COMPUTATIONAL INTELLIGENCE

Transcription

1 COMPUTATIONAL INTELLIGENCE LABORATORY CLASSES Immentton smplstc verson of the network for some nference resons Adrn Horzyk

2 IMPLEMENTATION OF THE SIMPLISTIC OR AANG Imment the smplstc verson of n structure for Irs dt. You cn but there s no need to use AVB-trees or AVB+trees to crete t. You cn use sorted lsts or tbles of Vlue Vertces nsted of AVB+trees. You cn use hsh-tbles, c sortng lgorthms, sorted lsts, dctonres, but the result should be smlr nd correct. You don t need to present your results or network structure grphclly, Only text form of results s requred. Independently from your choce of mmentton use the selected one to: 1. Fnd the most smlr object(s) to the gven object or group of objects. 2. Fnd the most smlr object(s) to ny combnton of nput dt gven on the nput. 3. Usng ssoctons generte the lst of ll objects sorted by the smlrty to the gve object (Tsk 1) or ny combnton of nput dt (Tsk 2). 4. Try to mment fer usng structure. 5. Compute mn, mx, verge, medns usng c lgorthms nd computed the tme to smlr opertons on structures.

3 You cn crete ths grph n the followng steps for gven dt set: ASSOCIATIVE TRANSFORMATION IRIS PATTERNS n the tree-bsed grph structure IRIS PATTERNS IRIS PATTERNS To represent Vlue Nodes, use sorted lsts or tbles together wth the hlf-serch lgorthm or (the more mbtous soluton: wth the AVB+trees) whch wll llow you to fnd two closest vlues when the serched one wll not be found. Stndrd hsh-tbles nd sorted-lsts hve no such functonlty!

4 nodes representng neghborng (subsequent) vlues of ech ttrbute k re connected nd the weght of ths connecton (edge) s computed fter the followng formul: w v k,v j k = 1 v k v j k r k WEGIHTS COMPUTATION weghts do not need to be stored n ths structure but computed on demnd when necessry. In ths cse, you don t need to updte weghts when ddng new objects to ths structure. where v k, v k j - re vlues represented by the neghborng ttrbute nodes, whch re connected by n edge n the grph, r k = v k mx k vmn - s the current rnge of vlues of the ttrbute k. The weght of the connecton from the vlue node v k of the ttrbute k to the object node R m s determned fter the number of occurrences N k of ths vlue (v k ) n ll objects: w v k = 1,R m N k = 1 v k These numbers (N k = v k ) re stored n the ndvdul vlue nodes of ech ttrbute. Ths number s equl to the number or ll connectons of ths vlue node to ll object nodes f there re no duplcted objects n the tble used to crete the structure. In the opposte drecton, the weghts of connectons from the object nodes to the vlue nodes re lwys equl to one: w Rm,v k = 1 w, = 1 =

5 ASSOCIATIVE INFERENCE USING STRUCTURES Assoctve dt structures cn be now used for ssoctve nference, whch s bsed on movng long the connectons to the connected nodes nd computng some vlues n these nodes on the bss of the send vlues multpled by weghts of these connectons. In such wy we get the nformton bout e.g. smlrty of objects represented by other nodes of the sme knd or bout the objects tht stsfy some gven condtons defned by the represented ttrbute vlues. Let s use our grph creted for 13 Irses for such nference lookng for objects (Irses) Rx whch re most smlr to. 1. We strt n the node whch ssumes the smlrty vlue x=, becuse ths node s 100% smlr to tself. 2. Next, we ssgn vlues x of the connected nodes representng the followng vlues:,,,, nd by multplyng the vlue comng from the node wth the connecton weghts, whch re equl. So, s result, we cheve x= for ll these connected nodes

6 ASSOCIATIVE INFERENCE USING STRUCTURES 3. Subsequently, the vlues computed for these nodes re multpled by next connecton weghts nd send to the neghbor connected vlue nodes, for whch we lso compute ther smlrty vlues x. 4. Smlrly, we compute the smlrty vlues x for connected object nodes wth regrds to the necessty to dd the pssed weghted vlues to the sums lredy stored n these nodes, e.g. for the node we compute x = * * * 0.2 = 0.48 x=0.61 x=0.80 x= x=0.78 x=0.88 x=0.74 x=0.66 x=0.61 x=0.64 x=0.80 x=0.70 x=0.63 x=0.48 x=0.48 x=0.38 x=0.39 x=0.14 x= x= x=0.37 3

7 ASSOCIATIVE INFERENCE USING STRUCTURES 5. Fnlly, when we go through ll the connected (ssocted) vlues nodes computng thers vlues of smlrtes by multplyng the sender smlrty vlues by connecton weghts. We lso computed weghted sums for ll object nodes, where these weghts re here equl w = 1/5 = 0.2. The computed smlrty vlues for the nodes Rx cn be used to compre nd desgnte the most smlr objects to the object : (78%), (77%), (75%), x=0.58 x=0.61 x=0.78 x=0.88 x=0.73 x=0.65 x=0.58 x=0.67 x=0.74 x=0.66 x=0.54 x=0.49 x=0.61 x=0.64 x=0.60 x=0.53 x=0.50 x=0.80 x=0.70 x=0.63 x=0.57 x=0.51 x=0.46 x=0.41 x=0.75 x=0.77 x=0.70 x=0.78 x=0.56 x= x= x= x= x=0.42 It s lso worth notng tht grphs re not neurl structures, so we re not oblgted to multply the nodes smlrty vlues by connecton weghts, but we cn lso use nother formuls, e.g. we cn subtrct the comment of the connecton weght vlue from the smlrty vlue represented by the sender: x = x - (1 w). Consequently, we get nother mesure of smlrty represented by the vlue nodes nd object nodes. We cn lso used DASNG grph formuls to clculte weghts between vlue nodes nd object nodes to emphsze rrty of the vlue usng the frequency of connectons comng out from vlue nodes: w = 1 / the number of outgong connectons.

8 Bblogrphy nd References