A Fast Density-Based Clustering Algorithm for Real-Time Internet of Things Stream

Algorithm 1

HDC-Stream (DS, MinPts, λ, and α).

Input: a data stream, MinPts, 𝜆, and 𝛼

Output: arbitrary shape clusters

(1)   𝑡_𝑝𝑡=log^{𝛼/(𝛼−𝑁(1−2−𝜆}_𝜆⁾⁾

(2)  𝑡_𝑐=0

(3)  while not end of stream do

(4)  Read data point 𝑥 from Data Stream

   {***** MM-Step *****}

(5)   Find the nearest mini-cluster MIC to 𝑥

(6)   if distance (𝑥,center_MIC)<𝑟_MIC  then

(7)    Merge 𝑥 to the MIC

(8)   else

(9)    Map the new data point 𝑥 to the grid

(10)    𝑛_𝑔=𝑛_𝑔+1;𝑤_𝑔=2^{−𝜆(𝑡𝑐−𝑡𝑝)}𝑤_𝑔(𝑡_𝑝)+1;𝑡_𝑝=𝑡_𝑐

(11)    Update GS(𝑛_𝑔,𝑡_𝑝,𝑤_𝑔)

(12)   if  𝑛_𝑔 ≥ MinPts and 𝑤_𝑔 ≥  𝛼𝑁(1−2^−𝜆)  then

(13)    𝑤_MIC=𝑤_𝑔

(14)    𝑐_MIC=∑^𝑛_𝑖=1𝑓(𝑡_𝑐−𝑇_𝑖)(𝑝_𝑖)𝑤_MIC

(15)    𝑟_MIC=∑^𝑛_𝑖=1𝑓(𝑡_𝑐−𝑇_𝑖)distance(𝑝_𝑖𝑗,𝑐_MIC)𝑤_MIC

(16)    Remove grid 𝑔 from the grid list

(17)   end if

(18)  end if

   {***** PGM-Step *****}

(19)  if  𝑡 mod 𝑡_𝑝𝑡==0  then

(20)   for all grid 𝑔  do

(21)    OWT(𝑡_𝑐,𝑡_𝑝)=𝛼(1−2^{−𝜆(𝑡𝑐−𝑡𝑝+1)})𝑁(1−2^{−𝜆(𝑡𝑝)})

(22)    if  𝑤_𝑔<OWT  then

(23)     Remove grid 𝑔 from the grid list

(24)    end if

(25)   end for

(26)   for all   {MIC}  do

(27)    if  𝑤_MIC<𝛼𝑁(1−2^−𝜆)  then

(28)     Remove MIC from {MIC}

(29)    end if

(30)   end for

(31)  end if

(32)  𝑡_𝑐=𝑡_𝑐+1

(33) end while

  {***** FCC-Step *****}

(34) if the clustering request is arrived then

(35)  Generate clusters using a modified DBSCAN

(36) end if