Please help with the understanding of this concept having trouble. Provide Final answer and explanation for understanding. Is the average squared distance between two clusters equal to the squared distance of the difference in the two centroids?1Simplify Σ Σxxwhere C₁ and C₂ are two different clusters.72172₂For simplicity, use the Euclidean distance for x - x||Choose all expressions below that are equal to the above expression.X1 Σ Σma-pelle1110₂2020 20₂1121702111 12Σ Σ(x-₂) + (1₂−µ₂) — (x(³) — µ₂)||²Σ Σ (x-μ₂||²+₂ M₂||²+ ||Xx²¹ μµ₂₁)|| ²) Hierarchical ClusteringHierarchical clustering does not start with a fixed chosen number of clusters, but builds a hierarchy of clusters with differentlevels corresponding to different numbers of clusters.We can use a bottom-up or top-down approach:• Agglomerative clustering (Bottom-Up)• Divisive clustering (Top-down)We will only discuss the bottom-up approach.Agglomerative Clustering (Bottom-Up approach)Agglomerative clustering starts with 1 data point per cluster, and at each consequent stage, merges pairs of clusters thatare the closest together according to a dissimilarity measure between clusters.This merging can be depicted by a tree, also known as a dendrogram. The bottom-most level has n clusters (of 1observation each), and as merging occurs as the levels go up, the number of clusters decreases, and the top-most level hasonly 1 cluster (encompassing all observations). See the recitation in this module for an example of hierarchical clustering andthe associated dendrogram.Dissimilarity between clustersIn order to choose which pair of clusters to merge at each stage, we need to define a dissimilarity measure betweenclusters, and the dissimilarity measure between clusters is often based on dissimilarity between points. A few commonlyused distances between individual points are:• -norm, i.e. the usual Euclidean distance(x,x) = √√(x − ¹)* + (x − xª)* + +...+¹-norm (also known as Manhattan distance)(xx) = + | − | + + | − |-norm, Le. the maximum distance among all coordinatesd(x,x)= maxd(x,x) 20(positivity)d(x,x!)(x²)x(i)• Other dissimilarity measures d (x,x) that do not satisfy all properties of distances, but still meet the followingcriteria:Now we can define dissimalarity measures between clusters:d (C₁, C₂) -d (x²), x))d(C₁,C₂) =• Minimum distance between points in the two clusters, also known as single linkage:d(C₁,C₂)min-24(x1) =RP)max* EDEC17172(symmetry)• Maximum distance between points in the two clusters, also known as complete linkage:d(x,x).(x²)d(x,x).• Average distance between points in the two different clusters, also known as average linkageΣΣ d(x,x).

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Given the average squared distance between two clusters equal to the squared distance in the two…