detecting concept
drift. Section IV discusses about statistical tests for concept drift. In Section V classifiers for dealing with
concept drifts are discussed. Section VI gives a summary on possible datasets based on the type of drifts present
and Section VII summarizes consideration of concept drift in various real-world applications.
II. Overview
Problem of Concept Drift:
There has been increased importance of concept drift in machine learning as well as data mining tasks.
Today, data is organized in the form of data streams rather than static databases. Also the concepts and data
distributions ought to change over a long period of time.
Need for Concept drift adaptation:
In dynamically changing or non-stationary environments, the data distribution can change over time
yielding the phenomenon of concept drift[4]. The concept drifts can be quickly adapted by storing concept
descriptions, so that they can be re-examined and reused later. Hence, adaptive learning is required to deal with
data in non-stationary environments. When concept drift is detected, the current model needs to be updated to
maintain accuracy.
Types of Concept drift:
Depending on the relation between the input data and target variable, concept change take different
forms. Concept drift between time point t0 and time point t1 can be defined as-
∃X : pt0(X, y) ≠ pt1(X, y) (1)
where pt0 denotes the joint distribution at time t0 between the set of input variables X and the target variable y.
Kelly et al. presented the three ways in which concept drift may occur [3]:
 prior probabilities of classes, p(y) may change over time
 class-conditional probability distributions, p(X,y) might change
 posterior probabilities p(y|X) might change.
Concept drift may be classified in terms of the [4] speed of change and the reason of change as shown
in figure 1. When 'a set of examples has legitimate class labels at one time and has different legitimate labels at
another time', it is real drift, i.e. reason of change[20], refers to changes in p(y|X).

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Fig 1: Types of drift: circles represent instances; different colors represent different classes[4]
Fig 2: Patterns of concept change [4]
When 'the target concepts remain the same but the data distribution changes'[6], it is virtual drift, i.e.
speed of change, refers to changes in p(X).
A drift can be sudden or abrupt, when concept switching is from one to another (refer figure 2)[4]. The
concept change can be incremental, consisting of many intermediate concepts in between. Drift may be gradual;
change is not abrupt, but goes back to previous pattern for some time. Concept drift handling algorithms should
not mix the true drift with an outlier (blip) or noise, which refers to an anomaly. A recurring drifts is when new
concepts that were not seen before, or previously seen concepts may reoccur after some time.
Detecting Concept changes:
The ways to monitor concept drift are as given below:
 Concept drift is monitored by checking with the data's probability distribution, since it changes with time.
 One can judge whether concept drift has happened, by monitoring and tracking the relevance between
various sample characteristics or attributions.
 Concept drifts leads to changes in features of classification models.
 Classification accuracy can be taken into account while detecting concept drift on a given data stream.
Recall, precision and F-measure are some of the accuracy indicators of classification
The arrival of the timestamp of single sample or block sample can be taken as an additional input attribute, to
determine occurrence concept drift. It keeps a check on whether the classification rule has become outdated.
III. Concept Drift Detectors
This section discusses algorithms allowing to detect concept drift, known as concept drift detectors.
They alarm the base learner, that the model should be rebuilt or updated.
DDM: In the Drift Detection Method (DDM), proposed by Gama et al. uses Binomial Distribution[14]. For
each point i in the sequence that is being sampled, the error rate is the probability of misclassifying (pi), with
standard deviation (si) given by eq 2-
si = (2)
they store the values of pi and si when pi + si reaches its minimum value during the process i.e. pmin and
smin. These values are used to calculate a warning level condition presented in eq. 3 and an alarm level condition
presented in eq. 4 -
pi + si ≥ pmin + α . smin (warning level) (3)
pi + si ≥ pmin + β.smin (alarm level ) (4)
Beyond the warning the examples are stored in anticipation of a possible change of context. Beyond the
alarm level, the concept drift is supposed to be true, the model induced by the learning method is reset, also pmin
and smin, and a new model is learnt using the examples stored since the warning level triggered. DDM works
best on data streams with sudden drift as gradually changing concepts can pass without triggering the alarm
level.

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EDDM:
Baena-García et al. proposed a modification of DDM called EDDM [16]. The same warning- alarm
mechanism, was used but instead of using the classifier‟s error rate, the distance-error-rate was proposed. They
denote p'i as the average distance between two consecutive errors and s'i as its standard deviation. Using these
values the new warning and alarm conditions are given by eq. 5 and eq. 6.
p'i +2 . s'i / p'max+2.s'max < α (warning level) (5)
p'i+3. s'i/ p'max+3.s'max < β (alarm level) (6)
the values of p'i and s'i are stored when reaches its maximum value p'i +2 .s'i (obtaining p'max and s'max). EDDM
works better than DDM for slow gradual drift, but is more sensitive to noise. Another drawback is that it
considers the thresholds and searches for concept drift when a minimum of 30 errors have occurred.
Adwin:
Bifet et al. proposed this method, that uses sliding windows of variable size, which are recomputed
online according to the rate of change observed from the data in these windows[13]. The window(W) is
dynamically enlarged when there is no clear change in the context, and shrinks it when a change is detected.
Additionally, ADWIN provides rigorous guarantees of its performance, in the form of limits on the rates of false
positives and false negatives. ADWIN works only for one-dimensional data. A separate window must be
maintained for each dimension, for n-dimensional raw data, which results in handling more than one window.
Paired Learners:
The Paired Learners, proposed by Stephen Bach et al., uses two learners: stable and reactive[17]. The
stable learner predicts based on all of its experience, while the reactive one predicts based on a window of recent
examples. It uses the interplay between these two learners and their accuracy differences to cope with concept
drift. The reactive learner can be implemented in two different ways; by rebuilding the learner with the last
w(window size) examples, or by using a retractable learner that can unlearn examples.
Exponentially weighted moving average for Concept Drift Detection (ECDD):
Ross et al., proposed a drift detection method based on Exponentially Weighted Moving Average
(EWMA)[15], used for identifying an increase in the mean of a sequence of random variables. In EWMA, the
probability of incorrectly classifying an instance before the change point and the standard deviation of the
stream are known. In ECDD, the values of success and failure probability(1 and 0) are computed online, based
on the classification accuracy of the base learner in the actual instance, together with an estimator of the
expected time between false positive detections.
Statistical Test of Equal Proportions (STEPD):
The STEPD proposed by Nishida et al., assumes that 'the accuracy of a classifier for recent W
examples will be equal to the overall accuracy from the beginning of the learning if the target concept is
stationary; and a significant decrease of recent accuracy suggests that the concept is changing'[18]. A chi-square
test is performed by computing a statistic and its value is compared to the percentile of the standard normal
distribution to obtain the observed significance level. If this value is less than a significance level, then the null-
hypothesis is rejected, assuming that a concept drift has occurred. The warning and drift thresholds are also
used, similar to the ones presented by DDM, EDDM, PHT, and ECDD.
DOF:
The method proposed by Sobhani et al. detects drifts by processing data chunk by chunk, the nearest
neighbor in the previous batch is computed for each instance in the current batch and comparing their
corresponding labels. A distance map is created, associating the index of the instance in the previous batch and
the label computed by its nearest neighbor; degree of drift is computed based on the distance map. The average
and standard deviation of all degrees of drift are computed and, if the current value is away from the average
more than s standard deviations, a concept drift is raised, where s is a parameter of the algorithm. [10]This
algorithm is more effective for problems with well separated and balanced classes.
IV. Statistical Tests For Concept Drift:
The design of a change detector is a compromise between detecting true changes and avoiding false
alarms. This is accomplished by carrying out statistical tests that verifies if the running error or class distribution
remain constant over time.

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CUSUM test:
The cumulative sum algorithm[24], is a change detection algorithm that raises an alarm when the mean
of the input data is significantly different from zero. The CUSUM input ϵ
t can be any filter residual, for
example, the prediction error from a Kalman filter. The CUSUM test is as follows-
go = 0
gt = max (0, gt-1 + ϵ
t - υ)
if gt > h then alarm and gt = 0 (7)
The CUSUM test is memoryless, and its accuracy depends on the choice of parameters υ and h.
Page Hinkley test: It is a sequential analysis technique, proposed by, that computes the observed values and their
mean up to the current moment. The Page-Hinkley test[5] is given as -
go = 0, gt = gt-1 + ϵ
t - υ
Gt = min(gt)
if gt - Gt > h then alarm and gt = 0 (8)
Geometric moving average test:
The Geometric Moving Average (GMA) test [25] is as below:
go = 0
gt = λgt−1 + (1 − λ)ϵ
t
if gt > h then alarm and gt = 0 (9)
The forgetting factor λ is used to give more or less weight to the last data arrived. The threshold h is
used to tune the sensitivity and false alarm rate of the detector.
Statistical test:
CUSUM and GMA are methods those deal with numeric sequences. A statistical test is a procedure for
deciding whether a hypothesis about a quantitative feature of a population is true or false. We test an hypothesis
by drawing a random sample from the population in question and calculating an appropriate statistic on its
items.
To detect change, we need to compare two sources of data, and decide if the hypothesis H0 that they
come from the same distribution is true. Otherwise, a hypothesis test will reject H0 and a change is detected. The
simplest way for hypothesis, is to study the difference from which a standard hypothesis test can be formulated.
0 - 1 Є N(0, σ20 + σ21 ), under H0
or, to make a χ2 test, [( 0 - 1)2/ σ20 + σ21] Є χ2(1), under H0
The Kolmogorov-Smirnov test (non-parametric) is another statistical test to compare two populations.
The KS-test has the advantage of making no assumption about the distribution of data.
V. Concept Drift Handling
Kuncheva proposes to group ensemble strategies for changing environments[9] as follows:
 Dynamic combiners (horse racing): component classifiers are trained and their combination is changed
using forgetting process.
 Updated training data : component classifiers in the ensemble are created incrementally by incoming
examples.
 Updating the ensemble member : ensemble members are updated online or retrained with blocks of data.
 Structural changes of the ensemble : ensemble members are reevaluated and the worst classifiers are
updated or replaced with a classifier trained on the most recent examples, with any concept change.
 Adding new features - The attributes used are changed, as an attribute becomes significant, without
redesigning the ensemble structure.
The approaches to handle concept drifts includes single classifier and ensemble classifier approaches.
The single classifiers are traditional learners that were modeled for stationary data mining and have the qualities
of an online learner and a forgetting mechanism. Basically, ensemble classifiers are sets of single classifiers
whose individual decisions are aggregated by a voting rule. The ensemble classifiers provide better
classification accuracy as compared to the single classifiers due combined decision. They have a natural way of
adapting to concept changes due to their modularity.
Streaming Ensemble Algorithm(SEA): The SEA[8], proposed by Street and Kim, changes its structure based
on concept change. It is a heuristic replacement strategy of the weakest base classifier based on accuracy and
diversity. The combined decision was based on simple majority voting and base classifiers unpruned. This
algorithm works best for at most 25 components of the ensemble.

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Accuracy Weighted Ensemble (AWE): In SEA, it is crucial to properly define the data chunk size as it
determines the ensembles flexibility. The algorithm AWE, proposed by Wang et al., trains a new classifier C' on
each incoming data chunk and use that chunk to evaluate all the existing ensemble members to select the best
component classifiers. AWE is best suited for large data streams and works well for recurring and other drifts.
Adaptive Classifier Ensemble(ACE): To overcome AWE‟s slow drift reactions, Nishida proposed a hybrid
approach in which a data chunk ensemble is aided by a drift detector, called Adaptive Classifier Ensemble
(ACE), aims at reacting to sudden drifts by tracking the classifier‟s error rate with each incoming example,
while slowly reconstructing a classifier ensemble with large chunks of examples.
Hoeffding option trees(HOT) and ASHT Bagging: Hoeffding Option Trees (HOT) provide a compact
structure that works like a set of weighted classifiers, and are built in an incremental fashion. This
algorithms[27] allows each training example to update a set of option nodes rather than just a single leaf.
Adaptive-Size Hoeffding Tree Bagging (ASHT Bagging) diversifies ensemble members by using trees of
different sizes and uses a forgetting mechanism. Compared to HOT, ASHT Bagging proves to be more accurate
on most data sets. But both are time and memory expensive than option trees or single classifiers.
Accuracy Diversified Ensemble(ADE): The algorithm called Accuracy Diversified Ensemble (ADE)[22], not
only selects but also updates components according to the current distribution. ADE differs from AWE in
weight definition, the use of online base classifiers, bagging, and updating components with incoming examples.
Compared to ASHT and HOT, we do not limit base classifier size, do not use any windows, and update
members only if they are accurate enough according to the current distribution.
Accuracy Updated Ensemble(AUE): Compared to AWE, AUE1 [7] conditionally updates component
classifiers. It maintains a weighted pool of component classifiers and predicts classes for incoming examples
based on weighted voting rule. It substitutes the weakest performing ensemble member and new classifier is
created with each data chunk of examples, also their weights are adjusted. It uses Hoeffding trees as component
classifiers. Compared to AUE1, AUE2 introduces a new weighting function[22], does not require cross-
validation of the candidate classifier, does not keep a classifier buffer, prunes its base learners, and always
updates its components. It does not limit base classifier size and use any windows. The OAUE[23], tries to
combine block-based ensembles and online processing.
VI. Datasets With Concept Drift
Artificial datasets give the ground truth of the data, however, real datasets are more interesting as they
correspond to real-world applications where the algorithms‟ usability is tested[22].
6.1 Real datasets:
 Forest Covertype, obtained from US Forest Service (USFS) Region 2 Resource Information System (RIS)
data, contains 581, 012 instances and 54 attributes.
 Poker-Hand consists of 1,000, 000 instances and 11 attributes.
 Electricity dataset, collected from the Australian New South Wales Electricity Market, contains 45, 312
instances.
 Airlines Dataset contains 539,383 examples described by seven attributes.
 Ozone level detection data set consists of 2,534 entries and is highly unbalanced (2% or 5% positives
depending on the criteria of “ozone days”).
6.2 Synthetic datasets:
The synthetic datasets allow us to analyze how the methods deal with the types of drift included in the datasets,
as it is known in advance when the drifts begin and end. For abrupt or sudden drifts, Stagger, Gauss, Mixed2
can be used. The Waveforrm, LED generator or Circles dataset best suited for gradual drifts. Hyperplane dataset
works well for both gradual and incremental drift. Radial basis function(RBF) can also be used for incremental
drift, and blips can also be incorporated.
Applications
This sections describes various real-life problem [11,12] in different domains related to the concept drifts in the
data generated from these real domains.

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Fig 3: Applications of Real-domain concept drift
Monitoring and control often employs unsupervised learning, which detects abnormal behavior. In
monitoring and control applications the data volumes are large and it needs to be processed in real time.
Personal assistance and information applications mainly organize and/or personalize the flow of
information. the class labels are mostly „soft‟ and the costs of mistake are relatively low.
Decision support includes diagnostics, evaluation of creditworthiness. Decision support and diagnostics
applications usually involve limited amount of data. Decisions are not required to be made in real time but high
accuracy is essential in these applications and the costs of mistakes are large.
Artificial intelligence applications include a wide spectrum of moving and stationary systems, which
interact with changing environment. The objects learn how to interact with the environment and since the
environment is changing, the learners need to be adaptive.
VII. Conclusion
This paper describes about the problem of concept drift. It summarizes the need, types and reasons for
concept change. The various concept drift detection methods viz. DDM, EDDM, Paired learners, ECDD,
ADWIN, STEPD and DOF are discussed and methods it adopts to detect concept change. To identify if concept
drift has occurred, statistical tests like CUSUM, Page-Hinkley and GMA test are explained. Various classifier
approaches, especially, ensemble classifiers provide better accuracy in case of concept change. The ensemble
classifiers SEA, AWE, ACE, ADE, HOT, ASHT, AUE adapt according to the drift that occurs, yielding good
classifier accuracy. Later, applications and the datasets, real and synthetic, suited for various concept drifts can
be used to check the adaptability of any algorithm handling concept drift.
In future, we can enhance the classification performance of the ensemble algorithms discussed above,
by adapting it to various drifts and diversity.
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