Adaptive Business Intelligence
Why need Adaptive Business Intelligence
In order to answer two questions:
1. What is likely to happen in the future?
2. What is the best decision right now?
We need to predicte what will happen in the future.
Adaptive Business Intelligence is combining prediction, optimization and adaptability in a system capable of answering these two fundamental question.
"The answer to my problem is hidden in my data... but I cannot dig it up!"
business managers gathered and stored massive amounts of data in the belief that they contain some valuable insight. But they eventually discovered that raw data are rarely of any beneift.Their real value depends on an organization;s ability to analyze them.
A lot of business intelligence companies established in order to meed the needs of data analysis for customers. They build software application to get the knowledge from raw data, such as sales information, market survey information and etc. The knowledge may be all kinds of reports for example, tables, graphs, pie, charts and etc.
The function of the business intelligence softwares are
1. collect data from many different sources;
2. make the data into table, sheet or etc.
BI: Business Intelligence --> DSS(Decision Support System)
BI1.0 = data analysis + consumption
Due to internet, data become huge, BI make more access(multiple versions of the truth)
BI2.0 = BI Tools (right data + right time + right person)
ABI: Adaptive Business Intelligence --> DMS(Decision Making System)
Example 1 :
Paths solution is 3
ADFC
AEFB
BDEC
BFEA(same as AEFB)
CEDB(same as BDEC)
CFDA(same as ADFC)
When the number of cities increase:
Number of cities Number of Path
4 (3*2)/2 = 3
5 (4*3*2)/2 = 12
6 (5*4*3*2)/2 = 60
7 (6*5*4*3*2)/2 = 360
N (n-1)! / 2
Example 2 :
BP GAS fuel price
Every time add over 40$ fuel, every liter discount 6C
This time you not use, next time the fuel discount add 6C
Max liter of you car is 80$
Find out the max benefit you may archive
First time 40$, discount 6C/liter
First time not use discount, second time 40$, discount 12C/liter
| Time | Money | Liter |
| 1 | 40 | 40/P |
| 2 | 40 | 40/P |
| N-1 | 40 | 40/P |
| N | 80/P(P-NX) | 80/P |
P: price per liter before discount
X: discount per liter
Total Money = 40(N - 1) + 80/P(P - NX) = 40N - 40 + 80 - 80NX/P
Total Liter = 40/P(N - 1) + 80/P = 40N/P - 40/P + 80/P
Price per Liter = (40N - 40 + 80 - 80NX/P) / (40N/P - 40/P + 80/P) = (40NP + 40P - 80NX) / (40N + 40) = (P(N+1)-2NX) / (N+1) = P - 2NX/(N+1)
Conlcusion:
If the price per liter and discount per liter not change, the max discount is almost n times of discount(n means the max of liter of your car / min of liter to get discount ).
More times you save, more the number close to n time. But it can not over n
Y=AX+B
A=[n*sum(xy) - sum(x)*sum(y)] / {n*sum(x^2) - [sum(x)]^2}
B=[sum(y)*sum(x^2) - sum(x)*sum(xy)] / {n*sum(x^2) - [sum(x)]^2}
Example in the attachment
Adaptive Business Intelligence Structure
Data Preparation
1. Data validation
Reason: exist unsatisfactory data (incompleteness / noise / inconsistency)
2. Data transformation
3. Data reduction
Data Exploration
Univariate analysis
Bivariate analysis
Multivariate analysis
Regression Analysis
Simple linear regression
Multiple linear regression
Validation of regression models
Selection of predictive variables
Time Series Model
Charaters: sequence/measured/successine/uniform interval
Why need time series model
Data from daily life is stochastic(random). In order to find out the regular from it, we need the time series model
Time series {Yt}
We use the time series to make up mode Ft
Example
Below is the cost I spend to go to school. I do not need to school on Monday and Tuesday.
Other day I want to school use hop card which gain discount for bus.
But last week Thursday I forget the card; On Sunday, My brother bring me to school
T Mon Tue Wed Thu Fri Sat Sun
Y 0 0 2.1 3.4 2.1 2.1 0
F 0 0 2.1 2.1 2.1 2.1 2.1
There is different between model and real value. We need to process it
Process measure
1. Distortion Measure
et = Yt - Ft
2. Dispersion Measure
et = Yt - Ft
3. Tracky signal
The result will be in [-1,1]
If the result is close to -1, the prediction value is greater than actural value
If the result is close to 1, the prediction value is smaller than actural value
Time Series Components: Trend / Seasonality / Random noise
Trend --> Mt
Seasonality --> Qt
Random noise --> Et
Actual value --> Y
The relation is Y=Mt * Qt * Et
The process is find out the trend from the real data
1. Find Moving average: mt(h)
define h
if h is odd then
if h is even then
2. Use the actural value to divide the mt(h), to get Qt * Et
3. Dig the Qt from the Qt * Et
4. Use actural value to divide the Qt, to get Mt * Et
5. Dig out the Mt from Mt * Et
The attachment is the example for the process
Description:
1. The H is 12, it makes the t is 7. Reason: t - h/2 > 0
2. For Qt, it need to choose every year the same month to make 12 values, then just copy the 12 values
How to prove the Pythagorean Theorem
For a right triangle with legs a and b and hypotenuse c
a^2 + b^2 = c^2
Reason: Rt EAD = Rt CBE
Result: <ADE=<CEB
Reason: <ADE=<CEB and <ADE + <AED=90 degree
Result: <CEB + < AED = 90 degree
Reason: <CEB + < AED = 90 degree and <CEB + < AED + <DEC =180 degree
Result: <DEC = 90 degree
1/2(a+b)^2 = 1/2(ab) + 1/2(ab) + 1/2(c^2)
1/2(a^2+ b^2 + 2ab) = ab + 1/2 (c^2)
1/2(a^2) + 1/2 (b^2) = 1/2 (c^2)
a^2 + b^2 = c^2
How to prove the sum degree of three angle in triangle is 180 degree
Make a line EF through A which is parallel with BC
Reason: EF is parallel with BC
Result: <EAB = <ABC and <FAC = <ACB
Reason:<EAB = <ABC and <FAC = <ACB and <EAB+<BAC+<CAF = 180 degree
Result < ABC+<BAC+<CAB = 180 degree
How to prove which area of the triangle is the biggest. cut one line into three parts to make the triangle.
According to Heron's formula, the area of the triangle is
S=1/2(a+b+c)
Reason: 1/3*(a+b+c) >= (abc)^1/3 and only when a=b=c, 1/3*(a+b+c) = (abc)^1/3
Result: 1/27*(a+b+c)^3 >= abc
Reason: 1/27*(a+b+c)^3 >=abc
Result: 1/27*[(s-a)+(s-b)+(s-c)]^3 >= (s-a)(s-b)(s-c)
Reason: 1/27*[(s-a)+(s-b)+(s-c)]^3 >= (s-a)(s-b)(s-c) and T=[s(s-a)(s-b)(s-c)]^1/2
Result: {1/27*s*[(s-a)+(s-b)+(s-c)]^3}^1/2 >= T
Only when s-a = s-b = s-c, T get max value
So only when a=b=c, T get max value
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