Internet, mobile communications, navigation, online gaming, sensing technologies and large scale computing infrastructures are producing large amounts of data every day. Big Data is data that is beyond the processing capacity of conventional database systems and analyzing capacity of traditional analyzing methods due to its large volume and fast moving and growing speed. More companies now rely on Big Data to make real-time decisions to solve various problems. Current methods involve utilizing a lot of computational resources, which are very costly, yet still may not satisfy the needs of real-time decision making based on the newest information, especially in the financial industry. How to efficiently, promptly and cost-effectively process and analyze Big Data presents a difficult challenge to data analysts and computer scientists.
Streamed data is data that is constantly being received by a receiver while being delivered by a provider. Streamed data may be real-time data gathered from sensors and continuously transferred to computing devices or electronic devices. Often this includes receiving similarly formatted data elements in succession separated by some time interval. Streamed data may also be data continuously read from storage devices, e.g., storage devices on multi-computing devices which store a Big Data set. Stream processing has become a focused research area recently due to the following reasons. One reason is that the input data are coming too fast to store entirely for batch processing, so some analysis have to be performed when the data streams in. The second reason is that immediate responses to any changes of the data are required in some application domains, e.g., mobile related applications, online gaming, navigation, real-time stock analysis and automated trading, etc. The third reason is that some applications or electronic devices require streaming processing due to their nature, e.g., audio, video and digital TV, etc.
In addition, algorithms on streamed data processing may be extended to Big Data processing, because Big Data sets are accumulated over time and may be considered as a data stream with irregular time intervals.
Processing Big Data or streamed data may include performing calculations on multiple data elements. When performing statistical calculations on streamed data elements, the number of data elements to be accessed may be quite large. For example, when calculating a Z-score a (potentially large) number of data elements may need to be accessed.
Further, some statistical calculations are recalculated as a data element is removed from a computation subset. Thus, the (potentially large) number of data elements may be repeatedly accessed. For example, it may be that a Z-score is calculated for a computation subset whose size n keeps decreasing to exclude some out-of-date data elements. For decremental Z-score calculation algorithms, the input is not a data to be added to the computation subset but a data to be removed from the computation subset. The input must be an existing data element in the computation subset, else the decremental algorithms will not work correctly. As such, every time a data element is received, the data element is removed from the computation subset. The n−1 data elements in the computation subset are then accessed to recalculate the Z-score.
When performing a Z-score on n−1 data elements using traditional methods, all the n−1 data elements in the computation subset will be visited and used. Depending on necessity, the computation subset size n may be extremely large, so the data elements in a computation subset may be distributed over a cloud comprising hundreds of thousands of computing devices. Re-performing Z-score calculations in traditional way on a Big Data set or a data stream after some data changes inefficiently use time and computing resources.