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This is the era of information and the amount of data has immensely increased since the last few years. This increase has resulted in dilemmas like the curse of dimensionality where we need a large number of resources to process the huge number of features. So far there are many tools available that process such large volumes of data among which Rough Set Theory is a prominent one. It provides the concept of Reducts which represent the set of attributes that provide the maximum of the information. However, the problem with Reducts is that they are not stable and keep on changing with the addition of more and more data. So, the concept of Dynamic Reducts is introduced in the literature to provide a more stable version of Reducts. There are many Dynamic Reduct finding algorithms available; however, these dynamic Reduct finding algorithms are computationally too expensive and inefficient for large datasets. In this research, we have presented an improved dynamic Reduct finding technique based on rough set theory. In this technique, Reducts are selected, optimized, and further generalized through Parallel Feature Sampling (PFS) algorithm. An in-depth investigation is performed using various benchmark datasets to justify the effectiveness of our proposed approach. Results have shown that the proposed approach outperforms the state-of-the-art approaches in terms of both efficiency and effectiveness. Overall, 96% average accuracy is achieved and 46.13% reduction in execution time is observed by the proposed algorithm against the compared contemporary approaches.

Recently, Cloud computing has emerged as one of the widely used platforms to provide compute, storage and analytics services to end-users and organizations on a pay-as-you-use basis, with high agility, availability, scalability, and resiliency. This enables individuals and organizations to have access to a large pool of high processing resources without the need for establishing a high-performance computing (HPC) platform. From the past few years, task scheduling in Cloud computing is reckoned as eminent recourse for researchers. However, task scheduling is considered an NP-hard problem. In this research work, we investigate and empirically compare some of the most prominent state-of-the-art scheduling heuristics in terms of Makespan, Average resource utilization (ARUR), Throughput, and Energy consumption. The comparison is then extended by evaluating the approaches in terms of individual VM level load imbalance. After extensive simulation, the comparative analysis has revealed that Task Aware Scheduling Algorithm (TASA) and Proactive Simulation-based Scheduling and Load Balancing (PSSLB) outperformed as compared to the rest of the approaches and seems to be optimal choice keeping in view the trade-of between the complexities involved and the performance achieved concerning Makespan, Throughput, resource utilization, and Energy consumption.

Feature selection is the process of selecting a subset of features without losing significant amount of useful information that is available in the original dataset. The use of rough set theory remains a prominent tool for this purpose. A number of techniques based on rough sets are based on the use of positive region based dependency measure which is a computationally expensive task. In this paper, we propose a novel dependency calculation technique termed as parallel dependency calculation technique. We propose to calculate dependency by directly finding the positive region based objects without calculating the positive region itself. As the objects are independent of each other so we propose to search these objects in parallel. The proposed technique was tested against the conventional dependency calculation technique and the results showed significant increase in performance, that is, overall 63.7% reduction in execution time and 96% reduction in required runtime memory was observed. In case of feature selection algorithms, there was 68% reduction in execution time when the proposed dependency calculation technique was used. The proposed method not only provides accuracy but is computationally less demanding than the conventional positive region based approach.

Feature selection is the process of selecting subset of features that still provide maximum amount of the information that otherwise is provided by the entire set of conditional attributes. Many approaches have been proposed so far in literature for this purpose. Recently the rough set based approaches have become dominant. Majority of these approaches use attribute dependency to find significance of attributes. Problem with this measure is that it uses positive region to calculate dependency which is a computationally expensive job. As a consequence, it degrades the performance of the feature selection algorithms using this measure. In this paper, we have proposed a new heuristic based dependency calculation technique by avoiding the positive region. The proposed method uses a heuristics approach by finding the consistent records regarding each decision class in the dataset. Using this method, allows us to calculate dependency by avoiding the positive region, which ultimately enhances the computational efficiency of the underlying feature selection algorithm thus enabling it to be used for dataset beyond smaller size. In order to calculate dependency by using the proposed method, we have used a two-dimensional grid as intermediate data structure. Number of feature selection algorithms were used with proposed solution on various publically available datasets to justify it. A comparison framework was used to compare the proposed solution with conventional methods. Results have justified the proposed solution both in terms of its efficiency and effectiveness.

Feature selection is the process of selecting a subset of features from the entire dataset such that the selected subset can be used on behalf of the entire dataset to reduce further processing. There are many approaches proposed for feature selection, and recently, rough set-based feature selection approaches have become dominant. The majority of such approaches use attribute dependency as criteria to determine the feature subsets. However, this measure uses the positive region to calculate dependency, which is a computationally expensive job, consequently effecting the performance of feature selection algorithms using this measure. In this paper, we have proposed a new heuristic-based dependency calculation method. The proposed method comprises a set of two rules called Direct Dependency Calculation (DDC) to calculate attribute dependency. Direct dependency calculates the number of unique/non-unique classes directly by using attribute values. Unique classes define accurate predictors of class, while non-unique classes are not accurate predictors. Calculating unique/non-unique classes in this manner lets us avoid the time-consuming calculation of the positive region, which helps increase the performance of subsequent algorithms. A two-dimensional grid was used as an intermediate data structure to calculate dependency. We have used the proposed method with a number of feature selection algorithms using various publically available datasets to justify the proposed method. A comparison framework was used for analysis purposes. Experimental results have shown the efficiency and effectiveness of the proposed method. It was determined that execution time was reduced by 63% for calculation of the dependency using DDCs, and a 65% decrease was observed in the case of feature selection algorithms based on DDCs. The required runtime memory was decreased by 95%.

Data is growing at an exponential pace. To cope with this data explosion, we need effective data processing and analysis techniques. Feature selection is selecting a subset of features from a dataset that still provides most of the useful information. Various tools are available as underlying framework for this process however, Rough Set Theory is the most prominent tool due to its analysis friendly nature. Majority of Rough Set based feature selection algorithms use positive region based dependency measure as the sole criteria to select feature subset. Calculating positive region requires calculation of lower approximation which consequently involves indiscernibility relation. In this paper, new definitions of two Rough Set preliminaries i.e. lower and upper rough set approximation are proposed. New definitions of approximations are computationally less expensive as compared to the conventional. The proposed redefinitions showed 42.78% decrease in execution time for redefined lower approximation and 43.06% decrease in case of redefined upper approximation, for five publicly available datasets while maintaining 100% accuracy. Finally based on these redefined approximations we proposed a feature selection algorithm, which when compared with state of the art techniques showed significant increase in performance without the affecting the accuracy.

In many fields, such as data mining, machine learning and pattern recognition, datasets containing large numbers of features are often involved. In such cases, feature selection is necessary. Feature selection is the process of selecting a feature subset on behalf of the entire dataset for further processing. Recently, rough set-based approaches, which use attribute dependency to carry out feature selection, have been prominent. However, this dependency measure requires the calculation of the positive region, which is a computationally expensive task. In this paper, we have proposed a new concept called the "Incremental Dependency Class" (IDC), which calculates the attribute dependency without using the positive region. IDCs define the change in attribute dependency as we move from one record to another. IDCs, by avoiding the positive region, can be an ideal replacement for the conventional dependency measure in feature selection algorithms, especially for large datasets. Experiments conducted using various publically available datasets from the UCI repository have shown that calculating dependency using IDCs reduces the execution time by 54%, while in the case of feature selection algorithms using IDCs, the execution time was reduced by almost 66%. Overall, a 68% decrease in required runtime memory was also found.

Classical Rough Set Theory (RST) is a prominent tool to deal with uncertainty of categorical data. However, it does not consider the preference order between the values of the attributes. Dominance Based Rough Set Approach (DRSA) provides dominance relation in this regard. Computation of the upper and lower approximation is a critical step in DRSA. However, computing these approximations is a computationally expensive task. Efficiently computing approximations will thus be helpful in reducing the execution time of algorithms using these approximations. In this paper, we have proposed an efficient approach to compute these measures. The proposed approach directly calculates approximations without considering the objects that do not play any role in the approximations. In our approach, one instance of a dataset is compared with another instance only once which avoids unnecessary comparisons. The proposed approach is compared with the conventional method using sixteen benchmark data sets from UCI. Results show that the proposed approach significantly reduces the execution time. The average reduction in the execution time was found to be almost 85%. This approach also reduces the memory consumption by 75%. The Big-O complexity is also reduced. These measures justify that the proposed approach is more effective and efficient as compared to the conventional DRSA.

This is an era of information. However, the data is only valuable if it is efficiently processed and useful information is derived out of it. It is now common to find applications that require data with thousands of attributes. Problem with processing such datasets is that they require huge amount of resources. To overcome this issue, research community has come up with an effective tool called feature selection. Feature selection lets us select only relevant data that we can use on behalf of the entire dataset. In this chapter we will discuss necessary preliminaries of feature selection.

Feature selection plays an important role in data mining and machine learning tasks. Rough set theory has been a prominent tool for this purpose. It characterizes a dataset by using two important measures called lower and upper approximation. Dominance based rough set approach (DSRA) is an extension to conventional rough set theory. It is based on persistence of preference order while extracting knowledge from datasets. Dominance principal states that objects belonging to a certain decision class should follow the preference order. Preference order states that an object having higher values of conditional attributes should belong to higher decision classes. However, some of the basic concepts like checking preference order consistency of a dataset, dominance based lower approximation and upper approximation are computationally too expensive to be used for large datasets. In this paper, we have proposed a parallel incremental approach called Parallel Incremental Approximation Calculation or PIAC for short, for calculating these measures of lower and upper approximations. The proposed approach incrementally calculates lower and upper approximations using parallel threads. We compare our method with the conventional approach using ten widely used datasets. Whilst achieving the same accuracy levels as the conventional approach, our approach significantly reduces the average computation time, i.e., 71% for the lower approximation and 70% for the upper approximation. Over all datasets, the decrease in memory usage achieved was 99%.

Feature selection is the process of selecting a subset of features that provides maximum of the information, present otherwise in entire dataset. The process is very helpful when input for different tasks including classification, clustering, rule extraction and many others, is large. Rough Set Theory, right from its emergence, has been widely used for feature selection due to its analysis friendly nature. Various approaches exist in literature for this purpose. However, majority of them are computationally too expensive and suffer a significant performance bottleneck. In this paper we have proposed a new feature selection approach based on rough set theory, using random feature vector generation method. The proposed approach is a two steps method. At first, it generates a random feature vector and verifies its suitability for being a potential candidate solution. If it fulfills the criteria, it is selected and optimized, otherwise a new subset is formed. The proposed approach was verified using five publicly available datasets. Results have shown that proposed approach is computationally more efficient and produces optimal results.

A dataset may have many irrelevant and unnecessary features, which not only increase computational space but also lead to a very critical phenomenon called curse of dimensionality. Feature selection process aims at selecting some relevant features for further processing on behalf of the entire dataset. However, to extract such information is non-trivial task, especially for large datasets. In literature many feature selection approaches have been proposed but recently rough set based heuristic approaches have become prominent ones. However, these approaches do not ensure the optimum solution. In this paper, a hybrid approach for feature selection has been proposed, based on heuristic algorithm and exhaustive search. Heuristic algorithm finds initial feature subset which is then further optimized by exhaustive search. We have used genetic algorithm and particle swarm optimization as preprocessor and relative dependency for optimization. Experiments have shown that our proposed approach is more effective and efficient as compared to the conventional relative dependency based approach.