Alpha complex filtration is a method used in topological data analysis (TDA) to analyze the shape and structure of a dataset. It is based on the concept of simplicial complexes, which are mathematical structures used to represent the connectivity between points. In TDA, the alpha complex filtration starts with a set of data points in a metric space (e.g., Euclidean space). The alpha complex is constructed by considering all possible simplices (i.e., vertices, edges, triangles, etc.) that can be formed from the data points. The alpha shape represents the subset of these simplices that are considered "meaningful" based on a threshold parameter called alpha. The alpha complex filtration then proceeds by gradually increasing the value of alpha from 0 to infinity. At each step, new simplices are added or removed from the alpha complex based on whether their corresponding alpha values fall below or above the current threshold. This process creates a sequence of nested simplicial complexes, which form a filtration. The resulting alpha complex filtration can be used to analyze various topological properties of the dataset, such as connected components, holes, voids, and higher-dimensional structures. By studying how these properties change as alpha increases, insights into the shape and structure of the dataset can be obtained. Overall, Alpha complex filtration is a fundamental technique in TDA that allows for a topological analysis of datasets and provides a way to understand their underlying geometric structure.