Normalize vs. Standardize

Attribute	Normalize	Standardize
Range of values	0 to 1	Mean of 0 and standard deviation of 1
Impact on outliers	Outliers can affect the normalization process	Outliers have less impact on standardization
Formula	(x - min) / (max - min)	(x - mean) / standard deviation
Application	Useful when the data has a defined minimum and maximum value	Useful when the data has a normal distribution

Introduction

When working with data in the field of statistics and machine learning, it is common to encounter the need to preprocess the data before feeding it into a model. Two popular techniques for data preprocessing are normalization and standardization. While both techniques aim to scale the data to make it more suitable for analysis, they have distinct differences in how they achieve this goal.

Normalize

Normalization is a technique used to scale the values of a feature to a fixed range, usually between 0 and 1. This is achieved by subtracting the minimum value of the feature from each data point and then dividing by the range of the feature. The formula for normalization is as follows:

normalized_value = (x - min(x)) / (max(x) - min(x))

One of the main advantages of normalization is that it preserves the shape of the original distribution of the data. This can be beneficial when the distribution of the data is not Gaussian or when there are outliers present in the dataset.

However, one drawback of normalization is that it is sensitive to outliers. Since the range of the data is fixed between 0 and 1, outliers can have a significant impact on the scaling of the data. This can result in the majority of the data being compressed into a small range, making it difficult to distinguish between different data points.

Standardize

Standardization, on the other hand, is a technique used to transform the data such that it has a mean of 0 and a standard deviation of 1. This is achieved by subtracting the mean of the feature from each data point and then dividing by the standard deviation of the feature. The formula for standardization is as follows:

standardized_value = (x - mean(x)) / std(x)

One of the main advantages of standardization is that it is less sensitive to outliers compared to normalization. Since standardization is based on the mean and standard deviation of the data, outliers have less impact on the scaling of the data compared to normalization.

However, one drawback of standardization is that it does not preserve the shape of the original distribution of the data. This can be a disadvantage when the distribution of the data is not Gaussian, as standardization assumes that the data is normally distributed.

Comparison

When deciding between normalization and standardization, it is important to consider the characteristics of the data and the requirements of the model being used. If the data has a fixed range and outliers are not a concern, normalization may be a suitable choice. On the other hand, if the data has a Gaussian distribution and outliers are present, standardization may be a better option.

Another factor to consider is the interpretability of the data after preprocessing. Since normalization preserves the shape of the original distribution, it may be easier to interpret the scaled data compared to standardization, which transforms the data to have a mean of 0 and a standard deviation of 1.

In conclusion, both normalization and standardization are valuable techniques for scaling data in statistics and machine learning. The choice between the two techniques depends on the characteristics of the data and the requirements of the model being used. By understanding the differences between normalization and standardization, data scientists can make informed decisions on how to preprocess their data effectively.