Information Systems Analysis and Design

Mini-project for optimal sample selection

It is known that the amount of data has been increasing tremendously in the last few years due to the ease of

accessing to internet, cheap or inexpensive mass storage devices, the ease of transferring data through internet,

communication lines and digital data are used in every walk of life. Nowadays, these big data have been used

for data mining, knowledge discovery, machine learning, statistical learning, statistical analysis and

experiments. In order to extract or discover useful data, information or knowledge from these big data, one of

methods we usually adopt is the sample selections.

In this mini-project, you are expected to extract a subset of samples from these big data. In order to extract this

subset of data (samples), we have to make sure that the subset extracted or selected should be as fair and

unbiased as possible and as optimal as possible. In the following we propose one method.

Assume there are m samples (45?m?54), any n (7?n?25) samples out of these m samples are selected. There

are mCn groups of n samples. From one of these groups of n samples, we randomly selected e.g., k=6 (4?k?7)

samples to form some groups. So there will be nCk groups of k=6 samples selected. Among these groups of k=6

samples, we would like to optimize them by selecting ONLY some of them. The conditions that need to be

fulfilled are listed as follows:

1. There are at least ONE group of k samples, in which s (3?s?7) samples have been selected from the j

(where s?j?k) samples, i.e., when j=4, we have s=3 or 4; when j=5, we have s=3, 4 or 5; when j=6, we

have s=3, 4, 5 or 6; and when j=7, we have s=3, 4, 5, 6 or 7.

E.g. 1, when m=45, n=7 (assume we have chosen 7 samples, A,B,C,D,E,F,G and k=6, j=5, s=5, we could

obtain the following minimum 6 groups of k=6 samples, which guarantee at least ONE group of k=6

samples has s=5 samples groups from ALL j=5 samples groups of n=7 samples, (i.e., 7C5 and 5C5).

1. A,B,C,D,E,G 2. A,B,C,D,F,G 3. A,B,C,E,F,G

4. A,B,D,E,F,G, 5. A,C,D,E,F,G 6. B,C,D,E,F,G

E.g. 2, when m=45, n=8 (assume we have chosen 8 samples, A,B,C,D,E,F,G,H and k=6, j=4, s=4, we could

obtain the following minimum 7 groups of k=6 samples, which guarantees at least ONE group of k=6

samples has s=4 samples groups from ALL j=4 samples groups of n=8 samples, (i.e., 8C4 and 4C4).

1. A,B,C,D,G,H 2. A,B,C,E,G,H 3. A,B,C,F,G,H

4. A,B,D,E,F,G 5. A,C,D,E,F,H 6. B,C,D,E,F,H 7. C,D,E,F,G,H

E.g. 3, when m=45, n=9 (assume we have chosen 9 samples, A,B,C,D,E,F,G,H,I and k=6, j=4, s=4, we

could obtain the following minimum 12 groups of k=6 samples, which guarantees at least ONE group of

k=6 samples has s=4 samples groups from ALL j=4 samples groups of n=9 samples, (i.e., 9C4 and 4C4).

1. A,B,C,D,E,I 2. A,B,C,E,G,H 3. A,B,C,F,H,I 4. A,B,D,E,F,G

5. A,B,D,G,H,I. 6. A,C,D,E,F,H 7. A,C,D,F,G,I 8. A,E,F,G,H,I

9. B,C,D,F,G,H 10. B,C,E,F,G,I 11. B,D,E,F,H,I 12. C,D,E,G,H,I

E.g.4, when m=45, n=8 (assume we have chosen 8 samples, A,B,C,D,E,F,G,H and k=6, j=6, s=5, we could

obtain the following minimum 4 groups of k=6 samples, which guarantees at least ONE group of k=6

samples has ONE s=5 samples group from ALL j=6 samples groups of n=8 samples, (i.e., 8C6 and 6C5).

1. A,B,C,E,G,H 2. A,B,D,F,G,H 3. A,C,D,E,F,H 4. B,C,D,E,F,G

E.g. 5, when m=45, n=9 (assume we have chosen 9 samples, A,B,C,D,E,F,G,H,I and k=6, j=5, s=4, we

could obtain the following minimum 3 groups of k=6 samples, which guarantees at least ONE group of k=6

samples has ONE s=4 samples group from ALL j=5 samples groups of n=9 samples, (i.e., 9C5 and 5C4).

1. A,B,D,F,G,H 2. A,C,E,G,H,I 3. B,C,D,E,F,I

E.g. 6, when m=45, n=10 (assume we have chosen 10 samples, A,B,C,D,E,F,G,H,I,J and k=6, j=6, s=4,

we could obtain the following minimum 3 groups of k=6 samples, which guarantees at least ONE group of

k=6 samples has ONE s=4 samples group from ALL j=6 samples groups of n=10 samples, (i.e., 10C6 and

6C4).

1. A,B,E,G,I,J 2. A,C,E,G,H,J 3. B,C,D,F,H,I

E.g. 7, when m=45, n=12 (assume we have chosen 12 samples, A,B,C,D,E,F,G,H,I,J,K,L and k=6, j=6, s=4,

we could obtain the following minimum 6 groups of k=6 samples, which guarantees at least ONE group of

k=6 samples has ONE s=4 samples group from ALL j=6 samples groups of n=12 samples. (i.e., 12C6 and

6C4).

1. A,B,D,G,K,L 2. A,C,D,H,J,L 3. A,D,E,F,I,L

4. B,C,G,H,J,K. 5. B,E,F,G,I,K 6. C,E,F,H,I,J

2. A user friendly interface should be provided. A system title is given, e.g, “An Optimal Sample Selection System”.

3. The user needs to input the values for parameters m, n, k, j and s.

4. The system can randomly select n numbers out of m numbers and display these numbers of n number.

5. Output groups of k samples (results) to a DB file, e.g., 45-9-6-4-4-x for m=45, n=9, k=6, j=s=4 for the x

th

run.

6. Provide a mechanism to DISPLAY and DELETE the obtained groups of k samples (results) onto the screen from a

DB file, e.g., 45-9-6-4-4-x.These groups of k samples are selected from the list.

7. Students are required to form groups yourselves. Each group should have 3 students. You are advised to include in

your group at least ONE student who knows how to do programming in MS ACCESS 20XX and VBA, C, C++, Java,

MATLAB, etc.

8. Use numeral values, e.g., positive INTEGERS, 01,02,03,…..,54 instead of big capital letters A,B,C,D,E,F….,Z for the

m and n numbers.

9. Submit to me names of your group members on 23/09/2020. Group numbers will be provided later for each group.

10. A presentation and demonstration is a MUST in week 15.

11. Each group is required to have a 10-15 minutes presentation which includes the introduction, description of method(s)

adopted, what have been achieved in this project, and a demonstration of your system is a MUST in this presentation.

12. A clear, succinct, easy to understand detailed REPORT of user manual/guide on how to INSTALL and EXECUTE

your DEVELOPED system. The REPORT must include method(s)/methodology (supported by diagram(s), etc.),

features you have developed/used, contributions such as good running time, optimal/near optimal results, etc.,

and problems such as long time to get results, results not good enough, etc. of your system, results of sample

runs, etc. should be submitted in hardcopy.

13. You are required to submit a USB which contains your developed system, all your source files (codes), free/share

wares, database files, DB files of k samples (sample runs outputs/results), and the REPORT mentioned in point 12.

14. Bonuses will be given to group(s) that allow users to select as many different parameters as possible for m, n, k, j and

s, good method(s) adopted, could generate optimal/ near optimal solutions. Furthermore, bonuses will be given to the

developed system(s) that could be executed in a short time, i.e., having good time complexity.

15. The deadline is Week 15 in the presentation sessions. All teams must submit their projects in a USB and hardcopy of

the REPORT in Week 15. Group number, names, student numbers of your group members should be listed in your

REPORT.

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