This document discusses various data reduction techniques including dimensionality reduction through attribute subset selection, numerosity reduction using parametric and non-parametric methods like data cube aggregation, and data compression. It describes how attribute subset selection works to find a minimum set of relevant attributes to make patterns easier to detect. Methods for attribute subset selection include forward selection, backward elimination, and bi-directional selection. Decision trees can also help identify relevant attributes. Data cube aggregation stores multidimensional summarized data to provide fast access to precomputed information.

1. Data Reduction:
Attribute Subset Selection
and Data Cube Aggregation
PREPARED BY: RAJAN SHAH
DMBI
SVIT, VASAD

2. Data Reduction
Data Reduction techniques can be applied to obtain
a reduced representation of the data set that is
much smaller in volume, yet closely maintains the
integrity of the original data.
That, is, Mining on the reduced data set should be
more efficient yet produce the same analytical
results.

3. Data Reduction Strategies
1. Dimensionality Reduction
2. Numerosity Reduction
3. Data Compression

4. Dimensionality Reduction
Dimensionality Reduction is the process of
reducing the number of random variables or
attributes under consideration.
Attribute Subset Selection is a method of
dimensionality reduction in which irrelevant,
weakly relevant, or redundant attributes are
detected and removed.

5. Numerosity Reduction
These techniques replace the original data volume
by alternative, smaller forms of data
representation. May be Parametric or Non-
Parametric.
Parametric Methods: A model is used to estimate
the data, so that only the data parameters need to
be restored and not the actual data. It assumes
that the data fits some model estimates model
parameters.
Examples: Regression and Log-Linear Models.

6. Cont…
Non-Parametric Methods: Do not assume the data
and are used for storing reduced representations of
the data which includes Histograms, Clustering,
Sampling and Data Cube Aggregation.

7. Data Compression
Transformations are applied so as to obtain a
“COMPRESSED” representation of the original data.
If the original data can be reconstructed from the
compressed one without loss of any information, it
is called Lossless Data Reduction, else it is called
Lossy Data Reduction.

8. Attribute Subset Selection
Also known as Feature Selection, which is a
procedure to find a subset of features (relevant to
mining task) to produce “better” model for given
dataset, i.e. removal of redundant data from the
data set which can slow down the mining process.
AIM: To find a minimum set of attributes such that
the mining process results are as close as possible
to the original distribution obtained using all
attributes.

9. Advantages
Mining on Reduced set of Attributes result in
reduced number of attributes and thus helping to
make patterns easier to detect and understand.

10. How To Find a GOOD Subset?
For n attributes, there are 2n possible subsets and
thus the methods applied are “greedy” in that,
while searching through attribute space, they
always make what looks to be the local best choice
assuming that it will lead to the global optimal
result.
The BEST and WORST attributes are determined
using tests of Statistical significance assuming the
attributes are independent of each other.
Information Gain can be used to evaluate attributes.

11. Methods: Stepwise Forward
Selection
It starts with no variables in the
model and testing the addition
of each variable using a chosen
model fit criterion, adding the
variable (if any) whose
inclusion gives the most
statistically significant
improvement of the fit, and
repeating this process until
none improves the model to a
statistically significant extent.
Example:

12. Stepwise Backward
Elimination
It involves starting with all
candidate variables, testing
the deletion of each variable
using a chosen model fit
criterion, deleting the
variable (if any) whose loss
gives the most statistically
insignificant deterioration of
the model fit, and repeating
this process until no further
variables can be deleted
without a statistically
significant loss of fit.
Example:

13. Bi-Directional Selection and
Elimination
The stepwise forward
selection and backward
elimination methods can
be combined so that, at
each step, the procedure
selects the best attribute
and removes the worst
from among the
remaining attributes.
Example: Suppose,
when A1(best) is
selected, at the same
time A2(worst) is
eliminated. And similarly
when A4 is selected, A5
gets eliminated and
when A6 is selected, A3
is eliminated, thus
forming the reduced set
{A1, A4, A6}.

14. Decision Tree Induction
Decision Tree Induction constructs a flowchart where
each internal non-leaf node denotes a test on an
attribute, each branch corresponds to an outcome of
the test, and each external leaf node denotes class-
prediction.
At each node, the algorithm chooses the “best”
attribute to partition the data into individual classes.
All the attributes that do not appear in the tree are
assumed to be irrelevant, while the attributes that
belong to the tree form the reduced data set.

15. Cont…

16. Data Cube Aggregation
A data cube is generally used to easily interpret
data. It is especially useful when representing data
together with dimensions as certain measures of
business requirements. A cube's every dimension
represents certain characteristic of the database.
Data Cubes store multidimensional aggregated
information.
Data cubes provide fast access to precomputed,
summarized data, thereby benefiting online
analytical processing (OLAP) as well as data mining.

17. Categories of Data Cube
Dimensions: Represents
categories of data such
as time or location.
Each dimension includes
different levels of
categories.
Example:

18. Cont…
Measures: These are the
actual data values that
occupy the cells as
defined by the
dimensions selected.
Measures include facts or
variables typically stored
as numerical fields.
Example:

19. Cont…
Example: For the data set of employees with their
dept_id, salary, data cube can be used to aggregate
the data so that resulting data summarizes the total
salary corresponding to the dept_id.
The Resulting data is smaller in volume, without loss
of information necessary for analysis task.

20. Cont…
Concept Hierarchies may exist for each attribute,
allowing the analysis of data at multiple abstraction
levels.
The Cube created at the lowest abstraction level is
called– Base Cuboid.
The Cube created at the highest abstraction level is
called– Apex Cuboid.
Data cube can be 2-D, 3-D or higher dimension.
When replying to data mining requests, the smallest
available cuboid relevant to the given task should be
used.

21. Example

22. References
https://www.slideshare.net/algum/data-cubes-
7923771
https://en.wikipedia.org/wiki/Data_cube