What are the benefits and drawbacks of different normalization techniques?

Min-max normalization technique has following benefits and drawbacks - Benefits: 1. Simplifies interpretation and visualization by scaling all features to a common range, typically between 0 and 1. 2. Preserves the shape of the original distribution, maintaining relative relationships between data points. 3. Suitable for algorithms like neural networks and SVMs that require inputs to be on a similar scale. Drawbacks: 1. Sensitivity to outliers can skew the scaled data, particularly if there are extreme values in the dataset. 2. May compress the data if the range of values is small, reducing the variability and potentially the information content. 3. Does not handle missing values, requiring additional pre-processing steps.

Min-max normalization scales data to a fixed range, typically [0, 1], by subtracting the minimum value and dividing by the range (max value minus min value). It preserves the relative relationships between data points and is straightforward to implement. However, it is sensitive to outliers, as extreme values can disproportionately influence the scaled results.

Segun lo vivido en clase, es una escala fácil de interiorizar ya que al mantener un orden y rango facilmente equivalente (como de temperatura pasar a porcentaje) hace sencillo determinar la relación de la variable transformada (a pesar de no tener unidades), muy util al implementar algoritmos de jerarquía y ponderación como el AJP.

**Min-Max normalization** scales features to a fixed range, typically [0, 1], which is useful for algorithms sensitive to scale but can be affected by outliers. **Z-score normalization** standardizes features to have a mean of 0 and a standard deviation of 1, making it robust to outliers and suitable for many algorithms but less intuitive for interpretation. **Robust scaling** uses median and interquartile range, handling outliers effectively but potentially less effective for data with a normal distribution. Each technique has trade-offs between handling outliers, interpretability, and the impact on model performance, so the choice depends on the specific characteristics of the dataset and the requirements of the analysis.

Muy util para la aplicación de ciertos modelos donde se deben cumplir supuestos como varianzas iguales (como en las regresiones), es práctica para algoritmos que exigen que los datos estén centrados como en el Análisis de Componentes Principales.

Z-score normalization, also known as standardization, transforms data to have a mean of 0 and a standard deviation of 1. It achieves this by subtracting the mean and dividing by the standard deviation of the data set. This method is useful for algorithms that assume normally distributed data and reduces the impact of outliers compared to min-max normalization. However, it assumes data follows a Gaussian distribution, which may not always be true, and requires recalculating mean and standard deviation if new data is added.

Es util en modelos donde el orden establecido es claro como en algoritmos de análisis jerárquico ponderado. No obstante, es importante determinar que tan dispersos son los datos puesto que si bien se escalan de manera proporcional por un efecto multiplicador (o divisorio) no tiene presente el sentido de la variable (por ejemplo, puede ser una unidad de distancia donde a mayor distancia es peor, en esos casos esta malformación no capta ese efecto o sentido de la variable sobre el proceso de toma de decisiones.

Decimal scaling normalization scales data by moving the decimal point of each value to a consistent position, typically resulting in values between -1 and 1. This technique divides each value by a scaling factor that is a power of 10 based on the maximum absolute value in the dataset. It preserves the relative relationships between data points and is straightforward to implement. However, it can be sensitive to extreme values and may require careful handling of very small or large numbers.

En mi experiencia es util en procesos estocásticos, sobre todo cuando los errores no son normales sino longnormales. Además, es muy práctica cuando la serie es asimétrica como las valoraciones de criptomonedas.

Log transformation normalization involves applying the natural logarithm or other logarithmic functions to data, which reduces skewness and compresses large ranges. It is effective for data with skewed distributions or wide ranges of values. However, it can only be applied to data with strictly positive values and may require careful interpretation and reverse transformation for analysis and visualization.

Lo más importante es pensar en el tipo de relación que se espera evidenciar entre la variable a transformar y el fenómeno bajo estudio. De allí se seleccionarán aquellas transformaciones que afecten o no el sentido de la relación, así como el rango de valores o los supuestos que debe tener la variable transformada según los algoritmos a usar.