/// <summary>
/// Returns the last in last appearance of the prefix ei event in sequence.
/// </summary>
/// <param name="ei">I-th event of the prefix.</param>
/// <param name="last">Last in last appearance of ei+1 event.</param>
/// <returns></returns>
public static int GetLastInLast(this PseudoSequence me, uint[] ei, int last)
{
var items = me.RawItems;
int i = (last == 0 ? items.Length : last) - 1;
for (; i >= 0; i--)
{
if (ei.IsSubsetOf(items[i]))
{
return(i);
}
}
return(0);
}
/// <summary>
/// Returns the last in first appearance of a given ei event.
/// </summary>
/// <param name="i">Index of ei event in prefix.</param>
/// <param name="ei">I-th event of the prefix.</param>
/// <param name="last">Last in first appearance of ei+1 event.</param>
public static int GetLastInFirst(this PseudoSequence me, int i, uint[] ei, int last)
{
if (last == 0)
{
return(me._firstInstances.Last());
}
var items = me.RawItems;
for (int j = last - 1; j >= 0; j--)
{
if (ei.IsSubsetOf(items[j]))
{
return(j);
}
}
return(0);
}
protected void addSequenceToProjection(Sequence sequence)
{
// keeps record of encountered items in the sequence
// to adding sequence more than once
HashSet<Item> seen = new HashSet<Item>(Item.EqComp);
for (int i = 0; i < sequence.NumTransactions; i++)
{
for(int k = 0; k < sequence[i].NumItems; k++)
{
Item item = sequence[i][k];
// already processed
if (seen.Contains(item))
continue;
else
seen.Add(item);
var pSeq = new PseudoSequence();
pSeq.Init(_nextPseudoSequenceIndex, i, k);
// point to the next item
// in the sequence
pSeq.PointToNextItem(sequence);
// add pseudo sequence to the list of projections
// for the current item
List<PseudoSequence> itemProjection;
if (!_projections.TryGetValue(item, out itemProjection))
{
itemProjection = new List<PseudoSequence>();
_projections.Add(item, itemProjection);
}
if (pSeq.IsValid)
itemProjection.Add(pSeq);
}
}
_nextPseudoSequenceIndex++;
}
private ProjectedDatabase ConstructProjectedDatabase(Sequence prefix, ProjectedDatabase database)
{
var prefixLastItem = prefix.LastItem;
var projectedDatabase = new ProjectedDatabase(prefix);
// The count of sequences in a database which dont have to contains prefix
// and projected database can still contains some sequential pattern.
var minSequencesInProjectedDb = database.Size - (int)_minSupport;
for (int sid = 0, lastSid = database.Size; sid < lastSid; sid++)
{
// If sequence contains the last item of a prefix, project sequence and add it to db.
int itemsetIndex;
if ((itemsetIndex = database[sid].Contains(prefixLastItem)) >= 0)
{
var pseudoSequence = PseudoSequence.MakeProjection(database[sid], prefix, itemsetIndex, false);
if (pseudoSequence != null)
{
projectedDatabase.Add(pseudoSequence);
continue;
}
}
// If projected database can not contains new sequential pattern stop projection sooner.
if (--minSequencesInProjectedDb >= 0)
{
continue;
}
return(null);
}
return(projectedDatabase);
}
/// <summary>
/// Checks if a given database contains backward-I-extension event.
/// </summary>
private static bool BackwardIExtensionCheck(ProjectedDatabase projectedDatabase)
{
var lastInLastAppearances = new int[projectedDatabase.Count];
var seqBackwardIExtensionItemset = new HashSet <uint>();
for (int i = projectedDatabase.Prefix.Size - 1; i >= 0; i--)
{
var ei = projectedDatabase.Prefix[i];
var ithBackwardIExtensionItemset = default(HashSet <uint>);
var isIthBackwardIExtensionItemsetEmpty = false;
for (int sid = 0; sid < projectedDatabase.Count; sid++)
{
PseudoSequence sequence = projectedDatabase[sid];
// The i-th I-extensions period of a prefix sequence is defined:
// 1) 1 < i <= n: it is the piece of sequence between the end
// of the first instance of prefix e1e2..ei-1
// and the beginning of the first event after the LLi.
// 2) i == 1: it is the piece of sequence located before the first event after LL1.
int lastInLast = sequence.GetLastInLast(ei, lastInLastAppearances[sid]);
lastInLastAppearances[sid] = lastInLast;
// If ith maximum period is empty just continue fill in lastInLastAppearances for the checking (i-1)-th maximum period.
if (isIthBackwardIExtensionItemsetEmpty)
{
continue;
}
int firstInstance = 0;
if (i != 0)
{
firstInstance = sequence.GetFirstInstance(i) + 1;
}
seqBackwardIExtensionItemset.Clear();
for (; firstInstance <= lastInLast; firstInstance++)
{
if (ei.IsSubsetOf(sequence.RawItems[firstInstance]))
{
seqBackwardIExtensionItemset.UnionWith(sequence.RawItems[firstInstance]);
}
}
seqBackwardIExtensionItemset.ExceptWith(ei);
// ScanSkip:
if (ithBackwardIExtensionItemset == null)
{
ithBackwardIExtensionItemset = new HashSet <uint>(seqBackwardIExtensionItemset);
}
else
{
ithBackwardIExtensionItemset.IntersectWith(seqBackwardIExtensionItemset);
}
// If ith maximum period is empty and i==0 there cant exist any backward-I-extension,
// otherwise if i>0, try find backward-I-extension in (i-1)-th maximum period.
if (ithBackwardIExtensionItemset.Count != 0)
{
continue;
}
if (i == 0)
{
return(false);
}
isIthBackwardIExtensionItemsetEmpty = true;
}
// If all ith maximum periods (in every sequence) contains some items we got a backward-I-extension.
if (ithBackwardIExtensionItemset.Count > 0)
{
return(true);
}
}
return(false);
}
private static bool BackScanI(ProjectedDatabase projectedDatabase)
{
var lastInFirstAppearances = new int[projectedDatabase.Count];
var seqSemiMaximumPeriod = new HashSet <uint>();
var n = projectedDatabase.Prefix.Size - 1;
for (int i = n; i >= 0; i--)
{
var ei = projectedDatabase.Prefix[i];
var eiLastItemId = ei.Last();
var ithSemiMaximumPeriod = default(HashSet <uint>);
var isIthSemiMaximumPeriodEmpty = false;
for (int sid = 0; sid < projectedDatabase.Count; sid++)
{
PseudoSequence sequence = projectedDatabase[sid];
int lastInFirst = sequence.GetLastInFirst(i, ei, lastInFirstAppearances[sid]);
lastInFirstAppearances[sid] = lastInFirst;
// If i-th semimaximum period is empty just continue fill in lastInFirstAppearances for the checking (i-1)-th semimaximum period.
if (isIthSemiMaximumPeriodEmpty)
{
continue;
}
int firstInstance = 0;
if (i != 0)
{
firstInstance = sequence.GetFirstInstance(i) + 1;
}
seqSemiMaximumPeriod.Clear();
for (; firstInstance <= lastInFirst; firstInstance++)
{
if (!ei.IsSubsetOf(sequence.RawItems[firstInstance]))
{
continue;
}
seqSemiMaximumPeriod.UnionWith(
i == n
? sequence.RawItems[firstInstance].Where(a => a < eiLastItemId)
: sequence.RawItems[firstInstance]);
}
seqSemiMaximumPeriod.ExceptWith(ei);
// ScanSkip:
if (ithSemiMaximumPeriod == null)
{
ithSemiMaximumPeriod = new HashSet <uint>(seqSemiMaximumPeriod);
}
else
{
ithSemiMaximumPeriod.IntersectWith(seqSemiMaximumPeriod);
}
// If i-th maximum period is empty and i==0 there cant exist any backward-S-extensions,
// otherwise if i>0, try find backward-S-extensions in (i-1)-th maximum period.
if (ithSemiMaximumPeriod.Count != 0)
{
continue;
}
if (i == 0)
{
return(false);
}
isIthSemiMaximumPeriodEmpty = true;
}
// If all i-th maximum periods (in every sequence) contains any items, we got a backward-S-extension.
if (ithSemiMaximumPeriod.Count != 0)
{
return(true);
}
}
return(false);
}
/// <summary>
/// Checks if a given database contains backward-S-extension event.
/// </summary>
private static bool BackwardSExtensionCheck(ProjectedDatabase projectedDatabase)
{
var lastInLastAppearances = new int[projectedDatabase.Count];
var seqMaximumPeriod = new HashSet <uint>();
for (int i = projectedDatabase.Prefix.Size - 1; i >= 0; i--)
{
var ei = projectedDatabase.Prefix[i];
var ithMaximumPeriod = default(HashSet <uint>);
var isIthMaximumPeriodEmpty = false;
for (int sid = 0; sid < projectedDatabase.Count; sid++)
{
PseudoSequence sequence = projectedDatabase[sid];
// The i-th maximum period of a prefix sequence is defined:
// 1) 1 < i <= n: it is the piece of sequence between the end
// of the first instance of prefix e1e2...ei-1 and LLi.
// 2) i == 1: it is the piece of sequence located before the first last-in-last appearance (LL1).
int lastInLast = sequence.GetLastInLast(ei, lastInLastAppearances[sid]);
lastInLastAppearances[sid] = lastInLast;
// If i-th maximum period is empty just continue fill in lastInLastAppearances for the checking (i-1)-th maximum period.
if (isIthMaximumPeriodEmpty)
{
continue;
}
int firstInstance = 0;
if (i != 0)
{
firstInstance = sequence.GetFirstInstance(i) + 1;
}
seqMaximumPeriod.Clear();
for (; firstInstance < lastInLast; firstInstance++)
{
seqMaximumPeriod.UnionWith(sequence.RawItems[firstInstance]);
}
// ScanSkip:
if (ithMaximumPeriod == null)
{
ithMaximumPeriod = new HashSet <uint>(seqMaximumPeriod);
}
else
{
ithMaximumPeriod.IntersectWith(seqMaximumPeriod);
}
// If i-th maximum period is empty and i==0 there cant exist any backward-S-extensions,
// otherwise if i>0, try find backward-S-extensions in (i-1)-th maximum period.
if (ithMaximumPeriod.Count != 0)
{
continue;
}
if (i == 0)
{
return(false);
}
isIthMaximumPeriodEmpty = true;
}
// If all i-th maximum periods (in every sequence) contains any items, we got a backward-S-extension.
if (ithMaximumPeriod.Count != 0)
{
return(true);
}
}
return(false);
}
public bool IsPrefixOf(Dictionary <Item, int> fDict, Sequence seq, PseudoSequence pSeq, out PseudoSequence suffix)
{
suffix = new PseudoSequence();
if (seq.IsEmpty)
{
return(false);
}
if (seq.NumTransactions - pSeq.TransactionIndex < 0)
{
return(false);
}
// current transaction index in prefix
var prefixTransactionIndex = 0;
// current item index in current prefix transaction
var prefixItemIndex = 0;
// current transaction index in suffix
var suffixTransactionIndex = pSeq.TransactionIndex;
// current item index in current suffix transaction
var suffixItemIndex = pSeq.ItemIndex;
// whether or not only last item needs to be matched to form a prefix
// e.g. prefix=<(abc)> suffix=<(_c)> only item c needs to be checked
// to validate new prefix
if (pSeq.ItemIndex != 0 || this.LastTransaction.NumItems == 1)
{
// only check last item since prefix already established
// from previous rounds
prefixTransactionIndex = this.NumTransactions - 1;
prefixItemIndex = this[prefixTransactionIndex].NumItems - 1;
if (pSeq.ItemIndex != 0 && this.LastTransaction.NumItems == 1)
{
suffixTransactionIndex++;
suffixItemIndex = 0;
}
}
for (int i = suffixTransactionIndex; i < seq.NumTransactions; i++)
{
int k = (i == suffixTransactionIndex) ? suffixItemIndex : 0;
for (; k < seq[i].NumItems; k++)
{
// if the current prefix item does not equal suffix item at [i, k]
if (!this[prefixTransactionIndex][prefixItemIndex].Equals(seq[i][k]))
{
// to form a prefix, all items in the last transaction of the prefix
// must be alphabetically AFTER all previous items in the transaction.
// The sorting step takes care of that, however, need to check for cases
// where two items have the same support making their ordering arbitrary
int support;
if (pSeq.ItemIndex == 0 || (fDict.TryGetValue(seq[i][k], out support) && support == fDict[this[prefixTransactionIndex][prefixItemIndex]]))
{
// items have same support, continue
continue;
}
// prefix not found in this transaction
break;
}
// items matched, continue to next item in prefix (if any)
prefixItemIndex++;
// no more items in current prefix transaction
// continue to next transaction (if any)
if (prefixItemIndex >= this[prefixTransactionIndex].NumItems)
{
// move to next transaction in prefix
prefixTransactionIndex++;
prefixItemIndex = 0;
// no more transactions, DONE!
if (prefixTransactionIndex >= this.NumTransactions)
{
// add the suffix pseudo sequence
suffix.Init(pSeq.SequenceIndex, i, k);
suffix.PointToNextItem(seq);
return(suffix.IsValid);
}
}
}
// reset the prefix transaction in the case that
// the transaction contains more than 1 item
// making a full transaction match necessary
if (this[prefixTransactionIndex].NumItems != 1)
{
prefixTransactionIndex = 0;
prefixItemIndex = 0;
}
}
return(false);
}
/// <summary>
/// Returns the first instance of the prefix (i-1)-th event in sequence.
/// </summary>
/// <param name="me">PseudoSequence.</param>
/// <param name="i">Index of i-th event in the prefix.</param>
public static int GetFirstInstance(this PseudoSequence me, int i)
{
return(me._firstInstances[i]);
}
