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CS3402 Normal Forms
Creation date：2024-05-25 15:43:10
Belonging category：计算机computer science
Tag CS3402
Normal Forms

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CS3402 

Normal Forms
Problems caused by redundancy
 Redundant storage
 Potential inconsistency
 Insertion anomaly: E.g., to insert a new tuple for an employee
who works in department number 5, we must enter all the
attribute values of department 5 correctly
CS3402 3
Problems caused by redundancy
 Deletion anomaly: E.g., If we delete an employee tuple that
happens to represent the last employee working for a particular
department, the information concerning that department is lost
inadvertently from the database.
CS3402 4
Problems caused by redundancy
 Update anomaly: E.g., If we change the value of one of the
attributes of a particular department—say, the manager of
department 5—we must update the tuples of all employees who
work in that department; otherwise, the database will become
inconsistent.
CS3402 5
Problems caused by redundancy
 Redundancy must be eliminated in a well guided fashion
 How?
Normalization based on functionality dependency
CS3402 6
Normalization
 Normalization
Proposed by Codd (1972)
 take a relation schema through a series of tests based on
functional dependency and primary keys to certify whether it
satisfies a certain normal form
Decompose a relation into several related relation to achieve:
 Minimizing redundancy
 Minimizing the insertion, deletion and update anomalies
CS3402 7
Relational Database Design
Normalization theory
- based on functional dependencies
* universe of relations
* 1st Normal Form (1NF)
* 2NF
* 3NF
* BCNF
* 4NF
* 5NF
1NF
2NF
3NF
BCNF
4NF
5NF
CS3402 8
Relational Database Design
 Issue: Which attributes should or should not be put in the same
table?
 Criteria: Avoid redundancies that may cause problems that we
discussed.
 If a relation is in a certain normal form, it is known that certain kinds
of problems can be avoided / minimized.
CS3402 9
Normalization
 Normalization requires two properties:
Non-additive or lossless join
 Decomposition is reversible and no information is lost
 No spurious tuples (tuples that should not exist) should be
generated by doing a natural-join of any relations
(Extremely important)
Preservation of the functional dependencies
 Ensure each functional dependency is represented in some
individual relation or could be inferred from other
dependencies after decomposition.
CS3402 10
First Normal Form with Primary Key
 First normal form (1NF)
 Disallow multi-values attributes, composite attributes and their
combination
 The domain of an attribute must be atomic (simple and
indivisible) values
Q. Is this relational schema in 1NF?
CS3402 11
CS3402 12
Nested relations
First normal form also disallows multivalued attributes that are
themselves composite. These are called nested relations because
each tuple can have a relation within it.
E.g., Ssn is the primary key of the EMP_PROJ relation in Figure (a)
Pnumber is the partial key of the nested relation; that is, within each
tuple, the nested relation must have unique values of Pnumber.
(a) Schema of the EMP_PROJ
relation with a nested relation
attribute PROJS.
(b) Sample extension of the
EMP_PROJ relation showing
nested relations within each
tuple.
CS3402 13
Nested relations
To normalize this into 1NF, we:
1. Remove the nested relation attributes into a new relation
2. Propagate the primary key into it;
the primary key of the new relation will combine the partial key with the
primary key of the original relation.
(c) Decomposition of EMP_PROJ into relations EMP_PROJ1 and
EMP_PROJ2 by propagating the primary key
CS3402 14
Problems with 1NF
 Problems with 1NF
 Insertion Anomalies
Deletion Anomalies
Update Anomalies
Q: Is it in 1NF?
What are the problems?
CS3402 15
Functional Dependency (Recap)
 Functional dependency is a constraint between two sets of
attributes from the database
 [Definition] A functional dependency denotes by X → Y, between
two sets of attributes X and Y that are subsets of a relation schema
R specifies a constraint on the possible tuples that can form a
relation state r of R
 The constraint is that, for any two tuples t1 and t2 in r that have t1[X] = t2[X],
they must also have t1[Y] = t2[Y]
 i.e., The values of the X component of a tuple uniquely (or functionally)
determine the values of the Y component.
 E.g., In DEPARTMENT, Dnumber and Dname
 If you know the department number, you know the department
name, so we have Dnumber → Dname
CS3402 16
Functional Dependency: Full vs Partial
 A FD X→ Y is a full functional dependency if removal of any
attribute A from X means that the dependency does not hold
anymore
 E.g., {Ssn, Pnumber} → Hours is a full dependency
 A FD X→ Y is a partial functional dependency if some attributes A
belonging to X can be removed from X and the dependency still
holds
 E.g., {Ssn, Pnumber} → Ename is a partial dependency
CS3402 17
Attributes: Prime vs Nonprime
 An attribute of relation schema R is called a prime attribute of R if it
is a member of some candidate key of R.
 Otherwise, it is nonprime.
 Example: Consider the CAR relation schema:
 CAR(State, Reg#, SerialNo, Make, Model, Year)
 Suppose CAR has two candidate keys:
 Key1 = {State, Reg#}
 Key2 = {SerialNo}
 Q. Which attributes are nonprime attributes?
CS3402 18
2NF with Primary Key
 [Definition] A relation R is in 2NF if every nonprime attributes A in
R is fully functional dependent on the primary key of R.
 Thus, if the primary key contains a single attribute, the test
need not be applied at all.
 Q.Is the EMP_PROJ relation in 2NF?
CS3402 19
2NF Normalization
 If a relation schema is not in 2NF, it can be 2NF normalized into a
number of 2NF relations in which nonprime attributes are
associated only with the part of the primary key on which they are
fully functionally dependent.
CS3402 20
Problems with 2NF
 Problems with 2NF
 Insertion Anomalies
Deletion Anomalies
Update Anomalies
Q: Is it in 2NF?
What are the problems?
CS3402 21
Transitive Dependency
 3NF is based on the concept of transitive dependency
 [Definition] A functional dependency X → Y in a relation R is
transitive dependency if
 there exists a set of attributes Z in R that is neither a candidate
key nor a subset of any key of R AND
both X → Z and Z → Y hold.
 E.g., The dependency Ssn→ Dmgr_ssn is transitive through
Dnumber
CS3402 22
3NF with Primary Key
 [Codd’s original definition] A relation schema R is in 3NF if it
satisfies 2NF and no non-prime attribute of R is transitively
dependent on the primary key.
 Q. Is EMP_DEPT in 3NF?
CS3402 23
3NF Normalization
 To normalize relation schema R into 3NF, R should be
decomposed to break the transitive dependency.
CS3402 24
Normal Forms Defined Informally
 1st normal form
All attributes are simple (no composite or multivalued attributes)
 2nd normal form
All non-prime attributes depend on the whole key (no partial
dependency)
 3rd normal form
All non-prime attributes only depend on the key (no transitive
dependency)
 In general, 3NF is desirable and powerful enough
 But, still there are cases where a stronger normal form is needed
CS3402 25
Test and Remedy for Normalization
CS3402 26
General Definitions of 2NF and 3NF
 The normalization procedure described is useful for analysis in
practical situations where primary keys have already been defined.
 These definitions, however, do not take other candidate keys of a relation, if any,
into account.
 Here, we give the more general definitions of 2NF and 3NF that
take all candidate keys of a relation into account.
 Notice that this does not affect the definition of 1NF since it is
independent of keys and functional dependencies.
 Partial and full functional dependencies and transitive
dependencies will now be considered with respect to all candidate
keys of a relation.
CS3402 27
General Definition of 2NF
 Alternative definition: A relation schema R is in 2NF is every
nonprime attribute A in R is fully dependent on every key of R.
CS3402 28
Example
 LOTS describes parcels of land for sale in various counties of a
state
 Two candidate keys: Property_id# and {County_name, Lot#}
 Property_id# is chosen as the primary key
 Q. Is LOTS in 2NF?
 A. LOTS violates 2NF due to FD3 as Tax_rate is partially dependent
on the candidate key {County_name, Lot#}
 County_name → Tax-rate (partial dependent)
Q&A
CS3402 29
Example (cont’d)
 Decomposing into the 2NF relations LOTS1 and LOTS2.
CS3402 30
General Definition of 3NF
 This general definition can be applied directly to test whether a
relation schema is in 3NF; it does not have to go through 2NF first.
 In other words, if a relation passes the general 3NF test, then it
automatically passes the 2NF test.
CS3402 31
General Definition of 3NF
 Two candidate keys: Property_id# and {County_name, Lot#}
 Q. Are LOTS1 and LOTS2 in 3NF?
LOTS2 is in 3NF
LOTS1 violates 3NF:
FD4 in LOTS1 violates 3NF because Area is not a superkey
and Price is not a prime attribute in LOTS1
Q&A
CS3402 32
Example (cont’d)
 Decomposing LOTS1 into the 3NF relations LOTS1A and LOTS1B.
CS3402 33
Example (cont’d)
 Progressive normalization of LOTS into a 3NF design..
CS3402 34
Boyce-Codd Normal Form
 BCNF was proposed as a simpler form of 3NF, but it was found to
be stricter than 3NF
 Every relation in BCNF is also in 3NF
BUT relation in 3NF is not necessarily in BCNF
 Difference with 3NF:
Condition which allows A to be prime is absent from BCNF
CS3402 35
Boyce-Codd Normal Form
 Suppose we have thousands of lots in the relation but the lots are
from only two counties: A and B
 Lot sizes in A are only 0.5, 0.6, 0.7, 0.8, 0.9 acres whereas lots in B
are 1.1, 1.2, …, 1.9
 Thus, we further have Area → County_name (FD 5) in LOTS1A
CS3402 36
Boyce-Codd Normal Form
 Recall that there are two candidate keys: Property_id# and
{County_name, Lot#}
 Q. Does LOTS1A satisfy 3NF? How about BCNF?
 FD5 satisfies 3NF in LOTS1A because County_name is a prime
attribute
 FD5 violates BCNF in LOTS1A because Area is not a superkey of
LOTS1A
Q&A
CS3402 37
BCNF Normalization
 This decomposition loses the functional dependency FD2 because
its attributes no longer coexist in the same relation after
decomposition.
CS3402 38
Summary of 3NF and BCNF
 In practice, most relation schemas that are in 3NF are also in
BCNF.
 Only if there exists some f.d. X → A that holds in a relation schema
R with X not being a superkey and A being a prime attribute will R
be in 3NF but not in BCNF.
 Ideally, relational database design should strive to achieve BCNF or
3NF for every relation schema.
 Achieving the normalization status of just 1NF or 2NF is not
considered adequate, since both were developed historically to be
intermediate normal forms as stepping stones to 3NF and BCNF.
CS3402 39
Boyce-Codd Normal Form
 Some notes on BCNF:
BCNF is stronger than 3NF
BCNF is useful when a relation has:
multiple candidate keys, and
these candidate keys are composite ones, and
they overlap on some common attributes
BCNF reduces to 3NF if the above conditions do not apply
Case category
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COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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COMSM0093 COMP281 AFM 333 IBUS1001 CP2501 Math 105A VE320 TEC101 SOCY2166 COM240 EFIM20033 ENGI4467 EFIM20034 EC 979 BE432 7EJ502 CSSE6400 COMP90025 Econ 312 ENG2031 ECO0006 EXERSCI 207 CAN209 ECO 137W FT312 ECO 2199 MATH32052 BDW4213 APS 360 SAS 6 CHME0017 PO92Q Economics 01AV MATH39512 MATH 5486 COMP8620 ISE102 ECON235 ECON 206 FI 345 PHAY0020 MATH0099 MATH0085 EFB106 PHY 134 MAE115 circuits Chemistry CSE12 MATH-UA 233 PHAS0038 COMP2140 CONMGNT 7049 COMP151101 ECON 485 ACX5903 ENGN6536 ARCH1162 Law PHAS0042 CCF1C03 MATH 351 Phys 139 AG942 MGT001371 APH106 ECON1051 MA4AM MA3Z7 NUMBER THEORY REST0006 SESS0026 STAT0023 TABL 2741 CMP4008Y EFIM10015 Acct 560 PSYC735 GEOG 5 ACCT3104 CSEC5616 PHIL1012 ITLS6111 ECON8022 5CCM226A compX123 MA4XJ R001 EWB LLP120 COMP643 ENG 103 ECON 23950 ACCT 207 FINC 616 Bio99 Math 137A Psychology BCPM0054 MATH20212 EC3450 CENV6141 PSY 205 CE335 CS365 Calculus ACSD INFT6800 MCIT INFO6030 PHYS 111LV H63EEJ ECON2151 ENGI 2181 MTRX1701 PLIT08009 CS240 Math 270 CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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