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#468easyMachine Learning

Feature Normalization

Time Limit: 2sMemory: 256MB
Part of:Machine Learning & Statistical Learning → Feature Engineering & Selection

Problem

Given a feature vector, compute two normalizations commonly used in machine learning:

  1. Z-score normalization (standardization): x~i=xi−μσ\tilde{x}_i = \frac{x_i - \mu}{\sigma} where μ\mu is the mean and σ\sigma is the population standard deviation.

  2. Min-max normalization: x~i=xi−xmin⁡xmax⁡−xmin⁡\tilde{x}_i = \frac{x_i - x_{\min}}{x_{\max} - x_{\min}}, scaling values to [0,1][0, 1].

Input Format

Space-separated floats: the feature values.

Output Format

  • Line 1: Z-score normalized values (space-separated, 4 decimal places)
  • Line 2: Min-max normalized values (space-separated, 4 decimal places)

Examples

Example 1
Input(Space-separated floats: the feature values.)
1 2 3 4 5
Output
-1.4142 -0.7071 0.0000 0.7071 1.4142
0.0000 0.2500 0.5000 0.7500 1.0000

Mean=3, pop std=sqrt(2)=1.4142. Z-scores: (-1.4142,-0.7071,0,0.7071,1.4142). Min=1, Max=5. Min-max: (0,0.25,0.5,0.75,1).

Example 2
Input(Space-separated floats: the feature values.)
10 20 30
Output
-1.2247 0.0000 1.2247
0.0000 0.5000 1.0000

Mean=20, pop std=8.1650. Z-scores: (-1.2247,0,1.2247). Min=10, Max=30. Min-max: (0,0.5,1).

Constraints

  • •2 ≤ number of values ≤ 50
  • •-10000 ≤ each value ≤ 10000
  • •Population standard deviation > 0 (not all values identical)
  • •Max > Min (not all values identical)
  • •Output to 4 decimal places
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