Add absolute category gaps to measure distance

Procedure distance(A,B)
    total = 0
    foreach category in categories {
        total = total + abs(A[category] - B[category])
    }
    return(total)
End distance

abs means absolute value: abs(8−13)=5 and abs(13−8)=5. Every gap is non-negative, so a larger Food count cannot cancel a smaller Utilities count. The sum of these absolute gaps is called Manhattan or rectilinear distance. Smaller distance means closer under THIS chosen representation and distance rule.

Distance from a profile to itself is zero. Distance is symmetric: D(A,B)=D(B,A). Zero between two different customers means their counted profiles match, not that they are the same person. Category row counts are the features; spending in rupees is not being measured here.