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SparseMatrixRecommenderFramework.m
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SparseMatrixRecommenderFramework.m
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(*
Sparse matrix recommender framework in Mathematica
Copyright (C) 2014-2016 Anton Antonov
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Written by Anton Antonov,
antononcube @ gmail . com,
Windermere, Florida, USA.
*)
(*
Mathematica is (C) Copyright 1988-2016 Wolfram Research, Inc.
Protected by copyright law and international treaties.
Unauthorized reproduction or distribution subject to severe civil
and criminal penalties.
Mathematica is a registered trademark of Wolfram Research, Inc.
*)
(* Version 1.0 *)
(*
The framework is described in the presentation
[1] Anton Antonov, "A fast and agile item-item recommender : design and implementation", October, WTC 2011.
URL: http://library.wolfram.com/infocenter/Conferences/7964/
The presentation is also available at MathematicaForPrediction project at GitHub:
[2] https://github.com/antononcube/MathematicaForPrediction/blob/master/Documentation/Antonov%20WTC-2011%20-%20A%20fast%20and%20agile%20IIR.pdf
NOTE, that there is a dependency on the package OutlierIdentifiers.m:
[3] Anton Antonov, "Implementation of one dimensional outlier identifying algorithms in Mathematica", Mathematica package, (2013).
URL: https://github.com/antononcube/MathematicaForPrediction/blob/master/OutlierIdentifiers.m .
The package [3] is imported below (using Import[...]).
*)
(* What is in the framework
1. Hooks
1.1. Sparse Matrix creators plug-ins
1.1.1. Constructors
1.1.2. Weights calculation
1.1.3. Weights parameters
1.2. Data
1.2.1. Data interpretation
1.3. Sparse Matrix Column interpretation to be used for ad-hoc profiles (search based, cold-start based)
1.4. Post-processing
1.4.1. Proofs
1.4.2. Distances
1.4.3. Ratings
1.4.4. Re-orderings
2. Algorithms
2.1. Basic recommendation algorithm
2.1.1. Parameters: user history, number of results
2.2. Recommendatons for a list of profile items
2.2.1. Takes number of results and profile vector or profile items list
2.3. Post-processing
2.3.1. Proofs -- common tags
2.3.2. Ratings --
2.3.3. Carousels --
3. Interface
3.1. Consumed items
3.2. Recommended items
3.3. User profile
3.4. Controls for weghts calculation
4. Major design decisions
4.1. Construct M01 and make M as M=M01.W .
4.2. After initialization, column interpreatation is always the same (because we keep M01).
4.3. Template method DP for the basic recommendation alorithm.
4.4. Strategy DP for matrix construction.
4.5. Observers for the interface parts.
4.6. Using rules to map tags to indexes and map local indexes to column indexes in M01.
*)
(* ::Section:: *)
(*Item recommender object definitions*)
(* ::Subsection:: *)
(*Data symbols*)
(* ::Subsubsection:: *)
(*Core recommender*)
(* ::Program:: *)
(*M01*)
(*M*)
(*W*)
(*weightsVector*)
(*metaDataNames*)
(*columnIndexToTagRules*)
(*tagToColumnIndexRules*)
(*tagTypes*)
(* ::Subsubsection:: *)
(*Interface*)
(* ::Program:: *)
(*recommendationDataIndexes*)
(*consumedDataIndexes*)
(*automaticWeights*)
(*useOutliers*)
(*panelWidth*)
(*panelHeight*)
(*=========================================================*)
(* Import packages *)
(*=========================================================*)
If[Length[DownValues[SSparseMatrix`MakeSSparseMatrix]] == 0,
Echo["Importing SSparseMatrix.m from GitHub...", "SparseMatrixRecommenderFramework:"];
Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/SSparseMatrix.m"]
Echo["...Done.", "SparseMatrixRecommenderFramework:"]
];
If[Length[DownValues[CrossTabulate`CrossTabulate]] == 0,
Echo["Importing CrossTabulate.m from GitHub...", "SparseMatrixRecommenderFramework:"];
Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/CrossTabulate.m"]
Echo["...Done.", "SparseMatrixRecommenderFramework:"]
];
If[Length[DownValues[OutlierIdentifiers`OutlierIdentifier]] == 0,
Echo["Importing OutlierIdentifiers.m from GitHub...", "SparseMatrixRecommenderFramework:"];
Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]
Echo["...Done.", "SparseMatrixRecommenderFramework:"]
];
(*=========================================================*)
(* Creation *)
(*=========================================================*)
Clear[ItemRecommender]
Clear[ItemRecommenderCreation]
ItemRecommenderCreation::rneq = "The row names of SSparseMatrix objects are not the same."
ItemRecommenderCreation::niid = "The specified item variable name is not one of the column names of the dataset."
ItemRecommenderCreation[id_String, smats : {_SparseArray ..},
tagTypeNames : {_String ..}, rowNames : {_String ..},
columnNames : {{_String ..} ..}] :=
Module[{objIR},
objIR = ItemRecommender[id];
objIR["itemNames"] = rowNames;
objIR["tagTypes"] = tagTypeNames;
objIR["M01"] = objIR["SpliceMatrices"][smats];
objIR["MakeRowInterpretation"][rowNames];
objIR["MakeColumnInterpretation"][tagTypeNames, columnNames];
objIR["UseTagTypeWeights"][ConstantArray[1, Length[tagTypeNames]]];
objIR
] /; Length[smats] == Length[tagTypeNames] == Length[columnNames];
ItemRecommenderCreation[id_String, smats : Association[ (_ -> _SSparseMatrix) ..]] :=
Block[{tagTypeNames, rowNames, columnNames},
tagTypeNames = Keys[smats];
rowNames = RowNames /@ Values[smats];
If[ !(Equal @@ rowNames),
Message[ItemRecommenderCreation::rneq];
Return[$Failed]
];
rowNames = First[rowNames];
columnNames = ColumnNames /@ Values[smats];
ItemRecommenderCreation[id, SparseArray /@ Values[smats], tagTypeNames, rowNames, columnNames ]
];
ItemRecommenderCreation[id_String, ds_Dataset, itemVarName_String ] :=
Block[{ncol, varNames, smats, idPos, rng},
ncol = Dimensions[ds][[2]];
varNames = Normal[Keys[ds[1]]];
idPos = Flatten[Position[varNames, itemVarName]];
If[ Length[idPos]==0,
Message[ItemRecommenderCreation::niid];
Return[$Failed]
];
idPos = First[idPos];
rng = Complement[Range[ncol], {idPos}];
smats = ToSSparseMatrix /@
Table[CrossTabulate[ds[All, {idPos, i}]], {i, rng}];
smats = AssociationThread[Flatten[List @@ varNames[[rng]] -> smats]];
ItemRecommenderCreation[id, smats]
];
Clear[MakeItemRecommender]
MakeItemRecommender = ItemRecommenderCreation;
(* Makes the item-tag sparse martix \[Element] {0,1}^(Subscript[n, items]*Subscript[n, tags]) *)
ItemRecommender[d___]["MakeM01"][args___]:=ItemRecommender[d]["M01"]=SparseArray[RandomInteger[{0,1},{100,20}]];
ItemRecommender[d___]["MakeBasicSparseMatrix"][args___]:=ItemRecommender[d]["MakeM01"][args];
(* Does not check for consistency witth M01.
I.e. make sure that M01.W should give a matrix (the M matrix) *)
ItemRecommender[d___]["MakeW"][weights_?VectorQ]:=
Block[{},
ItemRecommender[d]["W"]=SparseArray[DiagonalMatrix[weights]]
];
ItemRecommender[d___]["MakeWeightMatrix"][weights:{_?NumericQ...}]:=ItemRecommender[d]["MakeW"];
ItemRecommender[d___]["UseWeights"][weights_?VectorQ]:=
Block[{},
ItemRecommender[d]["MakeW"][weights];
ItemRecommender[d]["M"]=ItemRecommender[d]["M01"].ItemRecommender[d]["W"]
]/;Length[weights]==Dimensions[ItemRecommender[d]["M01"]][[2]];
ItemRecommender[d___]["UseTagTypeWeights"][tagTypeWeights:{_?NumericQ...}]:=
Block[{weights},
weights = Flatten@
Table[
ConstantArray[tagTypeWeights[[i]],
ItemRecommender[d]["tagTypeIndexOffsets"][[i+1]]-ItemRecommender[d]["tagTypeIndexOffsets"][[i]]
], {i,Length[tagTypeWeights]}];
weights=SparseArray[weights];
ItemRecommender[d]["UseWeights"][weights];
]/;Length[tagTypeWeights]==Length[ItemRecommender[d]["tagTypes"]];
ItemRecommender[d___]["MakeColumnInterpretation"][tagType_String,tags_List]:=
Block[{},
ItemRecommender[d]["ColumnInterpretationLocal"][tagType]=tags;
ItemRecommender[d]["ColumnIndexToTagRulesLocal"][tagType]=Dispatch[Thread[Range[1,Length[tags]]->tags]];
ItemRecommender[d]["TagToColumnIndexRulesLocal"][tagType]=Dispatch[Thread[tags->Range[1,Length[tags]]]];
];
ItemRecommender[d___]["MakeColumnInterpretation"][tagTypes:{_String...},tagsLists:{_List...}]:=
Block[{len=Total[Length/@tagsLists],offsets,ttlens=Length/@tagsLists},
ItemRecommender[d]["tagTypes"]=tagTypes;
(* assign local interpretations *)
MapThread[ItemRecommender[d]["MakeColumnInterpretation"][#1,#2]&,{tagTypes,tagsLists}];
(* assign global interpreation*)
ItemRecommender[d]["ColumnInterpretation"]=Join@@tagsLists;
ItemRecommender[d]["columnIndexToTagRules"]=Dispatch[Thread[Range[1,len]->Flatten[tagsLists,1]]];
ItemRecommender[d]["tagToColumnIndexRules"]=Dispatch[Thread[Flatten[tagsLists,1]->Range[1,len]]];
ItemRecommender[d]["aColumnIndexToTagRules"] = AssociationThread[ Range[1,len], Flatten[tagsLists,1] ];
ItemRecommender[d]["aTagToColumnIndexRules"] = AssociationThread[ Flatten[tagsLists,1], Range[1,len] ];
(* name alias *)
ItemRecommender[d]["columnIndexInterpretationRules"]:=ItemRecommender[d]["columnIndexToTagRules"];
(* global-local column indexes rules *)
offsets=FoldList[Plus,0,Length/@tagsLists];
ItemRecommender[d]["tagTypeIndexOffsets"]=offsets;
ItemRecommender[d]["tagTypeRanges"] = AssociationThread[tagTypes, Transpose[{Most[offsets]+1, Rest[offsets]}]];
ItemRecommender[d]["TypeFunction"]=With[{w=Which@@Flatten[Map[Function[{arg},{#>arg[[1]],arg[[2]]}],Transpose[{Rest[Reverse@offsets],Reverse@tagTypes}]]]},
Function[w]
];
Do[
ItemRecommender[d]["localIndexToGlobalIndexRules"][tagTypes[[i]]]=Dispatch[Thread[Range[1,ttlens[[i]]]->Range[offsets[[i]]+1,offsets[[i]]+ttlens[[i]]]]],
{i,1,Length[tagTypes]}];
]/;Length[tagTypes]==Length[tagsLists];
ItemRecommender[d___]["MakeRowInterpretation"][rowIDs:{(_Integer|_String)..}]:=
Block[{},
ItemRecommender[d]["RowIDs"]=rowIDs;
ItemRecommender[d]["itemNames"]=rowIDs; (* Note the redundancy of names here!*)
ItemRecommender[d]["RowIDToIndexRules"]=Dispatch[Thread[rowIDs->Range[Dimensions[ItemRecommender[d]["M01"]][[1]]]]];
ItemRecommender[d]["RowIndexToIDRules"]=Dispatch[Thread[Range[Dimensions[ItemRecommender[d]["M01"]][[1]]]->rowIDs]];
ItemRecommender[d]["aRowIDToIndexRules"] = AssociationThread[ rowIDs, Range[Dimensions[ItemRecommender[d]["M01"]][[1]]] ];
ItemRecommender[d]["aRowIndexToIDRules"] = AssociationThread[ Range[Dimensions[ItemRecommender[d]["M01"]][[1]]], rowIDs ] ;
]/;Dimensions[ItemRecommender[d]["M01"]][[1]]==Length[rowIDs];
ItemRecommender[d___]["SetFilterMatrix"][fmat_?MatrixQ,indexMappingRules_Dispatch]:=
Block[{},
ItemRecommender[d]["F"]=fmat;
ItemRecommender[d]["globalIndexToFilterIndexRules"]=indexMappingRules;
]/;Dimensions[ItemRecommender[d]["M01"]][[1]]==Dimensions[fmat];
ItemRecommender[d___]["SetFilterMatrix"][filterTagType_String]:=
Block[{indexMappingRules},
indexMappingRules=ItemRecommender[d]["localIndexToGlobalIndexRules"][filterTagType];
indexMappingRules=Reverse/@Normal[indexMappingRules];
ItemRecommender[d]["F"]=Transpose[ItemRecommender[d]["M01"][[All,indexMappingRules[[All,1]]]]];
ItemRecommender[d]["globalIndexToFilterIndexRules"]=Dispatch[indexMappingRules];
]/;MemberQ[ItemRecommender[d]["tagTypes"],filterTagType];
(*=========================================================*)
(* SpliceMatrices *)
(*=========================================================*)
ItemRecommender[d___]["SpliceMatrices"][smats:{_SparseArray...}]:=
ItemRecommender[d]["SpliceMatrices"][smats,ConstantArray[1,Length[smats]]];
ItemRecommender[d___]["SpliceMatrices"][smats:{_SparseArray...},weights:{_?NumberQ...}]:=
Block[{},
SparseArray[
MapThread[Join,MapThread[#1*#2&,{smats,weights}]]
]
]/;Length[smats]==Length[weights]==Length[ItemRecommender[d]["tagTypes"]];
(*=========================================================*)
(* SubMatrix *)
(*=========================================================*)
ItemRecommender::nott = "`1`: The ItemRecommender object does not have the tag type `2`."
ItemRecommender[d___]["SubMatrix"][tagType_String] :=
ItemRecommender[d]["SubMatrix"]["M", tagType];
ItemRecommender[d___]["SubMatrix"][m:("M"|"M01"),tagType_String] :=
Block[{},
If[ ! KeyExistsQ[ ItemRecommender[d]["tagTypeRanges"], tagType ],
Message[ItemRecommender::nott, "\"SubMatrix\"", tagType ];
Return[$Failed]
];
ItemRecommender[d][m][[ All, Range @@ ItemRecommender[d]["tagTypeRanges"][tagType] ]]
];
(*=========================================================*)
(* SubSSparseMatrix *)
(*=========================================================*)
ItemRecommender[d___]["SubSSparseMatrix"][tagType_String] :=
ItemRecommender[d]["SubSSparseMatrix"]["M", tagType];
ItemRecommender[d___]["SubSSparseMatrix"][m:("M"|"M01"), tagType_String] :=
Block[{rng, smat},
If[ ! KeyExistsQ[ ItemRecommender[d]["tagTypeRanges"], tagType ],
Message[ItemRecommender::nott, "\"SubSSparseMatrix\"", tagType ];
Return[$Failed]
];
rng = Range @@ ItemRecommender[d]["tagTypeRanges"][tagType];
smat = ItemRecommender[d][m][[ All, rng ]];
ToSSparseMatrix[
SparseArray[smat],
"RowNames" -> ItemRecommender[d]["itemNames"],
"ColumnNames" -> ItemRecommender[d]["ColumnInterpretation"][[rng]]
]
];
(*=========================================================*)
(* Recommendations *)
(*=========================================================*)
(* ::Text:: *)
(*The formulas we use for the version below are:*)
(* ::DisplayFormula:: *)
(*S=M Transpose[M]*)
(*v S=S v=M (Transpose[M] v)=M (v M)*)
(* ::Text:: *)
(*This is a a specification of the algorithm below in Recommendations.*)
(* ::Text:: *)
(*1. Make a vector v\[Element]\[DoubleStruckCapitalR]^Subscript[n, s] that has zeros everywhere except at the coordinates corresponding to showInds. The values at those coordinates are determined by ratings. *)
(*2. Do the two matrix-vector multiplications s:=M (v M), M\[Element]\[DoubleStruckCapitalR]^(Subscript[n, s]* Subscript[n, md]). The vector s is called the score vector for showInds or v. (Also the formula s:=(M M^T)v can be used, but M M^T might be large and dense.)*)
(*3. Make the list of pairs {Subscript[s, i],i},i\[Element][1,...,Subscript[n, s]], and name that list sp.*)
(*4. Sort descendingly sp according to the first value of each pair. *)
(*5. Take the indexes of the first k pairs, i.e. take sp(1:k,2).*)
ItemRecommender[d___]["UserItemsToLove"][args___] := ItemRecommender[d]["Recommendations"][args];
ItemRecommender[d___]["Recommendations"][ratedInds_Association, nRes_Integer, removeHistoryQ_:True] :=
Block[{},
ItemRecommender[d]["Recommendations"][Keys[ratedInds], Values[ratedInds], nRes, removeHistoryQ]
];
ItemRecommender[d___]["Recommendations"][inputShowInds:{_Integer...},inputRatings:{_?NumberQ...},nRes_Integer, removeHistoryQ_:True]:=
Block[{inds,vec,maxScores,smat=ItemRecommender[d]["M"]},
(*userMatrix=MapThread[#1*#2&,{smat\[LeftDoubleBracket]inputShowInds\[RightDoubleBracket],inputRatings},1];*)
(*1*)
vec=SparseArray[Thread[inputShowInds->inputRatings],{smat//Length}];
(*2*)
vec=smat.(vec.smat);
(*3 and 4 and 5*)
inds=Reverse@Ordering[vec//Normal];
If[TrueQ[removeHistoryQ],
If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],inds}],#[[1]]>0&&!MemberQ[inputShowInds,#[[2]]]&]],
If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],inds}],#[[1]]>0&]]
]
]/;Length[inputShowInds]==Length[inputRatings];
ItemRecommender[d___]["Recommendations"][{},_,nRes_Integer]:=
Block[{inds=Range[1,nRes]},Transpose[{ConstantArray[1,{Length[inds]}],inds}]];
ItemRecommender[d___]["UserItemsToLoveByProfile"][args___] := ItemRecommender[d]["RecommendationsByProfile"][args];
ItemRecommender[d___]["RecommendationsByProfile"][profileInds:{_Integer...},profileScores:{_?NumberQ...},nRes_Integer]:=
Block[{inds,vec,smat=ItemRecommender[d]["M"]},
vec=SparseArray[Thread[profileInds->profileScores],{Dimensions[smat][[2]]}];
vec=smat.vec;
inds=Reverse@Ordering[vec//Normal];
(*If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec\[LeftDoubleBracket]inds\[RightDoubleBracket],inds}],#\[LeftDoubleBracket]1\[RightDoubleBracket]>0&]]*)
If[Length[#]>nRes,Take[#,nRes],#]&[DeleteCases[Transpose[{vec[[inds]],inds}],{0.,_}]]
]/;Length[profileInds]==Length[profileScores];
ItemRecommender[d___]["RecommendationsByProfile"][profileVec_SparseArray,nRes_Integer]:=
Block[{inds,vec,smat=ItemRecommender[d]["M"]},
vec=smat.profileVec;
(*inds=Most[ArrayRules[vec]]\[LeftDoubleBracket]All,1,1\[RightDoubleBracket];
If[Length[#]>nRes,Take[#,nRes],#]&[SortBy[Select[Transpose[{vec\[LeftDoubleBracket]inds\[RightDoubleBracket],inds}],#\[LeftDoubleBracket]1\[RightDoubleBracket]>0&],-#\[LeftDoubleBracket]1\[RightDoubleBracket]&]]*)
inds=Reverse@Ordering[vec//Normal];
(*If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],inds}],#[[1]]>0&]];*)
If[Length[#]>nRes,Take[#,nRes],#]&[DeleteCases[Transpose[{vec[[inds]],inds}],{0.,_}]]
]/;Dimensions[ItemRecommender[d]["M"]][[2]]==Dimensions[profileVec][[1]];
ItemRecommender[d___]["RecommendationsByProfile"][tagsArg:(_Association | _List ), nRes_Integer] :=
Block[{profVec},
profVec = ItemRecommender[d]["MakeProfileVector"][tagsArg];
ItemRecommender[d]["RecommendationsByProfile"][ profVec, nRes ]
];
(*ItemRecommender[d___]["RecommendationsByProfile"][scoredTags_Association, nRes_Integer] :=*)
(*Block[{tagInds, t},*)
(*tagInds = Keys[scoredTags] /. ItemRecommender[d]["tagToColumnIndexRules"];*)
(*If[ VectorQ[tagInds, NumberQ],*)
(*ItemRecommender[d]["RecommendationsByProfile"][tagInds, Values[scoredTags]],*)
(*ELSE*)
(*Message[ItemRecommender::ntags];*)
(*t = Select[ Transpose[{tagInds, Values[scoredTags]}], NumberQ[#[[1]]]];*)
(*If[Length[t] > 0,*)
(*ItemRecommender[d]["RecommendationsByProfile"][t[[All,1]], t[[All,2]]],*)
(*ELSE*)
(*{}*)
(*]*)
(*]*)
(*];*)
(* The code is almost identical to the definition above *)
ItemRecommender[d___]["RecommendationsByProfile"][rowInds:{_Integer..},profileInds:{_Integer...},profileScores:{_?NumberQ...},nRes_Integer]:=
Block[{inds,vec,smat=ItemRecommender[d]["M"][[rowInds]]},
vec=SparseArray[Thread[profileInds->profileScores],{Dimensions[smat][[2]]}];
vec=smat.vec;
inds=Reverse@Ordering[vec//Normal];
If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],inds}],#[[1]]>0&]]
]/;Length[profileInds]==Length[profileScores];
ItemRecommender[d___]["RecommendationsByProfile"][rowInds:{_Integer..},profileVec_SparseArray,nRes_Integer]:=
Block[{inds,vec,smat=ItemRecommender[d]["M"][[rowInds]]},
vec=smat.profileVec;
inds=Reverse@Ordering[vec//Normal];
(*If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],inds}],#[[1]]>0&]];*)
If[Length[#]>nRes,Take[#,nRes],#]&[DeleteCases[Transpose[{vec[[inds]],inds}],{0.,_}]]
]/;Dimensions[ItemRecommender[d]["M"]][[2]]==Dimensions[profileVec][[1]];
(*=========================================================*)
(* RecommendationsByProfile with filtering *)
(*=========================================================*)
ItemRecommender[d___]["UserItemsToLoveByFilterAndProfile"][args___] := ItemRecommender[d]["RecommendationsByFilterAndProfile"][args];
ItemRecommender[d___]["RecommendationsByFilterAndProfile"][filterInds:{_Integer..},profileInds:{_Integer...},profileScores:{_?NumberQ...},nRes_Integer,strictQ:(True|False)]:=
Block[{finds,inds,vec,maxScores,smat,fmat=ItemRecommender[d]["F"],indexArray,tf=Length[filterInds]},
finds=filterInds/.ItemRecommender[d]["globalIndexToFilterIndexRules"];
vec=fmat.DiagonalMatrix[SparseArray[Thread[finds->1.],{Dimensions[fmat][[1]]}]];
If[TrueQ[strictQ],vec=SparseArray[Clip[vec,{tf,tf},{0.,1.}]]];
indexArray=Most[ArrayRules[vec]][[All,1,1]];
smat=ItemRecommender[d]["M"][[Most[ArrayRules[vec]][[All,1,1]]]];
vec=SparseArray[Thread[profileInds->profileScores],{Dimensions[smat][[2]]}];
vec=smat.vec;
inds=Reverse@Ordering[vec//Normal];
If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],indexArray[[inds]]}],#[[1]]>0&]]
]/;Length[profileInds]==Length[profileScores]&&MatrixQ[ItemRecommender[d]["F"]]&&Dimensions[ItemRecommender[d]["F"]][[2]]==Dimensions[ItemRecommender[d]["M"]][[1]];
ItemRecommender[d___]["RecommendationsByFilterAndProfile"][filterVec_SparseArray,profileVec_SparseArray,nRes_Integer,strictQ:(True|False)]:=
Block[{finds,inds,vec,maxScores,smat,fmat=ItemRecommender[d]["F"],indexArray,tf=Total[filterVec]},
finds=Most[ArrayRules[filterVec]][[All,1,1]]/.ItemRecommender[d]["globalIndexToFilterIndexRules"];
vec=SparseArray[Thread[finds->1.],{Dimensions[fmat][[1]]}].fmat;
If[TrueQ[strictQ],vec=SparseArray[Clip[vec,{tf,tf},{0.,1.}]]];
indexArray=Most[ArrayRules[vec]][[All,1,1]];
smat=ItemRecommender[d]["M"][[indexArray]];
vec=smat.profileVec;
inds=Reverse@Ordering[vec//Normal];
If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],indexArray[[inds]]}],#[[1]]>0&]]
]/;Dimensions[filterVec][[1]]==Dimensions[profileVec][[1]]==Dimensions[ItemRecommender[d]["M"]][[2]]&&MatrixQ[ItemRecommender[d]["F"]]&&Dimensions[ItemRecommender[d]["F"]][[2]]==Dimensions[ItemRecommender[d]["M"]][[1]];
(* Not an universal solution and it is only few %'s faster than the above *)
(*ItemRecommender[d___]["RecommendationsByFilterAndProfile"][filterVec_SparseArray,profileVec_SparseArray,nRes_Integer]:=
Block[{finds,inds,vec,maxScores,smat,fmat=ItemRecommender[d]["F"],indexRules,indexArray},
vec=filterVec[[ItemRecommender[d]["tagTypeIndexOffsets"][[2]]+1;;ItemRecommender[d]["tagTypeIndexOffsets"][[2+1]]]];
vec=vec.fmat;
vec=SparseArray[Clip[vec,{tf,tf},{0.,1.}]];
(*indexRules=Dispatch[MapIndexed[#2[[1]]->#[[1,1]]&,Most[ArrayRules[vec]]]];*)
(*indexRules=Dispatch[Thread[Range[Length[#]]->#]]&@Most[ArrayRules[vec]][[All,1,1]];*)
(*indexRules=Dispatch[Rule@@@Transpose[{Range[Length[#]],#}]]&@Most[ArrayRules[vec]][[All,1,1]];*)
indexArray=Most[ArrayRules[vec]][[All,1,1]];
smat=ItemRecommender[d]["M"][[indexArray]];
vec=smat.profileVec;
inds=Reverse@Ordering[vec//Normal];
If[Length[#]>nRes,Take[#,nRes],#]&[Select[Transpose[{vec[[inds]],indexArray[[inds]]}],#[[1]]>0&]]
]/;Dimensions[filterVec][[1]]==Dimensions[profileVec][[1]]==Dimensions[ItemRecommender[d]["M"]][[2]]&&MatrixQ[ItemRecommender[d]["F"]]&&Dimensions[ItemRecommender[d]["F"]][[2]]==Dimensions[ItemRecommender[d]["M"]][[1]];*)
(*=========================================================*)
(* UserProfile *)
(*=========================================================*)
ItemRecommender::notag = "`1`: Some of the specified tags are not known in the ItemRecommender object."
ItemRecommender[d___]["UserProfileVector"][args___] := ItemRecommender[d]["ProfileVector"][args];
ItemRecommender[d___]["ProfileVector"][inputShowInds:{_Integer...}]:=
ItemRecommender[d]["ProfileVector"][inputShowInds,ConstantArray[1.,Length[inputShowInds]]];
ItemRecommender[d___]["ProfileVector"][inputShowInds:{_Integer...},inputRatings:{_?NumberQ...}]:=
Block[{vec,smat=ItemRecommender[d]["M"]},
vec=SparseArray[Thread[inputShowInds->inputRatings],{smat//Length}];
vec.smat
]/;Length[inputShowInds]==Length[inputRatings];
ItemRecommender[d___]["UserProfile"][args___] := ItemRecommender[d]["Profile"][args];
ItemRecommender[d___]["Profile"][inputShowInds:{_Integer...}]:=
ItemRecommender[d]["Profile"][inputShowInds,ConstantArray[1.,Length[inputShowInds]]];
ItemRecommender[d___]["Profile"][inputShowInds:{_Integer...},inputRatings:{_?NumberQ...}]:=
Block[{inds,vec},
vec=ItemRecommender[d]["ProfileVector"][inputShowInds,inputRatings];
inds=Most[ArrayRules[vec]][[All,1,1]];
SortBy[Select[Transpose[{vec[[inds]],inds,inds/.ItemRecommender[d]["columnIndexToTagRules"]}],#[[1]]>0&],-#[[1]]&]
]/;Length[inputShowInds]==Length[inputRatings];
ItemRecommender[d___]["MakeProfileVector"][tags_List]:=
ItemRecommender[d]["MakeProfileVector"][tags,ConstantArray[1.,Length[tags]]];
ItemRecommender[d___]["MakeProfileVector"][tags_List,weights_]:=
ItemRecommender[d]["MakeProfileVector"][Thread[tags->weights]];
ItemRecommender[d___]["MakeProfileVector"][aTagWeights_Association]:=
ItemRecommender[d]["MakeProfileVector"][Normal[aTagWeights]];
ItemRecommender[d___]["MakeProfileVector"][tagWeightRules:{Rule[_,_?NumberQ]..}]:=
Block[{t=tagWeightRules},
t[[All,1]]=t[[All,1]]/.ItemRecommender[d]["tagToColumnIndexRules"];
t = Select[t, IntegerQ[#[[1]]]& ];
If[ Length[t] < Length[tagWeightRules],
Message[ItemRecommender::notag,"\"MakeProfileVector\""]
];
SparseArray[t,{Dimensions[ItemRecommender[d]["M01"]][[2]]}]
];
ItemRecommender[d___]["UserProfileFromVector"][args___] := ItemRecommender[d]["ProfileFromVector"][args];
ItemRecommender[d___]["ProfileFromVector"][pvec_SparseArray] :=
Block[{arules,res},
arules = Most[ArrayRules[pvec]];
res = Transpose[{arules[[All, 2]], Flatten[arules[[All, 1]]], ItemRecommender[d]["ColumnInterpretation"][[Flatten[arules[[All, 1]]]]]}];
res[[Reverse[Ordering[res[[All, 1]]]]]]
] /; VectorQ[pvec];
(*=========================================================*)
(* SMR Algebra *)
(*=========================================================*)
ItemRecommender::nmcols = "`1`: The column names of the specified SSparseMatrix object are not a subset of the column names of the recommender object."
ItemRecommender::nmtt = "`1`: The tag types of the ItemRecommender objects to be row-bound are not the same."
ItemRecommender[d___]["SSparseMatrix"][m:("M"|"M01")] :=
Block[{},
ToSSparseMatrix[
ItemRecommender[d][m],
"RowNames"->ItemRecommender[d]["itemNames"],
"ColumnNames"->ItemRecommender[d]["ColumnInterpretation"]
]
];
ItemRecommender[d___]["RowBind"][smat_SSparseMatrix] :=
Block[{bmat},
bmat = ItemRecommender[d]["SSparseMatrix"]["M01"];
Which[
ColumnNames[bmat] == ColumnNames[smat],
bmat = RowBind[ bmat, smat ],
Length[Complement[ ColumnNames[smat], ColumnNames[bmat] ]] == 0,
bmat = RowBind[ bmat, ImposeColumnNames[ smat, ColumnNames[bmat] ] ],
True,
Message[ItemRecommender::nmcols,"\"RowBind\""];
Return[$Failed]
];
If[ ! TrueQ[Head[bmat]===SSparseMatrix],
Return[$Failed]
];
ItemRecommender[d]["M01"] = SparseArray[bmat];
ItemRecommender[d]["MakeRowInterpretation"][ RowNames[bmat] ];
ItemRecommender[d]["UseTagTypeWeights"][ Table[1, {Length[ItemRecommender[d]["tagTypes"]]}] ];
ItemRecommender[d]
];
ItemRecommender[d___]["RowBind"][smr2_ItemRecommender] :=
Block[{smat1, smat2, t1, t2, cnames},
smat1 = ItemRecommender[d]["SSparseMatrix"]["M01"];
smat2 = smr2["SSparseMatrix"]["M01"];
Which[
ColumnNames[smat1] == ColumnNames[smat2],
ItemRecommender[d]["RowBind"][smat2],
ItemRecommender[d]["tagTypes"] == smr2["tagTypes"],
(* Separate into matrices for each tag type. *)
t1 = ItemRecommender[d]["SubSSparseMatrix"]["M01", #] & /@ ItemRecommender[d]["tagTypes"];
t2 = smr2["SubSSparseMatrix"]["M01", #] & /@ ItemRecommender[d]["tagTypes"];
(* Row bind each pair. *)
smat1 =
MapThread[
( cnames = Union[Join[ColumnNames[#1], ColumnNames[#2]]];
RowBind[ ImposeColumnNames[#1, cnames], ImposeColumnNames[#2, cnames] ])&,
{t1, t2}];
MakeItemRecommender[d, AssociationThread[ ItemRecommender[d]["tagTypes"], smat1] ],
True,
Message[ItemRecommender::nmtt,"\"RowBind\""];
$Failed
]
];
(*ItemRecommender[d___]["ColumnBind"][smat_SSparseMatrix] :=*)
(*Block[{},*)
(*];*)
(*ItemRecommender[d___]["Join"][smr2_ItemRecommender] :=*)
(*Block[{},*)
(*];*)
(*=========================================================*)
(* Classify *)
(*=========================================================*)
ItemRecommender[d___]["Classify"][tagType_String, tags:(_List | {_Rule..} | _Association), args___] :=
ItemRecommender[d]["Classify"][tagType, ItemRecommender[d]["MakeProfileVector"][tags], args];
ItemRecommender[d___]["Classify"][tagType_String, tags_List, weights_List, args___] :=
ItemRecommender[d]["Classify"][tagType, ItemRecommender[d]["MakeProfileVector"][tags,weights], args] /; Length[tags] == Length[weights];
ItemRecommender[d___]["Classify"][tagType_String, pvec_SparseArray, nTopNNs_Integer,
voting:(True|False):False, dropZeroScoredLabels:(True|False):True] :=
Block[{recs, clMat, s, t},
recs = ItemRecommender[d]["RecommendationsByProfile"][pvec,nTopNNs];
clMat = ItemRecommender[d]["M"][[All, Span @@ ItemRecommender[d]["tagTypeRanges"][tagType] ]];
If[ voting,
t = Most[ArrayRules[clMat]]; t[[All,2]] = 1;
clMat = SparseArray[t,Dimensions[clMat]];
recs[[All,1]] = 1;
];
s = (recs[[All,1]] / Max[recs[[All,1]]] ) . clMat[[ recs[[All,2]], All ]];
s = AssociationThread[ ItemRecommender[d]["ColumnInterpretation"][[ Span @@ ItemRecommender[d]["tagTypeRanges"][tagType] ]] -> s ];
Reverse[Sort[s]]
];
(*=========================================================*)
(* ItemRecommenderClassify *)
(*=========================================================*)
Clear[ItemRecommenderClassify]
Options[ItemRecommenderClassify] = {"tagType"->Automatic, "nTopNNs"->20, "voting"->False, "dropZeroScoredLabels"->True, "Normalize"->True};
ItemRecommenderClassify[smr_, record_, opts : OptionsPattern[]] :=
ItemRecommenderClassify[smr, record, "Decision", opts] /; FreeQ[{opts}, "Score"|"TopScores"|"TopProbabilities"];
ItemRecommenderClassify[smr_, record_, "Decision", opts : OptionsPattern[]] :=
First@Keys@ItemRecommenderClassify[smr, record, "Scores", opts];
ItemRecommenderClassify[smr_, record_, "Score" -> class_, opts : OptionsPattern[]] :=
Lookup[ItemRecommenderClassify[smr, record, "Scores", opts], class, 0];
ItemRecommenderClassify[smr_, record_, "TopScores", opts : OptionsPattern[]] :=
Select[ItemRecommenderClassify[smr, record, "Scores", opts], # > 0 &];
ItemRecommenderClassify[smr_, record_, "TopScores" -> n_Integer, opts : OptionsPattern[]] :=
Take[ItemRecommenderClassify[smr, record, "Scores", opts], UpTo[n]];
ItemRecommenderClassify[smr_ItemRecommender, record_, "Scores", opts:OptionsPattern[] ] :=
Block[{clParams, res},
If[ !AssociationQ[smr["classificationParameters"]],
clParams = <||>,
clParams = smr["classificationParameters"]
];
clParams = Join[ Association[Options[ItemRecommenderClassify]], clParams, Association[{opts}] ];
If[ !MemberQ[smr["tagTypes"], clParams["tagType"] ],
clParams = Join[ clParams, <|"tagType"->Last[smr["tagTypes"]] |> ]
];
res = smr["Classify"][clParams["tagType"], record, clParams["nTopNNs"], clParams["voting"], clParams["dropZeroScoredLabels"] ];
If[ TrueQ[clParams["Normalize"]] && TrueQ[Total[res] > 0],
res / Total[res],
res
]
];
(* Here we take the perspective that the scores top two items returned as SMR recommendations *)
(* can be used to form odds of selecting between the two. *)
Clear[ItemRecommenderScoresToProbabilities]
ItemRecommenderScoresToProbabilities[aScores_Association] :=
Block[{t, p},
t = Sort[aScores];
If[t[[1]] == 0,
ReverseSort@AssociationThread[Keys[t], {0, 1}],
(*ELSE*)
p = t[Keys[t][[1]]]/Total[t];
ReverseSort@AssociationThread[Keys[t], {p, 1 - p}]
]
] /; Length[aScores] == 2;
ItemRecommenderScoresToProbabilities[aScores_Association] :=
AssociationThread[Keys[aScores] -> {1}] /; Length[aScores] == 1;
ItemRecommenderClassify[smr_, record_, "TopProbabilities" -> n_Integer, opts : OptionsPattern[]] :=
Block[{clRes},
clRes = ItemRecommenderClassify[smr, record, "TopScores"->2, opts];
TakeLargest[ItemRecommenderScoresToProbabilities[clRes], UpTo[n]]
] /; 1 <= n <= 2;
(*=========================================================*)
(* RatingPrediction *)
(*=========================================================*)
(* ::Text:: *)
(*Designate the user u viewed show indexes with {Subscript[i, 1],Subscript[i, 2],...,Subscript[i, Subscript[n, u]]} and the items recommended for the user u with {Subscript[j, 1],Subscript[j, 2],...,Subscript[j, k]}. He has the ratings {Subscript[r, u Subscript[i, 1]],...,Subscript[r, u Subscript[i, Subscript[n, u]]]}. We are using the formula:.*)
(* ::DisplayFormula:: *)
(*Subscript[r, u j]=*)
(*\!\(\*UnderscriptBox[\(\[Sum]\), \(i \[Element] {*)
(*\*SubscriptBox[\(i\), \(1\)], ..., *)
(*\*SubscriptBox[\(i\), *)
(*SubscriptBox[\(n\), \(u\)]]}\)]\)Subscript[S, i j]Subscript[r, u i]/*)
(*\!\(\*UnderscriptBox[\(\[Sum]\), \(i \[Element] {*)
(*\*SubscriptBox[\(i\), \(1\)], ..., *)
(*\*SubscriptBox[\(i\), *)
(*SubscriptBox[\(n\), \(u\)]]}\)]\)Subscript[S, i j],j\[Element]{Subscript[j, 1],Subscript[j, 2],...,Subscript[j, k]}.*)
(* ::Text:: *)
(*We can do calculations of this formula with linear algebra operations.*)
(* ::DisplayFormula:: *)
(*A=M({Subscript[j, 1],...,Subscript[j, k]})M({Subscript[i, 1],...,Subscript[i, Subscript[n, u]]})^T*)
(*norms=A.[1,1,...,1]^T,where[1,1,...,1]\[Element]\[DoubleStruckCapitalR]^Subscript[n, u]*)
(*t=A.[Subscript[r, u Subscript[i, 1]],...,Subscript[r, u Subscript[i, Subscript[n, u]]]]^T*)
(*Subscript[r, u]=t/norms*)
ItemRecommender[d___]["RatingPrediction"][inputShowInds:{_Integer...},inputRatings:{_?NumberQ...},recInds:{_Integer...}]:=
Block[{inds,norms,t,smat=ItemRecommender[d]["M"]},
t=smat[[recInds]].Transpose[smat[[inputShowInds]]];
norms=Total/@t;
norms = If[#==0,1,#] & /@ norms;
t=t.inputRatings;
t=t/norms
Transpose[{t,recInds}]
];
(*=========================================================*)
(* Deteriorate old ratings *)
(*=========================================================*)
(* ::Text:: *)
(*Inherit dynamically ItemRecommender*)
ItemRecommender[d___]["UserItemsToLove"][inputShowInds:{_Integer...},inputRatings:{_?NumberQ...},inputTimes:{_?NumberQ...},{minRating_Integer,maxRating_Integer},deteriorationFunction_,nRes_Integer]:=
Block[{newRatings},
newRatings=MapThread[deteriorationFunction[#1,#2]&,{inputRatings,inputTimes}];
ItemRecommender[d]["UserItemsToLove"][inputShowInds,inputRatings,nRes]
]/;Length[inputShowInds]==Length[inputRatings]==Length[inputTimes];
ItemRecommender[d___]["RatingPrediction"][inputShowInds:{_Integer...},inputRatings:{_?NumberQ...},inputTimes:{_?NumberQ...},recInds:{_Integer...},deteriorationFunction_]:=
Block[{newRatings,res},
newRatings=MapThread[deteriorationFunction[#1,#2]&,{inputRatings,inputTimes}];
ItemRecommender[d]["RatingPrediction"][inputShowInds,inputRatings,recInds];
]/;Length[inputShowInds]==Length[inputRatings]==Length[inputTimes];
(*=========================================================*)
(* Utilities *)
(*=========================================================*)
(* ::Subsection:: *)
(*RowTags from the matrix*)
Clear[RowTags];
RowTags[obj_ItemRecommender,rowInd_Integer]:=
Block[{arules},
arules=Most[ArrayRules[obj["M"][[rowInd]]]];
SortBy[Transpose[{obj["ColumnInterpretation"][[Flatten[arules[[All,1]]]]],arules[[All,2]]}],-#[[2]]&]
];
RowTags[smat_SparseArray,columnNames_,rowInd_Integer]:=
Block[{arules},
arules=Most[ArrayRules[smat[[rowInd]]]];
SortBy[Transpose[{columnNames[[Flatten[arules[[All,1]]]]],arules[[All,2]]}],-#[[2]]&]
];
Clear[DeleteSpatialTags];
DeleteSpatialTags[res:{{_,_?NumberQ}...}]:=
Block[{},
(*DeleteCases[res,{s_,n_}/;StringMatchQ[s,"{"~~NumberString~~__~~NumberString~~"}"]]*)
DeleteCases[res,{s_List,n_?NumberQ}]
];
(* ::Subsection:: *)
(*GetProperties*)
Clear[GetProperties]
GetProperties[obj_ItemRecommender,itemInd_Integer]:=
GetProperties[obj,obj["M"],itemInd];
GetProperties[obj_ItemRecommender,M:(_SparseArray|{_SparseArray..}),itemInd_Integer]:=
GetProperties[obj["ColumnInterpretation"],M,itemInd];
GetProperties[properties_List,M:(_SparseArray|{_SparseArray..}),itemInd_Integer]:=
Block[{t},
t=Most[ArrayRules[M[[itemInd]]]];
Transpose[{properties[[Flatten@t[[All,1]]]],t[[All,2]]}]
];
(* ::Subsection:: *)
(*GetItems*)
Clear[GetItems,GetItemIndexes]
GetItemIndexes[obj_ItemRecommender,tag:(_String|{_?NumberQ,_?NumberQ})]:=
Block[{pos},
pos=Flatten@Position[obj["ColumnInterpretation"],tag];
If[pos=={},
{},
GetItems[Transpose[obj["M01"]],None,pos[[1]]]
]
];
GetItems[mat_,tagInd_]:=GetItems[mat,None,tagInd]
GetItems[obj_ItemRecommender,tag_String]:=
Block[{pos},
pos=Flatten@Position[obj["ColumnInterpretation"],tag];
If[pos=={},
{},
GetItems[Transpose[obj["M01"]],obj["itemNames"],pos[[1]]]
]
];
GetItems[mat_SparseArray,names:(_List|None),itemInd_Integer]:=
Block[{t},
t=Most[ArrayRules[mat[[itemInd]]]];
If[names===None,
Transpose[{Flatten@t[[All,1]],t[[All,2]]}],
Transpose[{names[[Flatten@t[[All,1]]]],t[[All,2]]}]
]
];
Clear[ItemsForTag]
ItemsForTag[IIR_ItemRecommender,tag:(_String|{_?NumberQ,_?NumberQ})]:=
Block[{res},
res=GetItemIndexes[IIR,tag];
Map[{#[[1]],IIR["itemNames"][[#[[1]]]],IIR["itemCoordinates"][[#[[1]]]],#[[2]]}&,res]
];
Clear[ItemsForTags]
ItemsForTags[IIR_ItemRecommender,tags_List]:=
Intersection@@Map[ItemsForTag[IIR,#]&,tags];
(* ::Subsection:: *)
(*FilterResults*)
Clear[FilterResults];
FilterResults[IIR_ItemRecommender,res_,filterTags_]:=
Block[{fvec},
fvec=IIR["MakeProfileVector"][filterTags];
Pick[res,Map[#>0&,IIR["M01"][[res[[All,2]]]].fvec]]
];
(* ::Subsection:: *)
(*FilterResultsWithDistanceInterval*)
Clear[FilterResultsWithDistanceInterval];
FilterResultsWithDistanceInterval::ircoords="The recommender object `1` does not have (correct) item coordinates.";
FilterResultsWithDistanceInterval[IIR_ItemRecommender,res_,geopoint:{_?NumberQ,_?NumberQ},{minDistance_?NumberQ,maxDistance:(Infinity|_?NumberQ)},spaceStep_:1609.]:=
Block[{dists},
If[Length[IIR["itemCoordinates"]]!=Dimensions[IIR["M01"]][[1]],
Message[FilterResultsWithDistanceInterval::ircoords,IIR];
Return[res];
];
dists=Map[EarthSphereDistance[geopoint,#]/N[spaceStep]&,IIR["itemCoordinates"][[res[[All,2]]]]];
Pick[res,Map[minDistance<=#<=maxDistance&,dists]]
];
(* ::Subsection:: *)
(*TableReport*)
Clear[RowMatrixForIIR]
RowMatrixForIIR[IIR_ItemRecommender]:=RowMatrixForIIR[IIR]=(#&/@IIR["M"]);
Clear[TableReport];
Options[TableReport]={"SortColumn"->1,"SortDirection"->"desc"};
TableReport[IIR_ItemRecommender,geopoint_,res_,spaceStep_,opts:OptionsPattern[]]:=
Block[{dists,data,sc=OptionValue[TableReport,"SortColumn"],sd=ToLowerCase[OptionValue[TableReport,"SortDirection"]]},
sd=If[sd=="asc"||sd=="ascending"||sd=="incr"||sd=="increasing",sd=1,sd=-1];
dists=Map[Floor[100*EarthSphereDistance[geopoint,#]/N[spaceStep]]/100.&,IIR["itemCoordinates"][[res[[All,2]]]]];
data=SortBy[Flatten[#,1]&/@Transpose[{res[[All,1]],dists,IIR["itemNames"][[res[[All,2]]]]/.{s_String:>If[StringLength[s]>35,StringTake[s,35],s]},Function[{ind},SortBy[Select[DeleteSpatialTags[GetProperties[IIR["ColumnInterpretation"],RowMatrixForIIR[IIR],ind]],(StringMatchQ[#[[1]],__~~":"~~__]&)],-#[[2]]&]]/@res[[All,2]]}],sd*#[[sc]]&];
TableForm[data,TableDepth->2,TableHeadings->{Automatic,Style[#,Blue,FontFamily->"Times"]&/@{"score","distance","name","tags"}}]
];