Resourceaware Mining of Data Streams
Mohamed Medhat Gaber
(Centre for Distributed Systems and Software Engineering
Monash University
900 Dandenong Rd, Caulfield East, VIC3145, Australia
Mohamed.Medhat.Gaber@infotech.monash.edu.au)
Shonali Krishnaswamy
(Centre for Distributed Systems and Software Engineering
Monash University
900 Dandenong Rd, Caulfield East, VIC3145, Australia
Shonali.Krishnaswamy@infotech.monash.edu.au)
Arkady Zaslavsky1
(Centre for Distributed Systems and Software Engineering
Monash University
900 Dandenong Rd, Caulfield East, VIC3145, Australia
Arkady.Zaslavsky@infotech.monash.edu.au)
Abstract: Mining data streams has raised a number of research
challenges for the data mining community. These challenges include the
limitations of computational resources, especially because mining streams
of data most likely be done on a mobile device with limited resources.
Also due to the continuality of data streams, the algorithm should have
only one pass or less over the incoming data records. In this article,
our Algorithm Output Granularity (AOG) approach in mining data streams
is discussed. AOG is a novel adaptable approach that can cope with the
challenging inherent features of data streams. We also show the results
for AOG based clustering in a resource constrained environment.
Keywords: data mining, data stream, clustering, and
resourceaware computing
Categories: H
1 Introduction
Knowledge extraction from data streams has attracted attention in recent
years. The continuous highspeed generation of data records from sensors,
web click streams, and stock market information has created new challenges
and open research issues for the data mining community [22],
[23]. The intuitive solution is the development of
onepass or less techniques that can result in acceptable approximation
mining results in a resource constrained environment; represented by low
computational power of mobile devices and limited bandwidth of wireless
networks. This represents the typical processing environment for data streams.
Different mathematical and algorithmic methods have been proposed to
be used for data stream processing. Sampling and projection have been used
to cope with the high data rate of data streams. Sampling refers to the
process of selecting data items from a data stream according to a statistical
measure.
Projection is used for dimensionality reduction using sketching techniques
[22]. Group testing, tree method, robust approximation
and exponential histograms have been used as algorithmic techniques for
reducing space and time complexity. [2], [22],
[23].
Querying and mining data streams have been studied intensively for the
last three years. The challenges for querying data streams are unbounded
memory requirement and high data rate. Thus, the computation time per data
element should be less than the data rate. Also, it is very hard due to
memory limitations to have an exact result. A number of techniques have
been proposed to approximate the query result. One of these techniques
is sliding window, in which the query result is computed over a recent
time interval. Batch processing, sampling, and synopsis data structures
are the other used techniques for data reduction in query processing [2].
Recently, load shedding and rate based query optimization have been
proposed as a solution approach for querying data streams. Load shedding
refers to the process of dropping data elements from the incoming data
stream randomly or semantically in order for the query processor program
to cope with the high data rate of incoming elements. Load shedding has
been implemented in Auora and STREAM systems [3], [29],
[30]. Rate based query optimization has been proposed
to optimize the number of outputs at any specified time given that the
higher the data rate the higher the output rate [31].
Mining data stream is the process of extracting interesting patterns
and trends from a sequence of elements that arrive continuously in a rapid
speed. Analogous to load shedding in query processing, data rate adaptation
is proposed as a solution approach for mining data streams. Data rate adaptation
could be used from the input side using sampling, filtering and aggregation.
We propose the use of data rate adaptation from the output side using algorithm
output granularity. Algorithm output granularity is the amount of mining
results that fits in main memory before any incremental integration.
The AOG [13], [14] in mining
data streams is unique from the other approaches by being adaptable to
the data rate and the available resources of memory and time constraints.
The approach has its potential by being general and could be adapted to
different data mining techniques. We aim by implementing this project to
provide business and scientific institutions by a realtime analysis toolset
for generated data streams that became a phenomenon.
The article is organized as follows. Section 2 shows
the related work in details. Section 3 discusses AOG
approach in mining data streams and its formalization. The empirical results
from AOGbased clustering in resourceconstrained environment are discussed
in section 4. Finally, the paper is concluded in section
5.
2 Related Work
This section presents a review of the state of the art in data stream
mining techniques and related projects in resource constrained environments.
The following subsections attempt to give an intensive overview of the
current state of the field in terms of proposed mining techniques as well
as applications that show the potential of the area.
2.1 Techniques
There are different algorithms proposed to tackle the high speed nature
for mining data streams using different techniques. In this section, we
review the state of the art of mining data streams.
Guha et al. [15] have studied clustering data streams
using Kmedian technique. Their algorithm makes a single pass over the
data and use small space. It requires O(nk) time and O(ne) space where
"k" is the number of centers, "n" is the number of
points and ε < 1. The algorithm is not implemented, but the analysis of
space and time requirements of it are studied analytically. They proved
that any kmedian algorithm that achieves a constant factor approximation
can not achieve a better run time than O(nk). The algorithm starts by clustering
a calculated size sample according to the available memory into 2k, and
then at a second level, the algorithm clusters the above points for a number
of samples into 2k and this process is repeated to a number of levels,
and finally it clusters the 2k clusters to k clusters.
Bubcock et al. [3] have used exponential histogram
(EH) data structure to enhance Guha et al. algorithm. They use the same
algorithm described above, however they try to address the problem of merging
clusters when the two sets off cluster centers to be merged are far apart
by marinating the EH data structure. They have studied their proposed algorithm
analytically.
Charikar et al [5] have proposed a kmedian algorithm
that overcomes the problem of increasing approximation factors in the Guha
et al algorithm with the increasing in the number of levels used to result
in the final solution of the divide and conquer algorithm. This techniques
has been studied analytically.
Domingos et al. [8], [9], [16]
have proposed a general method for scaling up machine learning algorithms.
This method depends on determining an upper bound for the learner's loss
as a function in number of examples in each step of the algorithm. They
have applied this method to Kmeans clustering "VFKM" and decision
tree classification "VFDT" techniques. These algorithms have
been implemented and tested on synthetic data sets as well as real web
data. VFDT is a decision tree learning systems based on Hoeffding trees.
It splits the tree using the current best attribute taking into consideration
that the number of examples used satisfies a statistical result which is
"Hoeffding bound". The algorithm also deactivates the least promising
leaves and drops the nonpotential attributes. VFKM uses the same concept
to determine the number of examples needed in each step of Kmeans algorithm.
The VFKM runs as a sequence of Kmeans executions with each run uses more
examples than the previous one until a calculated statistical bound is
satisfied.
Challaghan et al. [6] have proposed STREAM and LOCALSEARCH
algorithms for high quality data stream clustering. The STREAM algorithm
starts by determining the size of the sample and then applies the LOCALSEARCH
algorithm if the sample size is larger than a prespecified equation result.
This process is repeated for each data chunk. Finally, the LOCALSEARCH
algorithm is applied to the cluster centers generated in the previous iterations.
Aggarwal et al. [1] have proposed a framework for
clustering data steams called CluStream algorithm. The proposed technique
divides the clustering process to two components. The online component
stores summary statistic about the data streams and the offline one performs
clustering on the summarized data according to a number of user preferences
such as the time frame and the number of clusters.
A number of experiments on real datasets have been conducted to prove
the accuracy and efficiency of the proposed algorithm.
Keogh et al [19] have proved empirically that most
cited clustering time series data streams algorithms proposed so far in
the literature come out with meaningless results in subsequence clustering.
They have proposed a solution approach using kmotif to choose the subsequences
that the algorithm can work on.
Ganti et al. [11] have described an algorithm for
model maintenance under insertion and deletion of blocks of data records.
This algorithm can be applied to any incremental data mining model. They
have also described a generic framework for change detection between two
data sets in terms of the data mining results they induce. They formalize
the above two techniques into two general algorithms: GEMM and Focus. The
algorithms are not implemented, but are applied analytically to decision
tree models and the frequent itemset model. GEMM algorithm accepts a class
of models and an incremental model maintenance algorithm for the unrestricted
window option, and outputs a model maintenance algorithm for both windowindependent
and windowdependent block selection sequence. FOCUS framework uses the
difference between data mining models as the deviation in data sets.
Papadimitriou et al. [25] have proposed AWSOM (Arbitrary
Window Stream mOdeling Method) for interesting patterns discovery from
sensors. They developed a onepass algorithm to incrementally update the
patterns. Their method requires only O(log N) memory where N is the length
of the sequence. They conducted experiments on real and synthetic data
sets. They use wavelet coefficients as compact information representation
and correlation structure detection, and then apply a linear regression
model in the wavelet domain.
Giannella et al. [12] have proposed and implemented
a frequent itemsets mining algorithm over data stream. They proposed to
use tilted windows to calculate the frequent patterns for the most recent
transactions based on the fact that people are more interested in the most
recent transactions. They use an incremental algorithm to maintain the
FPstream which is a tree data structure to represent the frequent itemsets.
They conducted a number of experiments to prove the algorithm efficiency.
Munka and Motwani [21] have proposed and implemented
an approximate frequency counts in data streams. The implemented algorithm
uses all the previous historical data to calculate the frequent patterns
incrementally.
Wang et al. [29] have proposed a general framework
for mining concept drifting data streams. They observed that data stream
mining algorithms don't take attention to the concept drifting in the evolving
data. They proposed using weighted classifier ensembles to mine data streams.
The expiration of old data in their model depends on data's distribution.
They use synthetic and real life data streams to test their algorithm and
compare between the single classifier and classifier ensembles. The proposed
algorithm combines multiple classifiers weighted by their expected prediction
accuracy. Also the selection of number of classifiers instead of using
all is an option in the proposed framework without loosing the accuracy.
Ordonez [24] has proposed several improvements
to kmeans algorithm to cluster binary data streams. He proposed an incremental
kmeans algorithm. The experiments were conducted on real data sets as
well as synthetic data sets. They demonstrated that the proposed algorithm
outperforms the scalable kmeans in most of the cases.
The proposed algorithm is a one pass algorithm in O(Tkn) complexity,
where T is the average transaction size, n is number of transactions and
k is number of centers. The use of binary data simplifies the manipulation
of categorical data and eliminates the need for data normalization. The
main idea behind the proposed algorithm is that it updates the centers
and cluster weights after reading a batch of transactions which equals
square root of the number of transactions rather than updating them one
by one.
Datar et al [7] have proposed a sketch based technique
to identify the relaxed period and the average trend in a timeseries data
stream. The proposed methods are tested experimentally showing an acceptable
accuracy for the approximation methods compared to the optimal solution.
The main idea behind the proposed methods is the use of sketches as a dimensionality
reduction technique.
2.2 Projects
Recent projects stimulate the need for mining data stream. These projects
include:
 Bur et al. [4] have developed Diamond Eye
for NASA and JPL. They aim by this project to enable remote systems as
well as scientists to extract patterns from spatial objects in real time
image streams. The success of this project will enable "a new era
of exploration using highly autonomous spacecraft, rovers, and sensors"
[4].
 Kargupta et al. [17],[20]
have developed the first UDM system: MobiMine. It is a client/server
PDAbased distributed data mining application for financial data streams.
It should be pointed out that the mining component is located at the server
side. There are different interactions between the server and PDA till
the results finally displayed on the PDA screen.
 Kargupta et al. [18] have developed Vehicle Data
Stream Mining System (VEDAS). It is a ubiquitous data mining system
that allows continuous monitoring and pattern extraction from data streams
generated onboard a moving vehicle. The mining component is located at
the PDA.
 Tanner et al. [28] have developed EnVironment
for OnBoard Processing (EVE). The system mines data streams continuously
generated from measurements of different onboard sensors. Only interesting
patterns are sent to the ground stations for further analysis preserving
the limited bandwidth.
 Srivastava and Stroeve [26] work in a NASA project
for onboard detection of geophysical processes such as snow, ice and clouds
using kernel clustering methods for data compression preserving limited
bandwidth needed to send image streams to the ground centers. The kernel
methods have been chosen due to its low computational complexity.
The above techniques and projects show the increasing interest in the
research community in addressing the problem of mining data streams in
resource constrained environments. Our AOG approach to tackle this problem
is discussed in details in the next section.
3 Algorithm Output Granularity
AOG is a threestage, resourceaware distancebased mining data streams
approach. The process of mining data streams using AOG starts with a mining
phase.
In this step, a threshold distance measure is determined. The algorithm
can have only one look at each data element. Using distance threshold in
clustering has been introduced in BIRCH [33] for mining
large data sets. In the mining stage, there are three variations in using
this threshold according to the mining technique: a) clustering: the threshold
is used to specify the minimum distance between the cluster center and
the data element; b) classification: In addition of using the threshold
in specifying the distance, the class label is checked. If the class label
of the stored items and the new item that are similar (within the accepted
distance) is the same, the weight of the stored item is increased along
with the weighted average of the other attributes, otherwise the weight
is decreased and the new item is ignored; c) frequent patterns: the threshold
is used to determine the number of counters for the heavy hitters. A full
description about AOGbased mining algorithms (LWC for clustering, LWClass
for classification and LWF for the frequent patterns) could be found in
[14].
The second stage in AOGmining approach is the adaptation phase. In
this phase, the threshold value is adjusted to cope with the data rate
of the incoming stream, the available memory, and time constraints to fill
the available memory with generated knowledge. This stage gives the uniqueness
of our approach in adjusting the output rate according to the available
resources of the computing device. The work has been done in the area does
not pay attention to the rapid data rate of the incoming stream. The approximation
algorithms and sampling techniques that have been used so far might not
be sufficient with the very high data rate.
The last stage in AOG approach is the knowledge integration phase. This
stage represents the merging of generated results when the memory is full.
This integration allows the continuality of the mining process. Figure
1 shows the AOGmining process.
Figure 1: AOG Mining Approach
The following is a mathematical formalization of AOGbased data stream
mining. Table 1 shows the symbols used in the mathematical formulation:
Symbol 
Meaning 
AAO 
Atomic algorithm output size. The size of smallest element produced
from the mining algorithm. For example in clustering the AAO represents
the size of storing the cluster center and the weight of the cluster. 
D 
Duration of the time frame. 
M_{i} 
Remaining memory size by the end of time frame i. (M_{i}
= M_{i1}  (AAO x O(TF_{i}))) 
TF_{i} 
Time frame i by which the threshold is adjusted to cope with the data
rate. 
N(TF_{i}) 
Number of data elements arrived during the time frame i. 
O(TF_{i}) 
Number of outputs produced during the time frame i. 
AR_{i } 
The average algorithm rate during TF_{i}. (O(TF_{i})
/ D) 
DR_{i} 
The average data rate during TF_{i}. (N(TF_{i})
/ D) 
T_{i} 
Remaining time from the time interval threshold needed by the algorithm
to fill the main memory.
(T_{i} = T_{i1}  D) 
Th_{i} 
Threshold value during the time frame i. 
Table 1: AOG Symbols
The main idea behind our approach is to change the threshold value that
in turn changes the algorithm rate according to three factors:
 History of data rate to algorithm rate ratio.
 Remaining time.
 Remaining memory.
The target is to keep the balance between the algorithm rate and data
rate from one side and the remaining time and remaining memory from the
other side.
[(AR_{i+1} / DR_{i+1}) / (AR_{i} / DR_{i}
)] = [(M_{i} / AR_{i}) / t_{i} ] (1)
AR_{i+1} = (M_{i} / T_{i}) . (Dr_{i+1}/
Dr_{i}) (2)
Using the Ari+1 in the following equation to determine the new threshold
value:
Thi+1 = [(AR_{i+1} / DR_{i+1} ).th_{i}] / (AR_{i}
/ DR_{i} ) (3)
After a time frame we can use linear regression to estimate the threshold
using the values obtained from the AR and Th.
Th = a. AR + b, b= Σ th.ar / Σ ar2, a= (Σ th /
Σn )  (b Σ th / n)
(4)
Linear regression is used because of the fluctuating distribution of
the incoming data elements. Data stream distribution is an effective factor
in determining the algorithm output rate. The experimental results of using
AOG in clustering are discussed in the following section.
4 Experimental Results
We run LWC on iPAQ with 64 MB, running Microsoft Windows CE version
3.0.9348. The program has been developed using Microsoft embedded Visual
C++ 3.0. We run Kmeans in the same environment in order to compare the
accuracy and the running time. The choice of Kmeans for the comparison
is based on that kmeans has been used in the same environment in astronomical
applications due to its low complexity. Examples include: Clustering earth
science data in a NASA project using Kmeans [27]
and mission planning onboard Mars rovers using kmeans [10].
In these projects, it has been pointed out that the use of kmeans is due
to its low complexity and the scarce of computational resources for such
missions. The datasets used is the experiments are synthesized with different
sizes.
The first experiment is to compare the running time of LWC and Kmeans
with the same data set and same number of clusters generated. The following
figures show the running time of LWC and Kmeans with different threshold
values for the LWC. The number of clusters is passed to kmeans to generate
the same number of clusters. Figures 2, 3
and 4 show that LWC outperforms Kmeans even with the
fine threshold that leads to creating large number of clusters.
Figure 2: LWC Running Time
Figure 3: Kmeans Running Time in seconds
Figure 4: LWC and Kmeans Running Time in seconds
To show the accuracy of the LWC compared to kmeans. We run the algorithms
on the same data set and sorted the generated cluster centers. Figure
5 shows that the generated centers for both algorithms are very close
and have the same trend.
Figure 5: Kmeans and LWC comparison
The following experiment has been conducted to show the unpredictability
of the number of passes needed by Kmeans. This leads to fluctuating running
time with similar data set sizes. Figure 6 shows the
results of this experiment.
Figure 6: Kmeans number of passes
The above results accompanied with the results obtained in [14]
show that LWC is a costefficient clustering algorithm that can result
in an acceptable accuracy compared with traditional algorithms like Kmeans.
To show the scalability of AOG, we conducted this experiment. Figure
7 shows the experimental results that represent the AOG overhead.
This experiment has been done with an increase in the dataset
sizes. The experiment shows stability in the AOG overhead. This
feature of AOG validates the feasibility of the approach with
continuous streaming information.
Figure 7: AOG Overhead
5 Conclusions and Future Work
The paper reviewed the stateoftheart in mining data streams. Our
AOG approach in tackling the problem has been presented with encouraging
results in resource constrained environment. AOG is the first approach
that pays attention to the data stream rate with respect to the available
resources. The AOGbased clustering running onboard a PDA has been compared
with kmeans. The results showed that LWC outperforms Kmeans in running
time with almost the same results in terms of generated cluster centers.
The AOG overhead experiment shows the applicability and scalability of
the approach.
 Adaptation to resource constraints.
 Generality of the approach to different mining algorithms.
 Reliability of the approach depending on AOG parameters.
 Scalability to any number of computational nodes.
The AOGbased mining package is our ultimate objective. This package
has its potential by being applicationindependent. Different business,
industrial and scientific scenarios can use the package to gain realtime
insights over the generated data streams.
The adoption of AOG in querying data streams in another research future
research direction. Finally, the development of AOG as a web service would
enable any current streaming technique to benefit from the resourceawareness
provided by the approach.
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