ML | OPTICS Clustering Explanation

Prerequisites: DBSCAN Clustering

OPTICS Clustering stands for Ordering Points To Identify Cluster Structure. It draws inspiration from the DBSCAN clustering algorithm. It adds two more terms to the concepts of DBSCAN clustering. They are:-

  1. Core Distance: It is the minimum value of radius required to classify a given point as a core point. If the given point is not a Core point, then it’s Core Distance is undefined.


  2. Reachability Distance: It is defined with respect to another data point q(Let). The Reachability distance between a point p and q is the maximum of the Core Distance of p and the Euclidean Distance(or some other distance metric) between p and q. Note that The Reachability Distance is not defined if q is not a Core point.

This clustering technique is different from other clustering techniques in the sense that this technique does not explicitly segment the data into clusters. Instead, it produces a visualization of Reachability distances and uses this visualization to cluster the data.

Pseudocode:

The following Pseudocode has been referred from the Wikipedia page of the algorithm.

OPTICS(DB, eps, MinPts)

    #Repeating the process for all points in the database
    for each point pt of DB

       #Initializing the reachability distance of the selected point
       pt.reachable_dist = UNDEFINED
    for each unprocessed point pt of DB

       #Getting the neighbours of the selected point
       #according to the definitions of epsilon and
       #minPts in DBSCAN
       Nbrs = getNbrs(pt, eps)

       mark pt as processed
       output pt to the ordered list

       #Checking if the selected point is not noise
       if (core_dist(pt, eps, Minpts) != UNDEFINED)

          #Initializing a priority queue to get the closest data point
          #in terms of Reachability distance
          Seeds = empty priority queue

          #Calling the update function
          update(Nbrs, pt, Seeds, eps, Minpts)

          #Repeating the process for the next closest point
          for each next q in Seeds
             Nbrs' = getNbrs(q, eps)
             mark q as processed
             output q to the ordered list
             if (core_dist(q, eps, Minpts) != UNDEFINED)
                update(Nbrs', q, Seeds, eps, Minpts)

The pseudo-code for the update function is given below:

update(Nbrs, pt, Seeds, eps, MinPts)

    #Calculating the core distance for the given point
    coredist = core_dist(pt, eps, MinPts)

    #Updating the Reachability distance for each neighbour of p
    for each obj in Nbrs
       if (obj is not processed)
          new_reach_distance = max(coredist, dist(pt, obj))

          #Checking if the neighbour point is in seeds
          if (obj.reachable_dist == UNDEFINED)

              #Updation step
              obj.reachabled_dist = new_reach_distance
              Seeds.insert(obj, new_reach_distance)
          else               
              if (new_reach_distance < obj.reachable_dist)

                 #Updation step
                 o.reachable_dist = new_reach_distance
                 Seeds.move-up(obj, new_reach_distance)

OPTICS Clustering v/s DBSCAN Clustering:

  1. Memory Cost : The OPTICS clustering technique requires more memory as it maintains a priority queue (Min Heap) to determine the next data point which is closest to the point currently being processed in terms of Reachability Distance. It also requires more computational power because the nearest neighbour queries are more complicated than radius queries in DBSCAN.
  2. Fewer Parameters : The OPTICS clustering technique does not need to maintain the epsilon parameter and is only given in the above pseudo-code to reduce the time taken. This leads to the reduction of the analytical process of parameter tuning.
  3. This technique does not segregate the given data into clusters. It merely produces a Reachability distance plot and it is upon the interpretation of the programmer to cluster the points accordingly.


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