Data Transformation: Normalization, Discretization, Sampling, Compression

You scraped a dataset. One column is “age” in years (18 to 90). Another is “income” in rupees (₹10000 to ₹2000000). A model that just plugs these in raw will be dominated by income — the numbers are bigger, not because income matters more, but because nobody rescaled it.

That’s what data transformation fixes. Before any analysis we rescale, bucket, sample, or shrink the data so downstream tools see it on fair terms. Four small moves — let’s walk each.

Rescaling: min-max vs z-score

Two transformations cover almost every GATE question on rescaling.

Min-max normalization squashes every value into the range [0, 1]:

x' = (x − min) / (max − min)

The smallest value becomes 0, the largest becomes 1, everything else lands between them. Bounded and easy to read.

Z-score standardization centers the column at mean 0 and rescales so the standard deviation is 1:

z = (x − μ) / σ

Now most values lie in [−3, +3] — but z-scores can be negative, and they are not capped. A wildly extreme value can sit at z = 5 or beyond.

Discretization: turning numbers into bins

Sometimes you do not want a continuous number, you want a bucket — “young / middle / old” instead of an exact age. That’s discretization (binning).

• Equal-width bins — split the range into bins of the same width. Ages [18, 90] into three bins: [18, 42), [42, 66), [66, 90]. Simple, but one bin may end up almost empty.
• Equal-frequency bins — each bin holds the same count of rows. Sort the column, then cut at every n/k-th value. Bins differ in width but balance out the row counts.

Sampling: picking rows instead of using them all

When the dataset is too large to analyse whole, sample it:

• Random sampling — every row has the same chance of being picked.
• Stratified sampling — split the population into groups (strata) and sample from each in proportion. Use this when a small subgroup would otherwise be missed.
• With replacement — a picked row can be picked again (used by bootstrap, the resampling trick behind bagging and confidence intervals).
• Without replacement — once picked, a row is out (the default for surveys).

Compression: shrinking the bytes

Two flavours, one decision:

• Lossless — every original bit is recoverable. Used for text, numeric tables, code (zip, gzip).
• Lossy — drops detail to shrink harder. Used for images, audio, video (JPEG, MP3) where small reconstruction errors are invisible to humans.

Rule of thumb: tabular and textual data must be lossless; perceptual media can be lossy.

How GATE asks this

Almost always a NAT: a column value, a min/max or mean/SD, and “compute the normalized value to 3 decimals.” Sometimes an MCQ asking which rescaling preserves which property, or an MSQ listing sampling methods or compression properties. Read the question for μ, σ, min, max — they tell you instantly which formula to apply.

Worked example — a real 2024 question

A person’s salary is ₹106000. The population has mean μ = ₹96000 and standard deviation σ = ₹21000. Find the z-score of this salary.

Plug straight into the standardization formula:

z = (x − μ) / σ
  = (106000 − 96000) / 21000
  =      10000      / 21000
  ≈ 0.476

So z ≈ 0.476. This is the real GATE DA 2024, Q17. The salary is about half a standard deviation above the mean — comfortably above average, but well inside the typical range.

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