Explain binning method to handle noisy data with example.

Noise is a random error or variance in a measured variable. 

Binning method: Binning methods smooth a sorted data value by consulting its “neighborhood,” i.e. the values around it. The sorted values are distributed into a number of “buckets,” or bins.

Binning Methods for Data Smoothing

Let’s look at the following data smoothing techniques:

Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34

* Partition into (equal frequency) bins:

- Bin 1: 4, 8, 9, 15

- Bin 2: 21, 21, 24, 25

- Bin 3: 26, 28, 29, 34

* Smoothing by bin means:

- Bin 1: 9, 9, 9, 9

- Bin 2: 23, 23, 23, 23

- Bin 3: 29, 29, 29, 29

* Smoothing by bin boundaries:

- Bin 1: 4, 4, 4, 15

- Bin 2: 21, 21, 25, 25

- Bin 3: 26, 26, 26, 34

In smoothing by bin means, each value in a bin is replaced by the mean value of the bin. For example, the mean of the values 4, 8, and 15 in Bin 1 is 9. Therefore, each original value in this bin is replaced by the value 9.

Similarly, smoothing by bin medians can be employed, in which each bin value is replaced by the bin median.

In smoothing by bin boundaries, the minimum and maximum values in a given bin are identified as the bin boundaries. Each bin value is then replaced by the closest boundary value. In general, the larger the width, the greater the effect of the smoothing.