Segmentation by natural partitioning 3 4 5 rule

Segmentation by natural partitioning 3 -4 -5 rule can be used to segment numeric data into relatively uniform, “natural” intervals. * If an interval covers 3, 6, 7 or 9 distinct values at the most significant digit, partition the range into 3 equiwidth intervals * If it covers 2, 4, or 8 distinct values at the most significant digit, partition the range into 4 intervals * If it covers 1, 5, or 10 distinct values at the most significant digit, partition the range into 5 intervals Data Warehousing/Mining 1

Example of 3 -4 -5 rule count Step 1: Step 2: -$351 -$159 Min Low (i. e, 5%-tile) msd=1, 000 profit Low=-$1, 000 High(i. e, 95%-0 tile) $4, 700 Max High=$2, 000 (-$1, 000 - $2, 000) Step 3: (-$1, 000 - 0) ($1, 000 - $2, 000) (0 -$ 1, 000) (-$4000 -$5, 000) Step 4: (-$4000 - 0) (-$4000 -$3000) (-$3000 -$2000) (-$2000 -$1000) Data $1, 838 (-$1000 0) Warehousing/Mining ($1, 000 - $2, 000) (0 - $1, 000) (0 $200) ($1, 000 $1, 200) ($200 $400) ($1, 200 $1, 400) ($1, 400 $1, 600) ($400 $600) ($600 $800) ($800 $1, 000) ($1, 600 ($1, 800) $2, 000) ($2, 000 - $5, 000) ($2, 000 $3, 000) ($3, 000 $4, 000) ($4, 000 $5, 000) 2

Example of 3 -4 -5 rule (continued) v v v Step 1 – Min=-$351, 976, Max=$4, 700, 896, low (5 th percentile)=$159, 876, high (95 th percentile)=$1, 838, 761 Step 2 – For low and high, most significant digit is at $1, 000, rounding low -$1, 000, rounding high $2, 000 Step 3 – interval ranges over 3 distinct values at the most significant digit, so using 3 -4 -5 rule partition into 3 intervals, $1, 000 -$0, $0 -$1, 000, and $1, 000 -$2, 000 Step 4 – Examine Min & Max values to see how they “fit” into first level partitions, first partition covers Min value, so adjust left boundary to make partition smaller, last partition doesn’t cover Max value, so create a new partition (round max up to next significant digit) $2, 000 -$5, 000 Step 5 – Recursively, each interval can be further partitioned using 3 -4 -5 rule to form next lower level of the hierarchy Data Warehousing/Mining 3