Daniel Stanley Tan edited untitled.tex  about 8 years ago

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In the recent years, there has been an explosion of Visualizing  data and it continues to grow by the second. In fact, data generated in the past decade is much larger than all data collected in the past century combined \cite{data2013}. This enables scientists to get a deeper understanding of the helps reveal interesting patterns from large  data sets  that was might  not possible before. But be obvious in some representations. It also aids domain experts in extracting information, generating ideas, and formulating hypotheses from  the huge amount of data. However visualizing big and high dimensional  databeing collected also poses a bunch of new problems. Data  is growing faster than manufacturers can build computers that can process them \cite{chips2016}. Traditional techniques for data analytics are not capable of analyzing these huge amounts of data challenging  due totheir processing time increasing exponentially as the number of data increases. To make matters more challenging, this is usually coupled with high dimensionality thus, increasing  the complexity human limitation  of the problem further. No algorithm exists yet that tackles all the problems of handling big data but there has been many works that address some aspects of it. \cite{xu2016exploring} only being able to visualize up to three dimensions.  I am particularly interested Indeed,  in pursuing further research on visualizing big data. Visualizing the recent years, there has been an explosion of  data helps reveal interesting patterns from large and it continues to grow by the second. In fact,  data sets that might not be obvious generated  in some representations. It also aids domain experts the past decade is much larger than all data collected  inextracting information, generating ideas, and formulating hypotheses from  the data. However visualizing big and high dimensional past century combined \cite{data2013}. Traditional techniques for data analytics are not capable of analyzing these huge amounts of  datais challenging  due to their processing time that increases exponentially as  the human limitation number  of only being able to visualize up to three dimensions. data increases. To make matters more challenging, this is usually coupled with high dimensionality thus, increasing the complexity of the problem further. For now, no algorithm exists that tackles all the problems of handling big data, although there has been many works that address some specific aspects of it. \cite{xu2016exploring}  A common way Some existing ways  to handle these visualize high-dimensional data  are through dimensionality reduction techniques like Random Projections \cite{bingham2001random,kaski1998dimensionality}, Self Organizing Maps (SOM) \cite{kohonen1990self}, Multidimensional Scaling (MDS) \cite{kruskal1964multidimensional} and Principal Components Analysis (PCA) \cite{dunteman1989principal} which significantly reduce the dimensions by mapping high dimensional data into lower dimensions. This mapping inevitably loses information but these algorithms are creative in doing this in such a way that useful distances are preserved and information loss is minimized. The only problem is that the time complexity of these algorithms are exponential which is not suitable for handling big data. Parallelizable implementations of SOM \cite{carpenter1987massively}, MDS \cite{varoneckas2015parallel} and PCA \cite{andrecut2009parallel} exist but it only reduces the complexity by a linear factor, which may be good for now but it won't scale well for the future. Clustering is another technique used in data mining. For big data, the clustering algorithm needs to run in at least quasilinear time. There are many clustering algorithms that can do this such as BIRCH \cite{zhang1996birch}, FCM \cite{bezdek1984fcm}, DBSCAN \cite{ester1996density}, EM \cite{dempster1977maximum}, and OPTICS \cite{ankerst1999optics} to name a few. BFR (Bradley-Fayyad-Reina) \cite{bradley1998scaling} and CLIQUE \cite{agrawal1998automatic} seems promising for the task of big data visualization. BFR (Bradley-Fayyad-Reina) algorithm is a variant of K-Means that can handle large data. The idea is that if we assume the clusters to be normally distributed then we can summarize the clusters using its mean and standard deviation, effectively reducing the number of data points to be processed in the succeeding iterations. The notion of summarizing the data points and creatively reducing the number of data points may be applied to visualization to increase the speed with minimal loss of information. CLIQUE on the other hand is a subspace clustering algorithm, it looks for clusters in subsets of the dimensions. This may be useful in reducing the number of dimensions and also in revealing patterns that may be hidden due to the inclusion of some dimensions.