## I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm

I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm.

I Would be grateful if someone gives a logical and intuitive explanation of the ordering and also explain what `res$order`

does in the following code and what is the reahability plot(which can be obtained by the command 'plot(res)').

library(dbscan) set.seed(2) n <- 400 x <- cbind( x = runif(4, 0, 1) + rnorm(n, sd=0.1), y = runif(4, 0, 1) + rnorm(n, sd=0.1) ) plot(x, col=rep(1:4, time = 100)) res <- optics(x, eps = 10, minPts = 10) res res$order plot(res)

res$order gives the following output:

[1] 1 363 209 349 337 301 357 333 321 285 281 253 241 177 153 57 257 29 77 169 105 293 229 145 181 385 393 377 317 381 185 117 [33] 101 9 73 237 397 369 365 273 305 245 249 309 157 345 213 205 97 49 33 41 193 149 17 83 389 25 121 329 5 161 341 217 [65] 189 141 85 53 225 313 289 261 221 173 69 61 297 125 81 133 129 197 109 137 59 93 165 89 21 13 277 191 203 379 399 375 [97] 351 311 235 231 227 71 11 299 271 291 147 55 23 323 219 275 47 263 3 367 331 175 87 339 319 251 247 171 111 223 51 63 [129] 343 303 207 151 391 359 287 283 215 143 131 115 99 31 183 43 243 199 79 27 295 67 347 255 239 195 187 139 107 39 119 179 [161] 395 371 201 123 159 91 211 355 103 327 95 7 167 35 267 155 387 383 335 315 259 135 15 113 279 373 4 353 265 127 45 37 [193] 19 276 224 361 260 288 336 368 348 292 268 252 120 108 96 88 32 16 340 156 388 372 356 332 304 220 188 168 136 124 56 236 [225] 28 244 392 184 76 380 232 100 116 112 256 72 8 280 64 52 208 172 152 148 360 352 192 160 144 284 216 48 84 92 36 20 [257] 212 272 264 200 128 80 180 364 196 12 132 40 324 308 176 164 68 316 312 384 300 344 328 248 204 140 296 24 320 228 60 44 [289] 233 65 400 376 240 163 104 396 307 75 14 325 269 262 234 382 294 206 198 374 310 362 318 386 358 330 278 210 298 282 122 98 [321] 34 26 174 142 46 6 62 118 190 202 114 322 286 38 242 394 342 266 162 130 30 182 2 74 314 290 246 194 170 126 158 378 [353] 350 254 226 214 70 18 10 366 354 186 150 86 306 102 338 346 134 250 138 94 78 390 274 58 42 258 66 90 146 370 222 218 [385] 326 82 110 270 334 178 166 398 22 50 238 106 154 302 230 54

and the 'plot' produces a reachability plot which I am not able to post because this is my first question on StackExchange...but if you run the R code you can easily get it.

**[PDF] OPTICS: Ordering Points To Identify the Clustering Structure,** input parameters which are hard to determine but have a significant the result of the clustering algorithm describes the intrinsic cluster- algorithm OPTICS to create an ordering of a data set with re- mal definitions for this notion of a clustering are shortly for getting a clear understanding of the structure of the data. Its. It is a 2D plot, with the ordering of the points as processed by OPTICS on the x-axis and the reachability distance on the y-axis. Since points belonging to a cluster have a low reachability distance to their nearest neighbor, the clusters show up as valleys in the reachability plot.

A detailed description is included in the R packages.

library("dbscan") vignette("dbscan")

See Section **2.2. OPTICS: Ordering Points To Identify Clustering Structure**

OPTICS provides an augmented ordering. The algorithm starting with a point and expands it’s neighborhood like DBSCAN, but it explores the new point in the order of lowest to highest core-distance. The order in which the points are explored along with each point’s core- and reachability-distance is the final result of the algorithm.

**Clustering Using OPTICS,** There is a relative of DBSCAN, called OPTICS (Ordering Points to Identify Cluster only if you would like to try and speed up computation time. First, I will explain a little how this algorithm works, how it can include in-line Although the MinPts parameter is used in these calculations, the idea is that it 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:-Core Distance: It is the minimum value of radius required to classify a given point as a core point. If

It is a reordering (permutation) of your data set, such that nearby points usually are close in the order.

**[PDF] OPTICS: Ordering Points To Identify the Clustering Structure,** input parameters which are hard to determine but have a significant the result of the clustering algorithm describes the intrinsic cluster- algorithm OPTICS to create an ordering of a data set with re- mal definitions for this notion of a clustering are shortly fcp\ for getting a clear understanding of the structure of the data. OPTICS: Ordering Points to Identify the Clustering Structure. run-time of the algorithm OPTICS is nearly the same as the run- used by the OPTICS clustering algorithm to determine the clus-

**(PDF) OPTICS: Ordering Points to Identify the Clustering Structure,** sis which is intended to help a user to understand the natural gorithms require values for input parameters which are hard to algorithm OPTICS to create an ordering of a data set with re- nected by a line of few points having a small inter-object dis- The key idea of density-based clustering is that for each object. sic notions of density-based clustering are defined and our new algorithm OPTICS to create an ordering of a data set with re-spect to its density-based clustering structure is presented. The application of this cluster-ordering for the purpose of cluster analysis is demonstrated in section 4. Both, automatic as well

**OPTICS algorithm,** Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. Its basic idea is similar to DBSCAN, but it addresses one of DBSCAN's major we need to assume to have p and o belong to the same cluster. I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm. I Would be grateful if someone gives a logical and intuitive explanation of the ordering and also explain

**Optics ordering points to identify the clustering structure,** (Paper Presentation) OPTICS-Ordering Points To Identify The Clustering Structure. Such parameter settings are usually empirically set and difficult to determine. OPTICS works in principle like such an extended DBSCAN algorithm Having generated the augmented cluster-ordering of a database with Possible duplicate of I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm – onofricamila Oct 16 '19 at 2:02 add a comment | 1 Answer 1