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Figures Abstract Biclustering techniques are gaining attention in the analysis of large-scale datasets as they identify two-dimensional submatrices where both rows and columns are correlated. In this work we present ParBiBit, a parallel tool to accelerate the search of interesting biclusters on binary datasets, which are very popular on different fields such as genetics, marketing or text mining.

It is based on the state-of-the-art sequential Java tool BiBit, which has been proved accurate by several studies, especially on scenarios that result on many large biclusters.

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ParBiBit uses the same methodology as BiBit grouping the binary information into patterns and provides the same results. Our performance evaluation with 18 representative input datasets on two different eight-node systems shows that our tool is significantly faster than the original BiBit.

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This is an open access article distributed under the terms of the Creative Commons Attribution Licensewhich permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The experimental evaluation was performed with synthetic data. Competing interests: The authors have declared that no competing interests exist. Introduction The amount of data that can be collected and stored in several research and industry fields has significantly increased during the last years.

This information is often described in a two-dimensional way, where rows and columns represent the measured attributes and samples, respectively.

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The analysis of these data is a complex and computationally expensive procedure that often requires data mining techniques to extract valuable information and transform it into an understandable structure for further use.

A widely spread data mining approach is the clustering, that allows to identify some patterns and structures between the attribute and sample relationships. However, traditional clustering techniques are not able to provide information binary options platforms for pone understand local relationships between both samples and attributes.

In this case, biclustering approaches should be used in order to identify a subset of rows attributes that exhibit similar patterns on a subset of columns samples in a two-dimensional data matrix. There exist several biclustering techniques, with different advantages and drawbacks depending on the characteristics of the input datasets and the research field where the approach will be used [ 1 ].

Gene expression analyses are probably nowadays the most common application of biclustering techniques. In this case datasets contain information about the expression level of many genes on several individuals under different experimental conditions.

Rows and columns represent genes and samples, respectively.

Biclustering is able to diagnose genes responsible of certain diseases only on a group of individuals. Many research works have focused on analyzing the best biclustering approaches for gene expression data [ 2 — 4 ].

Other fields where biclustering has been satisfactorily applied are drug activity [ 5 ], text mining [ 6 ], information theory [ 7 ] or marketing [ 8 ].

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Among the different alternatives for biclustering, some algorithms are especially designed for binary data so that they are able to obtain results with better accuracy in lower runtime over these very common datasets. For instance, in genetics the data can be simplified so that each value one or zero represents whether a gene is differentially expressed in an individual or not.

A recent survey has proved that binary biclustering can provide high precision results for gene expression data analyses [ 9 ]. Binary data matrices are also useful in text mining values are one only when certain word appears in a document or marketing each value represents whether a costumer buys a product or not. Despite binary biclustering techniques are usually faster than those for quantitative data, the computational cost of the available methods that provide accurate results is still prohibitive for large datasets.

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This paper presents ParBiBit, a parallel application that exploits computational capability of ready business binary options distributed-memory systems to accelerate the search of biclusters on binary datasets. Related work Several biclustering approaches have been suggested to deal with binary two-dimensional matrices.

Among all of them, we have selected the Java-based application BiBit [ 12 ] as basis for our tool due to several reasons: A recent review of 17 available biclustering methods [ 9 ] has proved that BiBit obtains accurate results for gene expression data, especially on cases with many large biclusters.

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This work also shows that the BiBit approach can be useful for quantitative data if applying a binarization. BiBit exploits the binary nature of the data by efficiently using Boolean algebra operations.

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This makes it faster than Bimax [ 13 ], probably the most commonly employed binary biclustering tool. Although in the last years several algorithms not tested in the aforementioned review have been presented for binary biclustering [ 14 — 16 ], their related publications do not include tests that prove that any of these novel approaches are more accurate than BiBit.

Furthermore, these implementations are not publicly available for further testing. Previous works that address the biclustering on this type of facilities are available for quantitative datasets following either the message-passing paradigm [ 1718 ] or the MapReduce approach [ 1920 ].

The only work focused on binary options platforms for pone data [ 21 ] is implemented with this last MapReduce paradigm. However, all these previous works seem preliminary implementations as their parallel software have not been released. Consequently, up to our knowledge, ParBiBit is the first publicly available tool to accelerate binary biclustering on multicore CPU clusters.

Finally, implementations designed for other type of high performance computing architectures such as GPUs [ 22 — 24 ] or FPGAs [ 2526 ] have also been presented, but none of them dedicated to binary data. Background This section describes the main concepts and technologies on which ParBiBit relies on, and thus are necessary to understand the behavior and implementation of our tool. Additionally, most binary options platforms for pone search for only maximal biclusters, binary options platforms for pone.

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Similarly to BiBit, our tool uses the concept of bit-pattern in order to find the biclusters of a binary matrix with a minimum number of rows mnr and columns mnc specified by the user. The joint pattern of a subset of rows consists of n bits one per column where the bit k is set to one if the binary value of column k in all binary options platforms for pone rows of the subset is equal to one. Otherwise, the bit is set to zero.

The pattern of a bicluster is the joint pattern of all the rows contained in it. BiBit works as follows we refer to the BiBit main publication [ 12 ] for more details : Initializes an empty list of bicluster structures. Checks that the number of ones quick bets on binary options the pattern is equal or higher than mnc and the pattern has not been used for any bicluster already inserted in the list.

Otherwise, the bicluster is discarded and the algorithm returns to step 2. The bicluster is inserted in the list if the number of rows is equal or higher binary options platforms for pone mnr. The information of the list is printed in the output file.

The rows that belong to each bicluster were directly saved in the structure, while the columns can be obtained as those elements in the pattern equal to one. However, the dependencies among the iterations binary options platforms for pone the binary options platforms for pone in step 2 each iteration checks whether the pattern has already been used make the BiBit algorithm not adequate for parallel computing.

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Thus, it had to be modified in ParBiBit as will be explained in following sections. It is even possible to recursively spawn threads from within already spawned ones. The actual number of concurrently running threads should be adjusted to roughly match the amount of physical cores of the system since the OS might serialize their execution using expensive context switches if their number exceeds the amount of available cores.

All threads share the resources of the parent system process, i. This is advantageous since threads can be spawned with binary options platforms for pone latency and benefit from lightweight inter-thread communication using shared registers and arrays.

The instruction flow of the main thread continues independently of the work accomplished in the spawned threads until the end of the main function is reached.

In order to ensure that all spawned threads have finished their work, the main thread should wait for them. This is accomplished with a call to the method join of the class thread. As all threads share the same memory space, one of the most common causes of errors are the race conditions, i. As the thread scheduling algorithm can swap between threads at any time, we do not know the order in which the threads will attempt to access the shared data.

Therefore, the result of the change in data would be dependent on the thread scheduling algorithm, i. A mutex can be locked by a specific thread, i. While being locked a mutex cannot be locked or unlocked by other threads which have to wait for its release causing an implicit synchronization of threads.

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Nevertheless, it is not advisable to abuse of the use of mutexes as its synchronization leads to some performance overhead some threads stop their execution and remain idle. In ParBiBit, mutexes are used to serialize the modification of the list of biclusters to ensure that all threads have the most updated information when they check whether the pattern has already been used see point 2.

Message passing interface MPI The target parallel architecture of this work are distributed-memory systems that consist of several nodes interconnected through a network, each of them with a memory module and several CPU cores see Fig 1. The computational capability of the cluster depends on factors such as the number of nodes, the number of cores per node, the network characteristics, the memory bandwidth, etc.