|
1 | | -\d .ml |
| 1 | +// clust/init.q - Affinity propagation |
| 2 | +// Copyright (c) 2021 Kx Systems Inc |
| 3 | +// |
| 4 | +// Clustering using affinity propagation. |
| 5 | +// Affinity Propagation groups data based on the similarity |
| 6 | +// between points and subsequently finds exemplars, which best |
| 7 | +// represent the points in each cluster. The algorithm does |
| 8 | +// not require the number of clusters be provided at run time, |
| 9 | +// but determines the optimum solution by exchanging real-valued |
| 10 | +// messages between points until a high-valued set of exemplars |
| 11 | +// is produced. |
2 | 12 |
|
3 | | -// Affinity Propagation |
| 13 | +\d .ml |
4 | 14 |
|
5 | 15 | // @kind function |
6 | 16 | // @category clust |
7 | | -// @fileoverview Fit affinity propagation algorithm |
8 | | -// @param data {float[][]} Data in matrix format, each column is an individual datapoint |
9 | | -// @param df {symbol} Distance function name within '.ml.clust.df' |
10 | | -// @param dmp {float} Damping coefficient |
11 | | -// @param diag {func} Function applied to the similarity matrix diagonal |
12 | | -// @param iter {dict} Max number of overall iterations and iterations |
13 | | -// without a change in clusters. (::) can be passed in which case the defaults |
14 | | -// of (`total`nochange!200 15) will be used |
15 | | -// @return {dict} Data, input variables, clusters and exemplars |
16 | | -// (`data`inputs`clt`exemplars) required for the predict method |
17 | | -clust.ap.fit:{[data;df;dmp;diag;iter] |
| 17 | +// @desc Fit affinity propagation algorithm |
| 18 | +// @param data {float[][]} Each column of the data is an individual datapoint |
| 19 | +// @param df {symbol} Distance function name within '.ml.clust.df' |
| 20 | +// @param damp {float} Damping coefficient |
| 21 | +// @param diag {fn} Function applied to the similarity matrix diagonal |
| 22 | +// @param iter {dictionary} Max number of overall iterations and iterations |
| 23 | +// without a change in clusters. (::) can be passed in which case the |
| 24 | +// defaults of (`total`noChange!200 15) will be used |
| 25 | +// @return {dictionary} Data, input variables, clusters and exemplars |
| 26 | +// (`data`inputs`clust`exemplars) required, along with a projection of the |
| 27 | +// predict function |
| 28 | +clust.ap.fit:{[data;df;damp;diag;iter] |
18 | 29 | data:clust.i.floatConversion[data]; |
19 | | - defaultDict:`run`total`nochange!0 200 15; |
| 30 | + defaultDict:`run`total`noChange!0 200 15; |
20 | 31 | if[iter~(::);iter:()!()]; |
21 | 32 | if[99h<>type iter;'"iter must be (::) or a dictionary"]; |
22 | | - // update iteration dictionary with user changes |
| 33 | + // Update iteration dictionary with user changes |
23 | 34 | updDict:defaultDict,iter; |
24 | | - // cluster data using AP algo |
25 | | - clust.i.runap[data;df;dmp;diag;til count data 0;updDict] |
| 35 | + // Cluster data using AP algo |
| 36 | + modelInfo:clust.i.runAp[data;df;damp;diag;til count data 0;updDict]; |
| 37 | + returnInfo:enlist[`modelInfo]!enlist modelInfo; |
| 38 | + predictFunc:clust.ap.predict returnInfo; |
| 39 | + returnInfo,enlist[`predict]!enlist predictFunc |
26 | 40 | } |
27 | 41 |
|
28 | 42 | // @kind function |
29 | 43 | // @category clust |
30 | | -// @fileoverview Predict clusters using AP config |
31 | | -// @param data {float[][]} Data in matrix format, each column is an individual datapoint |
32 | | -// @param cfg {dict} `data`inputs`clt`exemplars returned by clust.ap.fit |
33 | | -// @return {long[]} List of predicted clusters |
34 | | -clust.ap.predict:{[data;cfg] |
| 44 | +// @desc Predict clusters using AP config |
| 45 | +// @param config {dictionary} `data`inputs`clust`exemplars returned by the |
| 46 | +// modelInfo key from the return of clust.ap.fit |
| 47 | +// @param data {float[][]} Each column of the data is an individual datapoint |
| 48 | +// @return {long[]} Predicted clusters |
| 49 | +clust.ap.predict:{[config;data] |
| 50 | + config:config`modelInfo; |
35 | 51 | data:clust.i.floatConversion[data]; |
36 | | - if[-1~first cfg`clt; |
37 | | - '"'.ml.clust.ap.fit' did not converge, all clusters returned -1. Cannot predict new data."]; |
38 | | - // retrieve cluster centres from training data |
39 | | - ex:cfg[`data][;distinct cfg`exemplars]; |
40 | | - // predict testing data clusters |
41 | | - clust.i.appreddist[ex;cfg[`inputs]`df]each$[0h=type data;flip;enlist]data |
42 | | - } |
43 | | - |
44 | | - |
45 | | -// Utilities |
46 | | - |
47 | | -// @kind function |
48 | | -// @category private |
49 | | -// @fileoverview Run affinity propagation algorithm |
50 | | -// @param data {float[][]} Data in matrix format, each column is an individual datapoint |
51 | | -// @param df {symbol} Distance function name within '.ml.clust.df' |
52 | | -// @param dmp {float} Damping coefficient |
53 | | -// @param diag {func} Function applied to the similarity matrix diagonal |
54 | | -// @param idxs {long[]} List of indicies to find distances for |
55 | | -// @param iter {dict} Max number of overall iterations and iterations |
56 | | -// without a change in clusters. (::) can be passed in where the defaults |
57 | | -// of (`total`nochange!200 15) will be used |
58 | | -// @return {long[]} List of clusters |
59 | | -clust.i.runap:{[data;df;dmp;diag;idxs;iter] |
60 | | - // check negative euclidean distance has been given |
61 | | - if[df<>`nege2dist;clust.i.err.ap[]]; |
62 | | - // calculate distances, availability and responsibility |
63 | | - info0:clust.i.apinit[data;df;diag;idxs]; |
64 | | - // initialize exemplar matrix and convergence boolean |
65 | | - info0,:`emat`conv`iter!((count data 0;iter`nochange)#0b;0b;iter); |
66 | | - // run ap algo until maximum number of iterations completed or convergence |
67 | | - info1:clust.i.apstop clust.i.apalgo[dmp]/info0; |
68 | | - // return data, inputs, clusters and exemplars |
69 | | - inputs:`df`dmp`diag`iter!(df;dmp;diag;iter); |
70 | | - exemplars:info1`exemplars; |
71 | | - clt:$[info1`conv;clust.i.reindex exemplars;count[data 0]#-1]; |
72 | | - `data`inputs`clt`exemplars!(data;inputs;clt;exemplars) |
73 | | - } |
74 | | - |
75 | | -// @kind function |
76 | | -// @category private |
77 | | -// @fileoverview Initialize matrices |
78 | | -// @param data {float[][]} Data in matrix format, each column is an individual datapoint |
79 | | -// @param df {symbol} Distance function name within '.ml.clust.df' |
80 | | -// @param diag {func} Function applied to the similarity matrix diagonal |
81 | | -// @param idxs {long[]} List of point indices |
82 | | -// @return {dict} Similarity, availability and responsibility matrices |
83 | | -// and keys for matches and exemplars to be filled during further iterations |
84 | | -clust.i.apinit:{[data;df;diag;idxs] |
85 | | - // calculate similarity matrix values |
86 | | - s:clust.i.dists[data;df;data]each idxs; |
87 | | - // update diagonal |
88 | | - s:@[;;:;diag raze s]'[s;k:til n:count data 0]; |
89 | | - // create lists/matrices of zeros for other variables |
90 | | - `matches`exemplars`s`a`r!(0;0#0;s),(2;n;n)#0f |
91 | | - } |
92 | | - |
93 | | -// @kind function |
94 | | -// @category private |
95 | | -// @fileoverview Run affinity propagation algorithm |
96 | | -// @param dmp {float} Damping coefficient |
97 | | -// @param info {dict} Similarity, availability, responsibility, exemplars, |
98 | | -// matches, iter dictionary, no_conv boolean and iter dict |
99 | | -// @return {dict} Updated inputs |
100 | | -clust.i.apalgo:{[dmp;info] |
101 | | - // update responsibility matrix |
102 | | - info[`r]:clust.i.updr[dmp;info]; |
103 | | - // update availability matrix |
104 | | - info[`a]:clust.i.upda[dmp;info]; |
105 | | - // find new exemplars |
106 | | - ex:imax each sum info`a`r; |
107 | | - // update `info` with new exemplars/matches |
108 | | - info:update exemplars:ex,matches:?[exemplars~ex;matches+1;0]from info; |
109 | | - // update iter dictionary |
110 | | - .[clust.i.apconv info;(`iter;`run);+[1]] |
111 | | - } |
112 | | - |
113 | | -// @kind function |
114 | | -// @category private |
115 | | -// @fileoverview Check affinity propagation algorithm for convergence |
116 | | -// @param info {dict} Similarity, availability, responsibility, exemplars, |
117 | | -// matches, iter dictionary, no_conv boolean and iter dict |
118 | | -// @return {dict} Updated info dictionary |
119 | | -clust.i.apconv:{[info] |
120 | | - // iteration dictionary |
121 | | - iter:info`iter; |
122 | | - // exemplar matrix |
123 | | - emat:info`emat; |
124 | | - // existing exemplars |
125 | | - ediag:0<sum clust.i.diag each info`a`r; |
126 | | - emat[;iter[`run]mod iter`nochange]:ediag; |
127 | | - // check for convergence |
128 | | - if[iter[`nochange]<=iter`run; |
129 | | - unconv:count[info`s]<>sum(se=iter`nochange)+0=se:sum each emat; |
130 | | - conv:$[(iter[`total]=iter`run)|not[unconv]&sum[ediag]>0;1b;0b]]; |
131 | | - // return updated info |
132 | | - info,`emat`conv!(emat;conv) |
133 | | - } |
134 | | - |
135 | | -// @kind function |
136 | | -// @category private |
137 | | -// @fileoverview Retrieve diagonal from a square matrix |
138 | | -// @param m {any[][]} Square matrix |
139 | | -// @return {any[]} Matrix diagonal |
140 | | -clust.i.diag:{[m] |
141 | | - {x y}'[m;til count m] |
142 | | - } |
143 | | - |
144 | | -// @kind function |
145 | | -// @category private |
146 | | -// @fileoverview Update responsibility matrix |
147 | | -// @param dmp {float} Damping coefficient |
148 | | -// @param info {dict} Similarity, availability, responsibility, exemplars, |
149 | | -// matches, iter dictionary, no_conv boolean and iter dict |
150 | | -// @return {float[][]} Updated responsibility matrix |
151 | | -clust.i.updr:{[dmp;info] |
152 | | - // create matrix with every points max responsibility |
153 | | - // diagonal becomes -inf, current max is becomes second max |
154 | | - mxresp:{[x;i]@[count[x]#mx;j;:;]max@[x;i,j:x?mx:max x;:;-0w]}; |
155 | | - mx:mxresp'[sum info`s`a;til count info`r]; |
156 | | - // calculate new responsibility |
157 | | - (dmp*info`r)+(1-dmp)*info[`s]-mx |
158 | | - } |
159 | | - |
160 | | -// @kind function |
161 | | -// @category private |
162 | | -// @fileoverview Update availability matrix |
163 | | -// @param dmp {float} Damping coefficient |
164 | | -// @param info {dict} Similarity, availability, responsibility, exemplars, |
165 | | -// matches, iter dictionary, no_conv boolean and iter dict |
166 | | -// @return {float[][]} Returns updated availability matrix |
167 | | -clust.i.upda:{[dmp;info] |
168 | | - // sum values in positive availability matrix |
169 | | - s:sum@[;;:;0f]'[pv:0|info`r;k:til n:count info`a]; |
170 | | - // create a matrix using the negative values produced by the availability sum |
171 | | - // + responsibility diagonal - positive availability values |
172 | | - a:@[;;:;]'[0&(s+info[`r]@'k)-/:pv;k;s]; |
173 | | - // calculate new availability |
174 | | - (dmp*info`a)+a*1-dmp |
175 | | - } |
176 | | - |
177 | | -// @kind function |
178 | | -// @category private |
179 | | -// @fileoverview Stopping condition for affinity propagation algorithm |
180 | | -// @param info {dict} Similarity, availability, responsibility, exemplars, |
181 | | -// matches, iter dictionary, no_conv boolean and iter dict |
182 | | -// @return {bool} Indicates whether to continue or stop running AP (1/0b) |
183 | | -clust.i.apstop:{[info] |
184 | | - (info[`iter;`total]>info[`iter]`run)¬ 1b~info`conv |
185 | | - } |
186 | | - |
187 | | -// @kind function |
188 | | -// @category private |
189 | | -// @fileoverview Predict clusters using AP training exemplars |
190 | | -// @param ex {float[][]} Training cluster centres in matrix format, |
191 | | -// each column is an individual datapoint |
192 | | -// @param df {symbol} Distance function name within '.ml.clust.df' |
193 | | -// @param pt {float[]} Current data point |
194 | | -// @return {long[]} Predicted clusters |
195 | | -clust.i.appreddist:{[ex;df;pt] |
196 | | - d?max d:clust.i.dists[ex;df;pt]each til count ex 0 |
| 52 | + if[-1~first config`clust; |
| 53 | + '"'.ml.clust.ap.fit' did not converge, all clusters returned -1.", |
| 54 | + " Cannot predict new data." |
| 55 | + ]; |
| 56 | + // Retrieve cluster centres from training data |
| 57 | + exemp:config[`data][;distinct config`exemplars]; |
| 58 | + // Predict testing data clusters |
| 59 | + data:$[0h=type data;flip;enlist]data; |
| 60 | + clust.i.apPredDist[exemp;config[`inputs]`df]each data |
197 | 61 | } |
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