641 lines
19 KiB
C++
641 lines
19 KiB
C++
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/*
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----
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This file is part of SECONDO.
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Copyright (C) 2020,
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Faculty of Mathematics and Computer Science,
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Database Systems for New Applications.
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SECONDO is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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SECONDO is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with SECONDO; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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----
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//[$][\$]
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//[_][\_]
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*/
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#include "tsdtwop.h"
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using std::string;
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using std::min;
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using std::cout;
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using std::to_string;
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using std::numeric_limits;
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TsDTWOp::TsDTWOp()
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{
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}
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// Type mapping for the timeseries algebra operators for
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// dynamic time warping(DTW)
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ListExpr TsDTWOp::tsDTWTypeMap(ListExpr args)
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{
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string error = "Type Mapping error for Operator tsdtw ";
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if(!nl->HasLength(args,2)){return listutils::typeError(error +
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" ( tworarguments exspected.)");}
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ListExpr timeseries_a = nl->First(args);
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ListExpr timeseries_b = nl->Second(args);
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if(!OrderedRelation::checkType(timeseries_a)
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|| !OrderedRelation::checkType((timeseries_b))){
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return listutils::typeError(error +
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" (first and second argument should be a ordered relation"
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" representing a timeseries.");
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}
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if(!listutils::isTupleDescription(nl->Second(timeseries_a))
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|| !listutils::isTupleDescription(nl->Second(timeseries_b))){
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return listutils::typeError((error +
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" (Tuple description should be valid!)"));
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}
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ListExpr typeinfo_a = nl->Second(nl->Second(timeseries_a));
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ListExpr typeinfo_b = nl->Second(nl->Second(timeseries_b));
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ListExpr result_a = checkAttributes( typeinfo_a );
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ListExpr result_b = checkAttributes( typeinfo_b );
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if (!nl->IsEmpty(result_a))
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{
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return result_a;
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}
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else if ( !nl->IsEmpty(result_b))
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{
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return result_b;
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}
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return timeseries_a;
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}
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//Value mapping for the derived dynamic time warping function.
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//Returns an warped first argument to match the second argument.
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int TsDTWOp::tsDDTWValueMap(Word *args, Word &result, int message,
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Word &local, Supplier s)
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{
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OrderedRelation* ts1 = (OrderedRelation*) args[0].addr;
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OrderedRelation* ts2 = (OrderedRelation*) args[1].addr;
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vector<double> ts1_data;
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vector<Tuple*> ts1_tuples;
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vector<double> ts2_data;
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GenericRelationIterator* ts1_iter = ts1->MakeScan();
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GenericRelationIterator* ts2_iter = ts2->MakeScan();
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int ts1_size = ts1->GetNoTuples();
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int ts2_size = ts2->GetNoTuples();
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Tuple* current = 0;
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while((current = ts1_iter->GetNextTuple()) != 0)
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{
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ts1_data.push_back(((CcReal*)current->GetAttribute(1))->GetRealval());
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ts1_tuples.push_back(current);
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}
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while((current = ts2_iter->GetNextTuple()) != 0)
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{
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ts2_data.push_back(((CcReal*)current->GetAttribute(1))->GetRealval());
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}
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vector<vector<double>> cost_matrix(ts1_size, vector<double>
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(ts2_size,numeric_limits<double>::infinity()));
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cost_matrix.at(0).at(0) = 0.0;
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cost_matrix[ts1_size-1][ts2_size-1] = 0.0;
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for ( int ts1_index = 1; ts1_index < ts1_size -1; ts1_index++)
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{
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for ( int ts2_index = 1; ts2_index < ts2_size -1; ts2_index++)
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{
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double cost = derivativeDistance(computeDerivative(
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ts1_data[ts1_index -1],
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ts1_data[ts1_index],
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ts1_data[ts1_index +1]),
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computeDerivative(ts2_data[ts2_index -1],
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ts2_data[ts2_index],
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ts2_data[ts2_index +1]));
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cost_matrix.at(ts1_index).at(ts2_index) = cost + min({
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cost_matrix.at(ts1_index-1).at(ts2_index),
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cost_matrix.at(ts1_index).at(ts2_index-1),
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cost_matrix.at(ts1_index-1).at(ts2_index-1)
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});
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}
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}
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vector<WarpingPathPoint> warping_path;
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optimalWarpingPath(cost_matrix, warping_path );
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double distance = 0;
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for(size_t i = 0; i < warping_path.size(); ++i)
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{
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WarpingPathPoint point = warping_path[i];
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distance += derivativeDistance(ts1_data[point._x], ts2_data[point._y]);
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}
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cout << "Distance: " << to_string(distance) << endl;
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result = qp->ResultStorage(s);
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OrderedRelation* warpedTS = (OrderedRelation*) result.addr;
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int no_warping_points = warping_path.size();
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for(int i = 0; i < no_warping_points; ++i)
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{
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Tuple* ts1_tuple = ts1_tuples[warping_path[i]._x]->Clone();
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int count_repeats = 1;
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while(count_repeats + 1 < no_warping_points && warping_path[i]._y
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== warping_path[i+count_repeats]._y)
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{
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count_repeats++;
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}
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if(count_repeats > 1)
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{
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i = i + count_repeats -1;
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}
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warpedTS->AppendTuple(ts1_tuple);
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}
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return 0;
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}
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//Implementation of the classic dynamic time warping algorithm
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//without optimization or limitations.
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int TsDTWOp::tsDTWValueMap(Word *args, Word &result, int message,
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Word &local, Supplier s)
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{
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OrderedRelation* ts1 = (OrderedRelation*) args[0].addr;
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OrderedRelation* ts2 = (OrderedRelation*) args[1].addr;
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vector<Tuple*> ts1_data;
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vector<Tuple*> ts2_data;
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int ts1_size = ts1->GetNoTuples();
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int ts2_size = ts2->GetNoTuples();
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vector<vector<double>> cost_matrix;
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GenericRelationIterator* ts1_iter = ts1->MakeScan();
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GenericRelationIterator* ts2_iter = ts2->MakeScan();
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while(!ts1_iter->EndOfScan())
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{
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ts1_data.push_back(ts1_iter->GetNextTuple());
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}
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while(!ts2_iter->EndOfScan())
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{
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ts2_data.push_back(ts2_iter->GetNextTuple());
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}
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for(int index_outer_loop = 0;
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index_outer_loop < ts1_size;
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index_outer_loop++)
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{
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vector<double> inner_vector;
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for(int index_inner_loop = 0;
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index_inner_loop < ts2_size;
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index_inner_loop++)
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{
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inner_vector.push_back(numeric_limits<double>::infinity());
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}
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cost_matrix.push_back(inner_vector);
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}
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cost_matrix.at(0).at(0) = 0.0;
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for ( int ts1_index = 1; ts1_index < ts1_size; ts1_index++)
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{
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for ( int ts2_index = 1; ts2_index < ts2_size; ts2_index++)
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{
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double cost = euklidianDistance(ts1_data.at(ts1_index),
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ts2_data.at(ts2_index));
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cost_matrix.at(ts1_index).at(ts2_index) = cost + min({
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cost_matrix.at(ts1_index-1).at(ts2_index),
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cost_matrix.at(ts1_index).at(ts2_index-1),
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cost_matrix.at(ts1_index-1).at(ts2_index-1)
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});
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}
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}
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vector<WarpingPathPoint> warping_path;
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optimalWarpingPath(cost_matrix, warping_path );
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result = qp->ResultStorage(s);
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OrderedRelation* warpedTS = (OrderedRelation*) result.addr;
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int no_warping_points = warping_path.size();
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for(int i = 0; i < no_warping_points; ++i)
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{
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Tuple* ts1_tuple = ts1_data.at(warping_path[i]._x)->Clone();
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int count_repeats = 1;
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while(count_repeats + 1 < no_warping_points && warping_path[i]._y
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== warping_path[i+count_repeats]._y)
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{
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count_repeats++;
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}
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if(count_repeats > 1)
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{
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i = i + count_repeats -1;
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}
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warpedTS->AppendTuple(ts1_tuple);
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}
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double distance = 0;
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for(size_t i = 0; i < warping_path.size(); ++i)
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{
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WarpingPathPoint point = warping_path[i];
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distance += euklidianDistance(ts1_data[point._x],ts2_data[point._y]);
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}
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cout << "Distance: " << to_string(distance) << endl;
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return 0;
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}
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//Typemapping function for the dynamic time warping utilizing
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//the Sakoe Chiba band.
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ListExpr TsDTWOp::tsDTWSCTypeMap(ListExpr args)
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{
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string error = "";
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if(!nl->HasLength(args,3)){
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return listutils::typeError(error + " ( three arguments exspected.)");
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}
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ListExpr timeseries_a = nl->First(args);
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ListExpr timeseries_b = nl->Second(args);
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if(!OrderedRelation::checkType(timeseries_a)
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|| !OrderedRelation::checkType((timeseries_b))){
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return listutils::typeError(error +
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" (first and second argument should be a ordered"
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" relation representing a timeseries.");
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}
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if(!listutils::isTupleDescription(nl->Second(timeseries_a))
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|| !listutils::isTupleDescription(nl->Second(timeseries_b))){
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return listutils::typeError((error +
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" (Tuple description should be valid!)"));
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}
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ListExpr typeinfo_a = nl->Second(nl->Second(timeseries_a));
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ListExpr typeinfo_b = nl->Second(nl->Second(timeseries_b));
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ListExpr result_a = checkAttributes( typeinfo_a );
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ListExpr result_b = checkAttributes( typeinfo_b );
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ListExpr band_size = nl->Third(args);
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if(!CcInt::checkType(band_size))
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return listutils::typeError(error +
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"(third argument must be a positive integer for the limit"
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" of the sakoe chiba band.)");
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if (!nl->IsEmpty(result_a))
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{
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return result_a;
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}
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else if ( !nl->IsEmpty(result_b))
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{
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return result_b;
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}
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return timeseries_a;
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}
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// Value mapping for the dynamic time warping Sakoe Chiba function.
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// Returns an warped first argument to match the second argument.
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int TsDTWOp::tsDTWSCValueMap(Word *args, Word &result, int message,
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Word &local, Supplier s)
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{
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OrderedRelation* ts1 = (OrderedRelation*) args[0].addr;
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OrderedRelation* ts2 = (OrderedRelation*) args[1].addr;
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int band_size = ((CcInt*) args[2].addr)->GetIntval();
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vector<Tuple*> ts1_data;
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vector<Tuple*> ts2_data;
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int ts1_size = ts1->GetNoTuples();
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int ts2_size = ts2->GetNoTuples();
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vector<vector<double>> cost_matrix;
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GenericRelationIterator* ts1_iter = ts1->MakeScan();
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GenericRelationIterator* ts2_iter = ts2->MakeScan();
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while(!ts1_iter->EndOfScan())
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{
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ts1_data.push_back(ts1_iter->GetNextTuple());
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}
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while(!ts2_iter->EndOfScan())
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{
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ts2_data.push_back(ts2_iter->GetNextTuple());
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}
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for(int index_outer_loop = 0;
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index_outer_loop < ts1_size;
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index_outer_loop++)
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{
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vector<double> inner_vector;
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for(int index_inner_loop = 0;
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index_inner_loop < ts2_size;
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index_inner_loop++)
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{
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inner_vector.push_back(numeric_limits<double>::infinity());
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|
}
|
||
|
|
cost_matrix.push_back(inner_vector);
|
||
|
|
}
|
||
|
|
|
||
|
|
cost_matrix.at(0).at(0) = 0.0;
|
||
|
|
|
||
|
|
for ( int ts1_index = 1; ts1_index < ts1_size; ts1_index++)
|
||
|
|
{
|
||
|
|
for ( int ts2_index = 1; ts2_index < ts2_size; ts2_index++)
|
||
|
|
{
|
||
|
|
double cost = euklidianDistance(ts1_data.at(ts1_index),
|
||
|
|
ts2_data.at(ts2_index));
|
||
|
|
cost_matrix.at(ts1_index).at(ts2_index) = cost + min({
|
||
|
|
cost_matrix.at(ts1_index-1).at(ts2_index),
|
||
|
|
cost_matrix.at(ts1_index).at(ts2_index-1),
|
||
|
|
cost_matrix.at(ts1_index-1).at(ts2_index-1)
|
||
|
|
});
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
vector<WarpingPathPoint> warping_path;
|
||
|
|
|
||
|
|
optimalWarpingPath(cost_matrix, warping_path, band_size );
|
||
|
|
|
||
|
|
|
||
|
|
result = qp->ResultStorage(s);
|
||
|
|
|
||
|
|
OrderedRelation* warpedTS = (OrderedRelation*) result.addr;
|
||
|
|
|
||
|
|
int no_warping_points = warping_path.size();
|
||
|
|
|
||
|
|
for(int i = 0; i < no_warping_points; ++i)
|
||
|
|
{
|
||
|
|
Tuple* ts1_tuple = ts1_data.at(warping_path[i]._x)->Clone();
|
||
|
|
int count_repeats = 1;
|
||
|
|
while(count_repeats + 1 < no_warping_points && warping_path[i]._y ==
|
||
|
|
warping_path[i+count_repeats]._y)
|
||
|
|
{
|
||
|
|
count_repeats++;
|
||
|
|
}
|
||
|
|
if(count_repeats > 1)
|
||
|
|
{
|
||
|
|
i = i + count_repeats -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
warpedTS->AppendTuple(ts1_tuple);
|
||
|
|
}
|
||
|
|
|
||
|
|
double distance = 0;
|
||
|
|
|
||
|
|
for(size_t i = 0; i < warping_path.size(); ++i)
|
||
|
|
{
|
||
|
|
WarpingPathPoint point = warping_path[i];
|
||
|
|
distance += euklidianDistance(ts1_data[point._x],ts2_data[point._y]);
|
||
|
|
}
|
||
|
|
|
||
|
|
cout << "Distance: " << to_string(distance) << endl;
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// @brief TsDTWOp::checkAttributes checks wheter the attributes of an
|
||
|
|
// ordered relation correspond to a timeseries
|
||
|
|
// @param rest attribute info
|
||
|
|
// @return empty nested list or type error
|
||
|
|
ListExpr TsDTWOp::checkAttributes(ListExpr rest)
|
||
|
|
{
|
||
|
|
ListExpr timestamp = nl->First(rest);
|
||
|
|
rest = nl->Rest(rest);
|
||
|
|
|
||
|
|
if(!Instant::checkType(nl->Second(timestamp)))
|
||
|
|
{
|
||
|
|
return listutils::typeError("First argument of tuple"
|
||
|
|
" should be of type INSTANT.");
|
||
|
|
}
|
||
|
|
|
||
|
|
while(!nl->IsEmpty(rest)){
|
||
|
|
ListExpr current = nl->First(rest);
|
||
|
|
rest = nl->Rest(rest);
|
||
|
|
|
||
|
|
if (!(CcReal::checkType(nl->Second(current))
|
||
|
|
|| CcInt::checkType(nl->Second(current))))
|
||
|
|
{
|
||
|
|
return listutils::typeError("All attributes but the first,"
|
||
|
|
" should be numeric to represent a timeseries.");
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
return rest;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
// Count the number of attributes which are a numeric value.
|
||
|
|
int TsDTWOp::countValues(ListExpr tuple_attr)
|
||
|
|
{
|
||
|
|
int attr_count= 0;
|
||
|
|
ListExpr rest = tuple_attr;
|
||
|
|
|
||
|
|
|
||
|
|
while(!nl->IsEmpty(rest)){
|
||
|
|
ListExpr current = nl->First(rest);
|
||
|
|
rest = nl->Rest(rest);
|
||
|
|
|
||
|
|
if (CcReal::checkType(nl->Second(current))
|
||
|
|
|| CcInt::checkType(nl->Second(current)))
|
||
|
|
{
|
||
|
|
attr_count++;
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
return attr_count;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Computes the euklidian distance between the values of
|
||
|
|
// two tuples represented in a time series.
|
||
|
|
double TsDTWOp::euklidianDistance(Tuple *ts1_tuple, Tuple *ts2_tuple)
|
||
|
|
{
|
||
|
|
double distance = 0;
|
||
|
|
|
||
|
|
for(int attr_no = 1; attr_no < ts1_tuple->GetNoAttributes(); attr_no++)
|
||
|
|
{
|
||
|
|
distance += pow(((CcReal*)ts1_tuple->GetAttribute(attr_no))->GetValue()
|
||
|
|
- ((CcReal*)ts2_tuple->GetAttribute(attr_no))->GetValue(),2);
|
||
|
|
}
|
||
|
|
|
||
|
|
return sqrt(distance);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Computes the optimal warping path utilizing a window size in order to
|
||
|
|
// keep the warping in the given limits of the Sakoe Chiba band.
|
||
|
|
void TsDTWOp::optimalWarpingPath(vector<vector<double>>& cost_matrix,
|
||
|
|
vector<WarpingPathPoint> &warpingPath,
|
||
|
|
int window_size)
|
||
|
|
{
|
||
|
|
int rows = cost_matrix.size() -1;
|
||
|
|
int columns = cost_matrix.at(0).size() -1;
|
||
|
|
|
||
|
|
//Add endpoint of path
|
||
|
|
warpingPath.push_back(WarpingPathPoint(rows, columns));
|
||
|
|
|
||
|
|
//compute minimal cost path from endpoint to startpoint.
|
||
|
|
while(rows > 1 && columns > 1)
|
||
|
|
{
|
||
|
|
if(rows == 1)
|
||
|
|
{
|
||
|
|
columns = columns -1;
|
||
|
|
}
|
||
|
|
else if(columns == 1)
|
||
|
|
{
|
||
|
|
rows = rows -1;
|
||
|
|
}
|
||
|
|
if(abs(columns -rows) <= window_size)
|
||
|
|
{
|
||
|
|
//normal dtw
|
||
|
|
if(cost_matrix.at(rows-1).at(columns) == min({
|
||
|
|
cost_matrix.at(rows -1).at(columns),
|
||
|
|
cost_matrix.at(rows).at(columns -1),
|
||
|
|
cost_matrix.at(rows -1).at(columns -1)
|
||
|
|
}))
|
||
|
|
{
|
||
|
|
rows = rows -1;
|
||
|
|
}
|
||
|
|
else if(cost_matrix.at(rows).at(columns -1) == min({
|
||
|
|
cost_matrix.at(rows -1).at(columns),
|
||
|
|
cost_matrix.at(rows).at(columns -1),
|
||
|
|
cost_matrix.at(rows -1).at(columns -1)
|
||
|
|
}))
|
||
|
|
{
|
||
|
|
columns = columns -1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
rows = rows -1;
|
||
|
|
columns = columns -1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else if(columns >= rows - window_size){ columns = columns -1;}
|
||
|
|
else{rows = rows -1;}
|
||
|
|
|
||
|
|
warpingPath.push_back(WarpingPathPoint(rows, columns));
|
||
|
|
}
|
||
|
|
//Add beginn of path to path
|
||
|
|
warpingPath.push_back(WarpingPathPoint(0,0));
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Computes the optimal warping path to minimize the cost of the
|
||
|
|
// warping path in order to receive the
|
||
|
|
// warped representation with minimal distance to the reference time series.
|
||
|
|
void TsDTWOp::optimalWarpingPath(vector<vector<double>>& cost_matrix,
|
||
|
|
vector<WarpingPathPoint> &warpingPath)
|
||
|
|
{
|
||
|
|
size_t rows = cost_matrix.size() -1;
|
||
|
|
size_t columns = cost_matrix.at(0).size() -1;
|
||
|
|
|
||
|
|
//Add endpoint of path
|
||
|
|
warpingPath.push_back(WarpingPathPoint(rows, columns));
|
||
|
|
|
||
|
|
//compute minimal cost path from endpoint to startpoint.
|
||
|
|
while(rows > 1 && columns > 1)
|
||
|
|
{
|
||
|
|
if(rows == 1)
|
||
|
|
{
|
||
|
|
columns = columns -1;
|
||
|
|
}
|
||
|
|
else if(columns == 1)
|
||
|
|
{
|
||
|
|
rows = rows -1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
if(cost_matrix.at(rows-1).at(columns) == min({
|
||
|
|
cost_matrix.at(rows -1).at(columns),
|
||
|
|
cost_matrix.at(rows).at(columns -1),
|
||
|
|
cost_matrix.at(rows -1).at(columns -1)
|
||
|
|
}))
|
||
|
|
{
|
||
|
|
rows = rows -1;
|
||
|
|
}
|
||
|
|
else if(cost_matrix.at(rows).at(columns -1) == min({
|
||
|
|
cost_matrix.at(rows -1).at(columns),
|
||
|
|
cost_matrix.at(rows).at(columns -1),
|
||
|
|
cost_matrix.at(rows -1).at(columns -1)
|
||
|
|
}))
|
||
|
|
{
|
||
|
|
columns = columns -1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
rows = rows -1;
|
||
|
|
columns = columns -1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
warpingPath.push_back(WarpingPathPoint(rows, columns));
|
||
|
|
}
|
||
|
|
//Add beginn of path to path
|
||
|
|
warpingPath.push_back(WarpingPathPoint(0,0));
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Computes the approximation of the derivative using three points.
|
||
|
|
double TsDTWOp::computeDerivative(double qiminus1, double qi, double qiplus1)
|
||
|
|
{
|
||
|
|
return ((qi - qiminus1) + ((qiplus1 - qi - 1)/2)) -2;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Computes the distance as the square of the difference of the estimated
|
||
|
|
// derivative of the timeseriespoints.
|
||
|
|
// Exspects the derivative, as the estimation needs three values each.
|
||
|
|
|
||
|
|
double TsDTWOp::derivativeDistance(double derivative_ts1, double derivative_ts2)
|
||
|
|
{
|
||
|
|
return pow((derivative_ts1 - derivative_ts2),2);
|
||
|
|
}
|
||
|
|
//End Class
|