The online index calculator is suspended now. Below the content and brief descripton of the service.
This educational resourse is devoted to a problem of an index construction. The index is the most informative description of an object. So, there is a set of objects. A rating is an ordering of the set according to the objects indices.
There are lots of ways to construct indices. However, when algorithms are chosen and some results obtained, the following question arises:
How to show adequacy of the calculated indices?
To answer the question analysts invite experts. The experts express their opinion and then the second question arises:
How to show that expert estimations are valid?
There is a technique that produces valid indices based on measurement data and expert estimates.
Here are the following sections:
Workbench when one can calculate its own index using his data and the simple algorithm.
Samples is a model and realworld indices and ratings library.
Help here are number of comments and articles on how ratings and indices could be created.
Support — do not hesitate to contact the index makers!
Note: this is the first version of the resource. We apologize for any mistakes and would be grateful, if you send us your comments.
Before making indices you have to prepare the following information.
Note the next simple facts
The base algorithm for indices computation is Principal Components Analysis.
If one obtain an index of his data table and features weights, he can use the weights as a fixed model for indices computation. To make the next index based on the same set of objects and the same set of features one have to do the following.
Denote the data table as mbyn matrix A with items a_{ij}, where m is the overall objects number and n is the overall features number. Denote features weights as w_{1},...,w_{n} and objects indices as q_{1},...,q_{m}. The index of ith object is
This model can be used if the source data were lightly changed. The strong side is: if the changes were in a small number of objects, those objects, whose data was not changes will keeps their indices unchanged. The weak side is: if there were drastic changes, the indices will be incorrect. Sometimes the drastic changes can occur even if one object changes its feature. To decide whether one should use the weighting model or not, he have to compute indices using changed data. If one desides that new indices and weights are changed too much, he must decline the old model's weighs.
SUMMARY
To make an index you have to make the following steps:
There is only one template in the database for now. You can download it in the CSV text format. Also you can copy the data from the examples.
Click here to learn how to fill the template.
Now you should click the browse button to find the file in your computer and upload it. If the file is wellformatted the system switch this tab to the View tab.
You can upload either XLSfile or CSVfile. The first one has the following format. The special word "Factor" is reserved. It shows whether the bigger feature values correspond to the bigger values of indices (Factor=1) or the smaller feature values correspond to the bigger values of indices (Factor=1). An XLS table example is below. You can select the whole table, then copy it, open your MSExcel, click the mouse poiner to the worksheet cell A1 and paste the table.

Feature1 
Feature2 
Feature3 
Factor 
1 
1 
1 
Object1 
0,69 
7,53 
4,69 
Object2 
0,69 
7,53 
7,38 
Object3 
4,34 
0,43 
5,69 
Object4 
8,48 
8,37 
5,29 
Object5 
5,31 
6,84 
4,02 
Object6 
7,08 
0,96 
4,02 
Object7 
4,68 
5,5 
3,42 
A CSV file (Comma Separated Values) is a text file. It contains the following lines.
, Feature1, Feature2, Feature3 
The data is the same as in the table above. Note that the decimal points are dots while the value separators are commas. You can select the whole table copy it, open your Notepad or another text editor, and paste the table.
An index is the most informative description of data. To make an index we use Singular Value Decomposition and Principal Components Analysis. It gives the indices that fit the source data the most precisely.
The first step is the features normalization. We need it to descale data. The table below shows the measure data if two scales: the scale of Feature1 and the scale of Feature two. We can not use the source scales since the values of Feature2 are two times bigger than the values of Feature1. In this case our index will pay attention to the Feature2 data and ignore the Feature1 data. So we have to make the both features to be in the same scale.

Feature1 
Feature2 

Feature1 
Feature2 
Factor 
1 
1 



Obj1 
2.66 
30.00 

0.8300 
0.0000 
Obj2 
1.00 
44.63 

0.0000 
0.4877 
Obj3 
3.00 
40.33 

1.0000 
0.3443 
Obj4 
1.98 
50.50 

0.4900 
0.6833 
Obj5 
1.23 
60.00 

0.1150 
1.0000 
Obj6 
2.49 
34.55 

0.7450 
0.1517 
Obj7 
1.89 
55.50 

0.4450 
0.8500 
Let the scale be the segment [0,1]. The minimal value of a feature will be 0 while the maximal value will be 1 (so each feature has at least one 0value and at least one 1value). The formula of the normalization is following. Denote a_{ij} a value of ith object and jth feature. Then the new value will be
The figure below shows the objects with normalized features data. Objects are marked by asterisks. The main idea of the algorithm is the next. We find a vector called as 1st Principal Component (red segment on the figure). Projections of the objects give on the 1st PC gives the maximal distribution. The Projections denoted by dots. The distance from the point (0,0) to an object projections is the object index.
The table below represents the object indices.
Objects 
Indices 
Obj1 
0.60 
Obj2 
0.34 
Obj3 
0.96 
Obj4 
0.83 
Obj5 
0.77 
Obj6 
0.64 
Obj7 
0.91 
The feature weights are very informative data. The weight table shows that both features have approximately equal importance. However, there is data with different weights values. This information discovers what features have great (or small)impact on indices.
Features 
Weights 
Feature1 
0.72 
Feature2 
0.69 
This resource is supported by the Department on mathematical modeling in ecology and medicine of the Dorodnicyn computing center of the Russian academy of sciences.