When dealing with data, whether analyzing, predicting, or anything else, the more is not always better.  Adding additional information leads to a higher dimension, meaning that the data points become more sparse.  The increased sparsity would make it harder to generalize accurately, which may lead to the "curse of dimensionality."


Curse of Dimensionality

Most statistics and data science textbooks use the letter p to represent this number, and sometimes, they call it the number of covariates.
In tabular datasets, this number is the number of columns.

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- Number of data points (instances)
- Attributes (variables)
- Types of attributes (variables)
- Number of attributes (variables)
- Statistical measures

Characteristics of a dataset

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Most statistics and data science textbooks use the letter n to represent this number, and sometimes, they call it the number of observations.
The number of distinct data points depends on how the unit of data is defined in the dataset. In tabular datasets, this number is the number of rows.

Number of data points (instances)

A datapoint, instance, sample, or observation, is a unit of data in a dataset.
When datasets are tabular, $x_{ij}$ usually represents the value of the $j$th variable (attribute) in the $i$th data point, where $i=1,2,...,n$ indicates the index of the variable and $j=1,2,...,p$ identifies the variable. This way, a dataset can be represented as an $n\times p$ matrix X, where the row (or vector) $x_i$ represents a datapoint that consists of the $p$ values of $x_{i1}, x_{i2}, x_{i3}, \dots , x_{ip}$ corresponding to each variable.
$$X=\begin{bmatrix}
    x_{11} & x_{12} & x_{13} & \dots  & x_{1p} \\
    x_{21} & x_{22} & x_{23} & \dots  & x_{2p} \\
    \vdots & \vdots & \vdots & \ddots & \vdots \\
    x_{n1} & x_{n2} & x_{n3} & \dots  & x_{np}
\end{bmatrix}
=\begin{bmatrix}
    x_1^T \\
    x_2^T \\
    \vdots \\
    x_n^T \\
\end{bmatrix}$$ 

Datapoint

Number of attributes/variables/predictors/independent variables/features

• mean

• median

• mode

• percentiles

• range

• variance

• standard deviation

• mean squared error

• consistency

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