Histogram

Definition

Given a relation R and an attribute X of R, the domain D of X is the set of all possible values of X, and a finite set V(⊆D)V(⊆D) denotes the distinct values of X in an instance r of R. Let V be ordered, that is, V = {vi : 1 ≤ i ≤ n}V = {vi : 1 ≤ i ≤ n}, where vi < vjvi < vj if i < ji < j. The instance r of R restricted to X is denoted by T, and can be represented as T = {(v1, f1), ⋯(vn, fn)}T = {(v1, f1), ⋯(vn, fn)}. In T, each v_i is distinct and is called a value of T; and f_i is the occurrence of v_i in T and is called the frequency of v_i, and T is called the data distribution. A histogram on data distribution T is constructed by the following two steps:

• 1. Partitioning the values of T into β(≥1)β(≥1) disjoint intervals (called buckets) – {Bi : 1 ≤ i ≤β}{Bi : 1 ≤ i ≤ β} – such that each value in B_i is smaller than that in B_i if i < ji < j

• 2. Approximately representing the frequencies and values in each bucket

Key Points

Histogram, as a summarization of the data...