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Temporal DB

by

Zbigniew W. Ras

04/19/23 2

1. Valid time – the time in which information is true .2. Transaction time – time associated with transaction that inserted this record.

- [ts, te] is associated with each record in DB [start time, end time] – time range. - continuous view of temporal data /printouts of heartbeats/- timestamps – equal intervals (time series data).

Types of Queries Vd = [tsd, ted] - valid time for tuple d. Intersection query q: tuple d is retrieved if Vd Vq Inclusion query q: tuple d is retrieved if tsq ≤ tsd ≤ ted ≤ teq

Containment query: tuple d is retrieved if tsd ≤ tsq ≤ teq ≤ ted

Point query : tuple d is retrieved if tsd = tsq = teq = ted

(tuple has to be valid at a particular point in time)

Temporal DB

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Temporal DB

• Four types of DB:

• Snapshot – no support for temporal attribute

• Transaction time only given

• Valid time only given

• Bitemporal (both transaction and valid time given)

• now – current time value.

• Modeling Temporal Events: 

• Markov Model (MM) – directed graph [V,A], V={v1, v2,…, vn} – states,

• A = {<i,j>: vi, vj V }- arcs (show transitions between states).

• Each arc is labeled with probability pij of transitioning from vi to vj .

• At time t, one state is designated as current state vt , and probability of any future transitions depends only on vt . Transition probabilities are learned in training phase.

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Temporal DB

 Time series for attribute A: {<t1, a1>, <t2, a2>,…, <tn, an>}. If points in time are well defined, we take < a1, a2,…, an> vector. If <y1, y2,…, yn> - time series, then its subsequence is called time subseries.Problems: Similarities between different time series. Predicting future value of an attribute.

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Temporal DB

Trend Analysis.

Smoothing – finding moving averages of attribute values (local average in a window is computed).Correlation between two attributes with time series X, Y and means X, Y (Pearson’s coefficient)

R = [ (xi - X )(yi - Y )]/sqr[(xi - X )2 (yi - Y ) 2].Value of R close to 1 – attributes strongly correlated.Value of R close to 0 – attributes not correlated at all. Pattern Detection (time series): KMP, Boyer-Moore algorithms. Sequences – ordered list of itemsets {s1, s2 ,…, sn}, where si I. (set of items).Subsequence T = {ti1 ,…, tim} of S if ( j)( k)[( tij ≤ sk) & ij ≤ ij+1)].

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Temporal DB

Customer-sequence: sequence of itemsets purchased by customer.

Example:S = {{A},{C}} – sequence.

Support of sequence S – percentage of total customers whose customer-sequence contains S. s(S)= 1/3. Confidence of S T : ratio of the number of customer-sequences that contain both S and T to the number that contain S.

Customer Time Itemset

C1 10 AB

C1 20 BC

C1 30 D

C2 15 ABC

C2 20 D

C3 15 ACD

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Temporal DB

SPADE Algorithm.A,B,C,D – attributes.{A}{B}{C}

SPADE Algorithm.A,B,C,D – attributes.

{A} {C}

{B} {D}

Customer TimeC1 10

C2 15

C3 15

Customer TimeC1 10

C1 20

C2 15

Customer Time

C1 20

C2 15

C3 15

Customer Time

C1 30

C2 20

C3 15

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Temporal DB

Candidates (2-sequences):

{AB} {AD}

({A}, {B}) ({A},{D})

Customer TimeC1 10C2 15

Customer TimeC1 10, 20

Customer TimeC3 15

Customer TimeC1 10, 30C2 15, 20

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Temporal DB

{AC} ({B},{C})

({A},{C})

{BC}

Customer TimeC2 15C3 15

Customer Time

C1 10, 20

Customer TimeC1 20C2 15

Customer TimeC1 10, 20

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Temporal DB

• Example explaining the next step:

• ({B}, {BC}, {DE}), ({AB}, {BC}, {D}) – have the overlap ({B}, {BC}, {D}) and because of this, two candidate sequences are generated:

• ({AB}, {BC}, {DE}), ({AB}, {BC}, {D}, {E}).

 

• In our example, from {AB}, ({B}, {C}) we generate:

({AB},{C})

From ({A}, {B}), {BC} we generate:

({A},{BC})

Customer TimeC1 10, 20

Customer TimeC1 10, 20