Introduction
In today’s dataheavy systems, where everything is captured for future use, you get a mammoth data set on every load; this data set could be both big in terms of observations or in terms of the number of features or columns, or both. Data mining becomes tedious in such cases, with only a few important features contributing to the value that you can take out of the data. Complex queries might take a long time to go through such huge data sets too. In such cases, a quick alternative is data reduction.
 What is Data Reduction
 Data Reduction Techniques
 Dimensionality Reduction
 Numerosity Reduction
 Parametric
 NonParametric
 Histogram
 Clustering
 Sampling
 Data Cube Aggregation
 Data Compression
 Key Takeaways
1. What is Data Reduction
According to Wikipedia, a formal definition of Data Reduction goes like this, “Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form.”.
2. Data Reduction Techniques
There are 2 primary methods of Data Reduction, Dimensionality Reduction and Numerosity Reduction.
3. Dimensionality Reduction
Dimensionality Reduction is reducing the number of dimensions the data is spread across, basically, the attributes or features that the data set carries as the number of dimensions increases the sparsity, which is critical to clustering, outlier analysis and other algorithms. With reduced dimensionality, it is easy to visualize data. There are at least 3 types of Dimensionality reduction.
 Wavelet Transform
Wavelet Transform is a lossy method for dimensionality reduction where a data vector X is transformed into another vector X’, in such a way that both X and X’ still represent the same length. The result of wavelet transform can be truncated, unlike it’s original, thus achieving dimensionality reduction. Wavelet transforms are well suited for data cube, sparse data or data which is highly skewed. Wavelet transform is often used in image compression.
 Principal Component Analysis
This method involves the identification of a few independent tuples with n attributes that can represent the entire data set. This method can be applied to skewed and sparse data.
 Attribute Subset Selection.
Here attributes irrelevant to data mining or redundant ones are not included in a core attribute subset. The core attribute subset selection reduces the data volume and dimensionality.
4. Numerosity Reduction
This method uses an alternate, small forms of data representation, thus reducing data volume. There are 2 types of Numerosity reduction, Parametric and NonParametric.
5. Parametric
This method assumes a model that the data fits to. Data model parameters are estimated, and only those parameters are store, and the data is discarded. For example, a regression model can be used to achieve Parametric reduction if the data fits the Regression model.
Linear Regression models a linear relationship between 2 attributes of the data set. Let’s say we need to fit a linear regression model between 2 attributes, x and y, where y is the dependant attribute, and x is the independent attribute or predictor attribute. The model can be represented by the equation y=wx b. w and b are regression coefficients. A multiple linear regression model lets us express the attribute y in terms of multiple predictor attributes.
Another method, LogLinear model discovers the relationship between 2 or more discrete attributes. Assume, we have a set of tuples in ndimensional space; the loglinear model helps to derive the probability of each tuple in this ndimensional space.
6. NonParametric
A nonparametric numerosity reduction technique does not assume any model. The nonParametric technique results in more uniform reduction, irrespective of data, but it may not achieve a high volume of data reduction like Parametric one. There are at least 4 types of NonParametric data reduction techniques, Histogram, Clustering, Sampling, Data Cube Aggregation.
7. Histogram
A histogram can be used to represent dense, sparse, skewed or uniform data, involving multiple attributes, effectively up to 5 together.
8. Clustering
In Clustering, the data set is replaced by the cluster representation, where the data is split between clusters depending on similarities to each other withincluster and dissimilarities to other clusters. The more the similarity withincluster, the close they appear within the cluster. The quality of the cluster depends on the maximum distance between any 2 data items in the cluster.
9. Sampling
Sampling is capable of reducing large data set into smaller sample data sets, reducing it to a representation of the original data set. There are 4 types of sampling data reduction methods.
Simple Random Sample Without Replacement of sizes
Simple Random Sample with Replacement of sizes
Cluster Sample
Stratified Sample
10. Data Cube Aggregation
Data Cube Aggregation is a multidimensional aggregation that uses aggregation at various levels of a data cube to represent the original data set, thus achieving data reduction.
Data Cube Aggregation, where the data cube is a much more efficient way of storing data, thus achieving data reduction, besides faster aggregation operations.
11. Data Compression
It employs modification, encoding or converting structure of data in a way that it consumes less space. Data compression involves building a compact representation of information by removing redundancy and representing data in binary form. Data that can be restored successfully from its compressed form is called Lossless compression while the opposite where it is not possible to restore the original form from the compressed form is Lossy compression.
12. Key Takeaways
 Data reduction achieves a reduction in volume, making it easy to represent and run through advanced analytical algorithms.
 Data reduction also helps in deduplication of data reducing the load on storage and the algorithms serving data science techniques downstream.
Conclusion
Data Reduction can be achieved in two principal ways. One by reducing the number of data records, or the features and the other by generating summary data and statistics at different levels.
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