# tabular data

*Entry of the [Dictionary of Applied Machine Learning](https://dictionaryofml.org) (course edition), by Alexander Jung, Aalto University. CC BY 4.0. Updated 2026-11-06. [HTML](https://dictionaryofml.org/terms/tabulardata.html) · [typeset PDF](https://dictionaryofml.org/terms/tabulardata.pdf) · [LaTeX](https://dictionaryofml.org/terms/tabulardata.tex) · [Python demo](https://dictionaryofml.org/terms/tabulardata.py) · [notebook](https://dictionaryofml.org/terms/tabulardata.ipynb)*

Math is LaTeX with the book's macros expanded, so no notation package is needed to read it.

## Abstract

Tabular data consist of data points that share a common, fixed set of attributes. The measured attributes serve as the features or as the label of a data point. The data points constitute the rows, or records, of a table, and the attributes are its columns. Every row has one cell per column, and the cells within one column hold values of the same attribute. The fixed attribute set separates tabular data from other types of data, such as text or graphs, whose data points carry no common set of attributes.

## Definition

A Finnish Meteorological Institute weather station measures the weather of each day, and the measurements are represented as a table with one row for each day (Fig. 1(a)). The table has four columns, one per attribute of a day: the date, the morning minimum temperature, the precipitation, and the maximum daytime temperature (Finnish Meteorological Institute, 2024). The date identifies the data point, and the three measured attributes are the candidates for its features and its label. Tabular data consist of data points that share such a common, fixed set of attributes (Everitt, 2002). As the name suggests, tabular data can be stored as a table: the rows of the table are the data points, and the columns of the table are the attributes.

In Fig. 1(b), the learning task is to forecast the maximum daytime temperature of a day from its morning minimum temperature. A machine learning method reads the minimum-temperature column as the feature and the maximum-temperature column as the label, while the precipitation column is left unused. It learns a hypothesis from the $366$ data points, shown as a scatterplot with the learned curve.

![Figure 1 of the entry tabulardata](https://dictionaryofml.org/terms/fig/tabulardata-fig1.svg)

*Figure 1: (a) Four of the $366$ rows of the table of daily weather measurements recorded in $2024$ at the Finnish Meteorological Institute station Helsinki Kaisaniemi (January 8–11). Each row is a data point, namely one day. The headers abbreviate the morning minimum temperature (min. temp.), the precipitation (precip.), and the maximum daytime temperature (max. temp.). Every row has one cell per column. The two shaded columns are the ones used in panel (b), and the braces above them name the roles: the light gray column holds the feature and the dark gray column the label of a day. (b) Scatterplot of $20$ of the $366$ days (every $19$th), with the minimum temperature of a day as its feature and the maximum temperature as its label; the curve depicts a hypothesis learned from all $366$ data points. Which columns serve as feature and label of a learning task is a design choice, and the panel shows one such choice. Data generated by pythondemos/tabulardata.py*

The distinct characteristic of tabular data is the rigid shape of a table. Every row contains the same number of cells, one per column, and the cells within one column hold values of the same attribute of the data points. The value range must be defined for each column, and every cell of a column holds a value from that range. The precipitation column of Fig. 1(a), for example, holds a daily amount in millimeters or the special value $-1.0$, which records that no precipitation was observed. A second, different use of a special value is a marker such as ``N/A'' reserved for an empty cell (Tennison et al., 2015). Missing data are represented by an empty cell: an attribute that was not recorded for a data point leaves its cell empty, while the table keeps its shape. Data imputation fills such a cell with an estimate computed from the cells that were recorded.

The fixed attribute set is what separates tabular data from other data types. For the weather measurements, the station records the same quantities every day, so the attribute set is fixed by the measurement process and shared by every data point. A text, in contrast, is a sequence of tokens whose length varies from data point to data point, and a graph varies in its node and edge sets. Such data points carry no attribute set of their own. One can be imposed, for example the number of occurrences of each word from a fixed word list, but such a set discards the order of the tokens. The table of weather measurements loses nothing in this way, since a day is fully described by its four attributes, while a text with its tokens in another order is a different text. Instead, feature learning methods are developed that map such data points to feature vectors (or embeddings) (Kipf and Welling, 2017; Mikolov et al., 2013).

In database theory, the relational model formalizes a table as a relation. A relation is a set of tuples of attribute values. The relational model also provides the operations, such as selecting rows or joining tables, that database systems use to manipulate tabular data (Silberschatz et al., 2019).

**See also:** [data](https://dictionaryofml.org/terms/data.html), [data point](https://dictionaryofml.org/terms/datapoint.html), [dataset](https://dictionaryofml.org/terms/dataset.html), [feature](https://dictionaryofml.org/terms/feature.html), [label](https://dictionaryofml.org/terms/label.html), [feature matrix](https://dictionaryofml.org/terms/featuremtx.html), relational model, missing data, [data imputation](https://dictionaryofml.org/terms/dataimputation.html), gradient-boosted decision tree, [feature learning](https://dictionaryofml.org/terms/featlearn.html).

## References

- Finnish Meteorological Institute (2024). The Finnish Meteorological Institute's open data. <https://opendata.fmi.fi/wfs>
- Everitt (2002). The Cambridge Dictionary of Statistics. *Cambridge Univ. Press*.
- Tennison et al. (2015). Model for Tabular Data and Metadata on the Web. <https://www.w3.org/TR/tabular-data-model/>
- Kipf and Welling (2017). Semi-Supervised Classification with Graph Convolutional Networks. *5th Int. Conf. Learn. Representations*. <https://openreview.net/forum?id=SJU4ayYgl>
- Mikolov et al. (2013). Efficient Estimation of Word Representations in Vector Space. *Int. Conf. Learn. Represent. (ICLR), Workshop Track*. <https://openreview.net/forum?id=idpCdOWtqXd60>
- Silberschatz et al. (2019). Database System Concepts. *McGraw-Hill Education*.

## Cite this entry

```bibtex
@misc{dictml_tabulardata,
  author = {Jung, Alexander},
  editor = {Olioumtsevits, Konstantina and Schnoor, Ekkehard},
  title = {tabular data},
  howpublished = {Dictionary of Applied Machine Learning (course edition)},
  year = {2026},
  doi = {10.5281/zenodo.21569296},
  note = {ISBN 978-952-64-3013-3, CC BY 4.0, retrieved 2026-11-11},
  url = {https://dictionaryofml.org/terms/tabulardata.html}
}
```