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Nadica Nikolova, 2016-03-31 11:46 AM


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\title{Measuring performance on clustering algorithms}

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%Eldon Tyrell\IEEEauthorrefmark{4}}
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%Georgia Institute of Technology,
%Atlanta, Georgia 30332--0250\\ Email: see}
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Petar Kjimov\IEEEauthorrefmark{1},
Ivica Obadik\IEEEauthorrefmark{2},
Nadica Nikolova\IEEEauthorrefmark{3} and
Marija Nikolova\IEEEauthorrefmark{4}}
\IEEEauthorblockA{Faculty of Computer Science and Engineering\\University of Ss. Cyril and Methodius (UCM),
Skopje, Macedonia\\
Email: \IEEEauthorrefmark{1},

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Clustering is a machine learning technique that takes
a central part in data analysis. It is a powerful technique with
whom we can group objects based on their characteristics without
any labels given. Clustering can be used for pattern
recognition, image processing, bioinformatics and etc. There are
a lot of clustering algorithms, and which one we use depends on the
nature of the data we have and on the utility that each output of the
different clustering algorithms brings to the research. In this paper, we describe testing and evaluation on the performances
of four different clustering algorithms.

The dataset used in this research consists of Facebook events where each event is described by the words in his description. The original dataset contained 130000 instances and
600000 features. In order to work with this dataset, on the resources available, modifications
on the default dataset were required such as using sparse matrix formats,
stemming the description of the events, computing n-grams and
applying data dimensionality reduction techniques.
The testing was made on different number of events and features, starting from 100 events
and 1000 features, ending with 15000 events and 120000 features.

The experiment was made using popular implementations of these algorithms in Python Programming Language, and R Programming Language.

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Clustering; Facebook events; Machine learning; Dimensionality reduction; Text processing; Natural Language Processing; Performance;Evaluation

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\section{Introduction} \label{sec:introduction}
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Today, we are aware that there are tons of big data
that need to be processed for purpose of gathering useful information and insights from that data .
In order to process that data we need
resources and techniques that are applicable to it.
Before we can use the data as input to any algorithm, it is desirable to preprocess the data because it can improve the performance and results
of the algorithms. Machine learning techniques allow us to manipulate raw data
in order to retrieve important information.

Clustering is one of the most popular techniques that is used for various
purposes nowadays. With clustering we can process images,
group patients sick from same disease, to find similarities,
do market analysis, and etc. There are a lot of different
groups of algorithms that perform clustering such as
centroid-based algorithms, hierarchical algorithms,
density based algorithms and distribution based algorithms.

In this paper, we have chosen four clustering algorithms. The algorithms that
have been chosen are: K-Means\cite{ref:dbscan}, Agglomerative Hierarchical clustering\cite{ref:agglomerativeios} ,
DBSCAN\cite{ref:dbscan} and BIRCH\cite{ref:zhang1996birch} .

Our dataset was generated by quering the Facebook Graph API for events
that are posted on this social network for certain cities and additionally processing those events to form dataset on which the above algorithms
can be applied. The detailed procedure is described below.

The performance testing and evaluation of the algorithms asserted above, was made with different numbers
of instances from the dataset with events.

The rest of this paper is organized as follow: Section II
describes briefly the methods we used for preprocessing the events and used clustering
algorithms. Section III introduces similar analysis on clustering algorithms.
In Section IV we have briefly described our approach. Section V contains the detailed approach. Results are available in Section VI. Finally Section VII, concludes the paper.

%short description on this techniques, few rows only
The problem of clustering Facebook events is equivalent to the problem of clustering small texts. These are very well known problems in machine learning and natural language processing. In this section, we briefly describe the existing techniques that we use to solve this problem.

\subsection{Compressed Sparse Row (CSR) Matrix}
The CSR (Compressed sparse row) matrix format is a format for sparse matrix representation. We use it for the "bag of words" representation which is always sparse.

Stemming is the process of reducing the word to its base or root form. For example the words "run" and "running" should represent a single feature. We use the implementation of the "Porter stemmer"\cite{ref:porter1980algorithm} of the NLTK library\cite{ref:nltk_bird2009natural}.

N-grams are continious sequence of N items(in our case words) from a given context. With N-grams probabilistic model can be built from context of the items occurence. \cite{ref:n-gram}
Word occurences in a document(in our case event) are normalized by inverse document frequency.\cite{ref:tf-idf}

\subsection{Latent Semantic Analysis (LSA)}
Latent Semantic Analysis is a technique which identifies different contexts of word usage and then groups together the words that are part of the same context. We used LSA to reduce the dimensions of the matrices of events and words (features).\cite{ref:landauer1998introduction}

\subsection{K - Means Algorithm}
The K-Means Algorithm is an unsupervised learning algorithm which places K centroids with random coordinates in space. Each instance is assigned in the group that has the closest centroid.
When all of the instances are assigned, the positions of the centroids are recalculated, and this is repeated until the centroids no longer move.\cite{ref:kmeans}

\subsection{Agglomerative hierarchical clustering}
The agglomerative hierarchical clustering is a clustering method that starts with assigning each point into a separate cluster. In each step, two closest clusters are merged . This process is repeated until one cluster is left when the algorithm terminates.\cite{ref:agglomerativeios}
DBSCAN is a density-based clustering algorithm which groups the points in three groups: core, reachable, and noise(outlier) points.
After assigning each point in a specific group, we take a core point and we assign it to one cluster, along with the other points that are reachable from it.\cite{ref:dbscan_ester1996density}
The Birch algorithm is another hierarchical clustering technique commonly used over particularly large data-sets.\cite{ref:zhang1996birch}

Silhouette is a metric for cluster's evaluation whose value is in range betwen -1 and 1. The higher the value, the better separation of clusters is obtained.\cite{ref:silhouettescore}

\section{Related work}
%Related papers here : small section, few rows, references
There are some papers which are related to ours in some ways.
The first paper is called "A comparison of document clustering techniques" by M. Steinbach, G. Karypis and V. Kumar.\cite{ref:steinbach2000comparison} In this paper, the authors are comparing K-means and other algorithms for clustering.
The second paper is called "An Introduction to Latent Semantic Analysis" by
Thomas K. Landauera, Peter W. Foltzb and Darrell Lahamc.\cite{ref:landauer1998introduction} This paper containes an explanation of the Latent Semantic Analysis, what it is used for, and etc.
\section{Overview of the solution}
%Description of the solution in short notes
Our project is contained from the following steps:
\item Consuming events for different world locations using the Facebook Graph API
\item Feature extraction and model creation
\item Dimensionality reduction
\item Clustering
\item \label{step:analyse_evaluate}Analyse the execution time of each algorithm and evaluate its results
\item Draw conclusions from \ref{step:analyse_evaluate}

\section{Our solution}
In this section we describe our test environment and the experiments we performed.

\subsection{Test environment}\label{sec:test_environment}
The Python implementations were executed on a computer with the following configuration: Intel Core i7-4710HQ CPU @ 2.50 GHz with 2 x 8 GB DDR3 RAM @ 1600 MHz. The OS is 64-bit Ubuntu 14.04.3.
Testing of the algorithms in R programming language were made on computer with 4GB RAM and processor: Intel(R) Core(TM) i3-2350M CPU @ 2.30GHz, running on 64-bit Windows 7 OS. We used the 3.2.3 R version.

\subsection{Consuming events and creating dataset}
We queried Facebook Graph API with HTTP requests
and obtained name and description for 130 000 events in 3098 world cities.
Our dataset consists of the descriptions of each event (each description is a sample).

\subsection{Feature extraction}\label{subsec:feature_extraction}
Next we created the "bag of words" model. We tokenized each description to create two models, the first exclusively with 1-grams and the second with 1, 2 and 3-grams as features. We also performed stemming using the "Porter stemmer" algorithm\cite{ref:porter1980algorithm}. The Python version additionally computed tf-idf\cite{ref:tf-idf}. To extract these features we used a combination of algorithms, both from the scikit-learn library\cite{ref:scikit-learn}\cite{ref:sklearn_api}, and some ours implementations too.

\subsection{The Compressed Sparse Row (CSR) Format}
Vectorizing texts to create "bag of words" models, results in a matrices with lot of zeros. In these matrices each column represents a single feature, and each row is a sample described with its feature vector. To store the model from \ref{subsec:feature_extraction} in memory we used the CSR matrix implementations from the SciPy and Bigmemory libraries\cite{ref:scipy_library}\cite{ref:rbigmemory}.

\subsection{Dimensionality reduction }
With the Latent Semantic Analysis(LSA)\cite{ref:lsa_original_paper}, we reduced the number of the features of our model. We tried with 100 and 1000 dimensions. To make visualization possible, the number of dimensions were further reduced to 50 with LSA and even further reduction to 2 dimensions was performed with t-SNE (t-distributed Stochastic Neighbor Embedding)\cite{ref:lsa_original_paper}\cite{ref:rlsafun}\cite{ref:scikit-learn}\cite{ref:sklearn_api}\cite{ref:tsne_van2008visualizing}.

\subsection{Running clustering algorithms}
We experimented with both, the Python and R implementations. In R the algorithms were run on sample from 100 to 1000 instances, with step 100.
In Python each algorithm was executed on datasets which size ranges from 100 to 3000 events with step 100. We set the number of the desired clusters to be the square root of the size of the input data set (rule of thumb), except for the DBSCAN algorithm which automatically selects the right number. The epsilon parameter in DBSCAN was taken to be 0.2. We used existing implementations for this algorithms, both in Python\cite{ref:scikit-learn}\cite{ref:sklearn_api} and in R\cite{ref:rbiganalytics}\cite{ref:rfastcluster}\cite{ref:rfpc}.
We did not perform experiments with the BIRCH algorithm in R because its implementations in this language are buggy.

\subsection{Measuring running time of algorithms }
For each algorithm we measured the elapsed time for it's execution. The results from the experiment in R and Python are shown in \ref{fig_ranalysis} respectively. In both languages we measured the time with the highest resolution timer available, which is platform dependent (we listed our test machines in \ref{sec:test_environment}).

\subsection{Evaluate and visualize clusters}
Out metrics for evaluation of the clustering results was silhouete score\cite{ref:silhouettescore} .
In R silhouette score\cite{ref:silhouettescore} was measured with the stats function from the cluster\cite{ref:rcluster} package and the clusters were visualized with fpc\cite{ref:rfpc} package, by using it's plotcluster function.
In python silhouette score\cite{ref:silhouettescore} was measured with metrics package from skicit-learn\cite{ref:scikit-learn}\cite{ref:sklearn_api} library. Clusters are visualized with matplotlib\cite{ref:matplotlib} package.

%Results, analysis, pictures, tables

\subsection{Result analysis in R}
In figure \ref{fig_ranalysis}, we can see the graphs that show the dependency of silhouette score\cite{ref:silhouettescore} as metric for cluster evaluation (\ref{fig_first_case}) and the dependency of time of execution in seconds towards different sized sample (\ref{fig_second_case}).

\subfigure[Cluster evaluation]{%
\includegraphics[width=3in,natwidth=770,natheight=582]{images/clusteringR1.jpg} \label{fig_first_case}
\subfigure[Time performance]{%
\includegraphics[width=3in,natwidth=765,natheight=613]{images/clusteringR2.jpg} \label{fig_second_case}
\caption{Results from execution of clustering algorithms in R}
\subsection{Result analysis in Python}

\subsubsection{Cluster evaluation}
In \ref{fig_first_case} the silhouette coeficient for DBSCAN algorithm is always near -1, which means that with this algorithm, the sample has been assigned to wrong cluster. Thus, the DBSCAN algorithm, is not a good choice for clustering this dataset.
The values of silhouette score for the hierarchical agglomerative clustering are around the 0, which means that the values from the sample are very close to the bounds of two neighboring clusters. This algorithm has shown better results than the DBSCAN algorithm.
With the k-means algorithm we can see that the silhouette score starts from 0.24 and goes down to around 0, which means that, also, that the sample is on border of two neighboring clusters\cite{ref:silhouettescore}.
\subsubsection{Measuring time performance}
In figure \ref{fig_second_case} we have the dependency of execution time of algorithms and the number of samples. We can immediately spot, that as the sample grows, so as the execution time. We see that, for this dataset, DBSCAN is the slowest algorithm, where as k-means algorithm and the algoritam for agglomerative hierarchical clustering have nearly the same values.

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In this paper, we measure clustering algorithms in R and Python programming languages. We can conclude from the results that in R, k-means algorithm, and the algoritam for agglomerative hierarchical clustering have better results on cluster evaluation and time performance, than DBSCAN. This means, that, for this data samples, the k-means algorithm and the algorithm for agglomerative hierarchical clustering are better suited for performing clustering.

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The authors would like to thank...

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% H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
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