What Is Data Cube Computation In Data Mining?

Tackling data cube computations can be an intimidating task, especially when they are just starting off with creating their first data query. But the great news is that there are several computation methods available to help make working with cubes a little easier. In this blog post, we’ll explain the most common data cube computation methods and provide some easy-to-follow examples so you can better understand how these processes work in practice. We’ll also go through several broad optimization strategies for speeding up the process of calculating data cubes. For an in-depth understanding of data computation methods, our data scientist course online helps you explore more about data computation in data mining, the most effective tool of data science.

What Is Data Computation?

Data computation is a crucial aspect of data mining, which involves examining large sets of data to uncover hidden patterns, relationships, and trends. Invariably, one of the earliest steps in data mining is to build a data cube that forms a multidimensional representation of the raw data. A data cube is essentially a tool that provides an intuitive interface for analyzing and visually representing complex data combinations. Data cube computation involves applying mathematical algorithms to attain diverse summaries that can uncover various patterns and trends. Through this process, data analysts can quickly uncover hidden relationships and insights that may not be readily apparent when looking at data in its raw form. Effective data computation is indispensable in data mining to enable actionable insights that can help organizations make informed decisions.

There are various methods of data computation in data mining. Some of the major methods have been discussed further in the blog. 

Data Cube Computation Methods

Given the variety of cubes available, it is reasonable to assume that several data cube computation methods for achieving high computational efficiency. To store cuboids, two primary data structures are in use which are ROLAP and MOLAP. Whereas relational OLAP (ROLAP) relies on traditional table-based data structures, multidimensional OLAP (MOLAP) relies on arrays of data elements (MOLAP). While ROLAP and MOLAP may each investigate unique data cube computation methods, there are likely some optimization "tricks" that can be used to both. Let’s learn in details about these methods.

1. Optimization by Sorting, Hashing, and Grouping: 

Dimension attribute procedures such as sorting, hashing, and grouping can be used to rearrange and classify pairs of data points that previously had no obvious place to go. A cube computation is an aggregation of tuples (or cells) that have the same values for a certain dimension. In order to access and combine such data together to enable computation of such aggregates, it is crucial to investigate sorting, hashing, and grouping processes.

Sorting tuples or cells by branch, then by day, then grouping them according to the item name is an efficient way to calculate total sales by branch, day, and item, for example. The database research community has devoted a lot of time to studying how to most effectively execute such procedures on massive data sets. Computational data cubes are within the scope of such systems. 

Data cube computation method 1 can be expanded upon to execute shared-sorts (i.e., dividing up the price of sorting between numerous cuboids when using a sort-based approach) or shared-partitions (i.e., sharing of partitioning cost across several cuboids when the hash-based algorithms are involved). 

2.  Optimizing Performance: Aggregating and Storing Intermediate Results at The Same Time:

Instead of starting from the basic fact table, it is more time efficient to compute higher-level aggregates from previously computed lower-level aggregates in a cube computation. Furthermore, it is possible that costly disc I/O operations can be reduced through the use of simultaneous aggregation from cached intermediate calculation results.It is possible to employ the intermediate results from the computation of a lower-level cuboid, such as sales by branch and day, in the computation of a higher-level cuboid, such as sales by branch. By maximizing the number of cuboids computed in parallel, disc reads can be amortized, allowing the technique to be used for amortized scans. 

3.  Optimization by Aggregation from The Smallest Child, When There are Numerous Kid Cuboids

To efficiently compute the required parent (i.e., more generalized) cuboid when there are several child cuboids, it is often best to start with the smallest child cuboid that has already been computed.The computational efficiency could be enhanced by a wide variety of additional optimization techniques.For instance, the values of a string dimension's attributes can be represented as a range of numbers, from 0 to the attribute's cardinality. The following data cube computation method, however, is crucial to the iceberg cube calculation process.

4. Optimization Strategy for Looking into The Apriori Pruning Approach to Efficiently Compute Iceberg Cubes is a Viable Option:

In the context of data cubes computation methods, the Apriori property reads as follows: No more specialized or detailed version of a particular cell will meet minimal support if that cell does not meet minimum support. Because of this characteristic, the time needed to calculate iceberg cubes can be drastically cut down. It is worth noting that the iceberg condition, a constraint on the cells to be realized, is included in the iceberg cube specification. The iceberg condition often requires the cells to meet some sort of minimal support level, which can take the form of a count or total.

This is where the Apriori property comes in handy, as it allows us to skip over the study of the cell's offspring. If the number of cells in a cuboid is less than a minimum support threshold, v, then the number of cells in any of the lower-level cuboids that descend from c can never be higher than or equal to v, and hence can be removed.To restate, if a particular condition is not met by some cell c (for example, the iceberg situation that is mentioned in the clause), then all descendants of c will not meet that condition.Anti-Monotonic measures are those that adhere to this property. This method of pruning is widely used in the field of association rule mining, but it can also be useful for computing data cubes by reducing processing time and disc space needs. Because cells that don't make the cut aren't likely to be relevant, this can lead to a more targeted examination. 

What are Full Data Cube Computation Methods Through Multiway Array Aggregation?

The Multiway Array Aggregation (or MultiWay) technique uses a multidimensional array as its foundational data structure to calculate a full data cube. Direct array addressing is a common method used in MOLAP systems, and it allows users to directly access the values of dimensions by referencing their index positions in the array. For this reason, MultiWay is unable to employ the optimization strategy of value-based reordering. For building cubes using arrays, a new strategy is created, which entails the following steps:

1. Split the array up into manageable pieces. To compute a cube, a subcube called a "chunk" must be tiny enough to fit in the memory at hand. The term "chunking" refers to a technique for storing an n-dimensional array as a series of smaller n-dimensional arrays on disc. Space that would otherwise be used up by empty array cells (those with no valid data and a cell count of zero) is squeezed out of the chunks. To condense a sparse array structure and conduct a search for cells within a chunk, for example, the notation "chunkID + offset" can be used as a cell addressing mechanism. These cubes can be compressed effectively enough for use on disc and in memory.
2. Access the values in cube cells to calculate aggregations. Memory access and storage costs can be minimized by optimizing the order in which cells are visited to reduce the number of times each cell must be reviewed. It's a clever strategy to take advantage of this ordering to compute partial aggregates simultaneously while avoiding wasteful cell revisitation.

This chunking method is called multiway array aggregation because it "overlaps" part of the aggregation operations. It is capable of simultaneous aggregation, which is the computation of aggregations across many dimensions at once. You can check out the data science certification guide to understand more about the skills and expertise that can help you boost your career in data science and data discretization in data mining. 

Example: Computational cube array with several dimensions Think of three dimensions of data as A, B, and C in a data array. Pieces of the three-dimensional array are stored separately in memory. Figure:1 depicts the 64-partitioned array used here, with dimensions A split into four equal-sized partitions labeled a0, a1, a2, and a3. Each of dimensions B and C also have four sub-dimensions. In this case, the subcubes a0b0c0, a1b0c0,..., a3b3c3 correspond to chunks 1, 2,..., 64. Let's pretend that A, B, and C each have a cardinality of 40, 400, and 4000. That's why the dimensions A, B, and C of the array are 40, 400, and 4000 elements wide, tall, and deep, respectively. Each partition in sets A, B, and C, therefore, has a size of 10, 100, and 1000. Computation of all cuboids defining the data cube is required for its full materialization. The final complete cube is made up of the cuboids shown here.

The ABC cuboid, from which all other cuboids can be computed either directly or indirectly. This cube is pre-calculated and matches the specified 3-dimensional array.The group-AB, by's AC, and BC have corresponding 2-dimensional cuboids, AB, AC, and BC. It is necessary to calculate these cuboids.

The 1-dimensional cuboids A, B, and C that map to the corresponding A, B, and C in the group-by notation. It is necessary to calculate these cuboids.

a group-by (); there is no group-by in this case — the 0-dimensional (apex) cuboid, denoted by all. It's necessary to calculate this cuboid. There is only one value in it. In the example given above, the value to be computed is the sum of the counts of all the tuples in ABC, as count is the measure of the data cube.

Let's analyze how this computation employs the multiway array aggregation technique. When reading chunks into memory for use in cube calculation, there are multiple alternative orderings. Think about the numbered order from 1 to 64. So, let's say we need to calculate the b0c0 face of the BC cube. The memory for this piece has been set aside. The b0c0 chunk is calculated by first processing the first four chunks of ABC. Specifically, b0c0 cells are clustered in areas a0–a3.Once the subsequent four ABC chunks (chunks 5 through 8) have been scanned, the chunk memory can be allocated to the following chunk, b1c0, completing its aggregate.

If we keep going like this, we will eventually be able to calculate the complete BC cuboid. Therefore, for the computation of all BC pieces, only one BC chunk needs to be in memory at a time. We will have analyzed all sixty-four sections in order to calculate the BC cuboid. Is it possible to compute other cuboids, such AC and AB, without rescanning all of these chunks? Certainly, yes is the correct response. Where the concept of "multiway computation" or "simultaneous aggregation" comes in. It is possible to simultaneously compute all of the other 2-D chunks related to chunk 1 (i.e., a0b0c0) while scanning it (for example, to compute the 2-D chunk b0c0 of BC, as mentioned above). In other words, when scanning a0b0c0, it is also necessary to compute the positions of the three pieces b0c0, a0c0, and a0b0 on the three 2-dimensional aggregate planes BC, AC, and AB. In other words, while a 3-D chunk is in memory, multiway computation aggregates simultaneously to each of the 2-D planes.

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Conclusion

We can predict that there will be a wide variety of methods for performing computations in a timely manner due to the fact that there are many different kinds of cubes. When it comes to storing cuboids, there are typically two basic data structures that are used. We hope you better understand the methods of data cube computation. If you have any query or questions you can drop them in the comment section. To understand more about data science and cube computation, you can visit our tutorial and learn data science online.