#machinelearning#learningmonkey
In this class, we discuss the Curse of Dimensionality with an example.
To understand the Curse of Dimensionality we go with an example.
Let's take an example data set.
The Housing prize prediction dataset.
In this, we consider only the prize column. we can plot in one dimension.
If we plot the data in one dimension it looks dense.
When we consider two columns house prize and house size. we need a two-dimensional coordinate space.
Here we considered only ten data points.
When we plot in the two-dimensional space data becomes sparse.
Why it becomes sparse?
Because look at the first two houses. 12 and 13 lakh prize.
When we consider the size of the house. it's changed from 1200 to 1100.
So data is becoming sparse with this extra column.
That's the reason why dimensionality increase data become sparse.
As we discussed in the previous class why machine learning models need large datasets to identify generalization of the data.
If the data becomes sparse it's difficult to identify generalization.
In order to make our two-dimensional space dense, we need a large dataset.
This is one of the curses of dimensionality.
As the number of dimensions increases dataset size should also increase.
The second problem with large dimensions is?
Take any two points in the data set the distance between any two points is approximately equal.
There is a mathematical proof for the above statement. we are not going into math.
This is another curse of dimensionality.
KNN is a machine learning algorithm that depends on a distance measure.
If the distance between any two points are all same then difficult to identify the nearest points.
So KNN doesn't work properly with high dimensions.
Not only KNN but any machine learning algorithm that depends on distance measure will have the curse of dimensionality.
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