The classification of cities in different countries involves various methods, each with its own criteria and considerations. The choice of the method depends on the specific context, data availability, and research objectives. Several approaches are commonly used for city classification:
Population Size and Density
Global City Classification
Functional Urban Areas
Some recent methods aim to harmonize city definitions and account for diverse factors, such as administrative functions, economic purposes, and political delineations. These approaches can impact the number of identified urban areas and the share of the population living in them.
Depends what you want to do and what kind of method you are interested. International organisation have a couple of typologies, e.g. take a look at OECD (e.g. urban-rural typology) or UN Habitat's world cities report or its city definition summary (https://unhabitat.org/sites/default/files/2020/06/city_definition_what_is_a_city.pdf).
However, those typologies might not be detailed enough for you, e.g. if you are interested in small and medium-sized cities then it gets more difficult. Global datasets often use cities of at least 50,000 inhabitants (see e.g. JRC's global urban accessibility study: https://forobs.jrc.ec.europa.eu/gam).
Of course there are also a lot of scientific studies from various researchers which you can find here on research gate - but again, depends you are actually interested in (e.g. a very advanced definition or rather something simple which more or less is applicable widely) and what you want to use it for.
classifying cities by population leverages various analytical techniques to group and understand urban areas based on demographic data. Clustering algorithms like K-Means and DBSCAN are commonly used to identify groups of cities with similar population sizes or densities, while classification algorithms such as decision trees and random forests help categorize cities based on predefined population thresholds. Dimensionality reduction techniques like PCA and t-SNE aid in visualizing population data, and statistical methods such as quantiles and z-scores provide categorical and normalized classifications. Geospatial analysis tools like spatial autocorrelation and hot spot analysis reveal patterns in population distribution, and time series analysis, including trend and seasonal decomposition, forecasts population changes over time. These methods collectively offer robust frameworks for analyzing and categorizing cities, aiding in urban planning, resource allocation, and policy-making.