1. TASK The starting point for your term paper will be the course book, the contents of which will serve as the basis for an in-depth examination of one of the following questions. You are expected to...

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1. TASK The starting point for your term paper will be the course book, the contents of which will serve as the basis for an in-depth examination of one of the following questions. You are expected to research and cite from sources corresponding to your chosen topic. 1.1 Description of the Task You get (A) 4 training datasets and (B) one test dataset, as well as (C) datasets for 50 ideal functions. All data respectively consists of x-y-pairs of values. Structure of all CSV-files provided: X Y x1 y1 ... ... xn yn Your task is to write a Python-program that uses training data to choose the four ideal functions which are the best fit out of the fifty provided (C) *. i) Afterwards, the program must use the test data provided (B) to determine for each and every x-ypair of values whether or not they can be assigned to the four chosen ideal functions**; if so, the program also needs to execute the mapping and save it together with the deviation at hand ii) All data must be visualized logically iii) Where possible, create/ compile suitable unit-test * The criterion for choosing the ideal functions for the training function is how they minimize the sum of all ydeviations squared (Least-Square) ** The criterion for mapping the individual test case to the four ideal functions is that the existing maximum deviation of the calculated regression does not exceed the largest deviation between training dataset (A) and the ideal function (C) chosen for it by more than factor sqrt(2) In order to give proof of your skills in Python related to this course, you need to adhere to certain criteria when solving the exercise; these criteria are subsequently described under ‘Details.’ Seite 3 von 5 EXAMINATION OFFICE IU.ORG 1.2 Details You are given four training datasets in the form of csv-files. Your Python program needs to be able to independently compile a SQLite database (file) ideally via sqlalchemy and load the training data into a single fivecolumn spreadsheet / table in the file. Its first column depicts the x-values of all functions. Table 1, at the end of this subsection, shows you which structure your table is expected to have. The fifty ideal functions, which are also provided via a CSV-file, must be loaded into another table. Likewise, the first column depicts the x-values, meaning there will be 51 columns overall. Table 2, at end of this subsection, schematically describes what structure is expected. After the training data and the ideal functions have been loaded into the database, the test data (B) must be loaded line-by-line from another CSV-file and – if it complies with the compiling criterion – matched to one of the four functions chosen under i (subsection above). Afterwards, the results need to be saved into another fourcolumn-table in the SQLite database. In accordance with table 3 at end of this subsection, this table contains four columns with x- and y-values as well as the corresponding chosen ideal function and the related deviation. Finally, the training data, the test data, the chosen ideal functions as well as the corresponding / assigned datasets are visualized under an appropriately chosen representation of the deviation. Please create a Python-program which also fulfills the following criteria: − Its design is sensibly object-oriented − It includes at least one inheritance − It includes standard- und user-defined exception handlings − For logical reasons, it makes use of Pandas’ packages as well as data visualization via Bokeh, sqlalchemy, as well as others − Write unit-tests for all useful elements − Your code needs to be documented in its entirety and also include Documentation Strings, known as ”docstrings“ Table 1: The training data's database table: X Y1 (training func) Y2(training func) Y3(training func) Y4(training func) x1 y11 y21 y31 y41 ... ... ... ... ... xn y1n y2n y3n y4n Seite 4 von 5 EXAMINATION OFFICE IU.ORG Table 2: The ideal functions’ database table: X Y1 (ideal func) Y2 (ideal func) ... Ym (ideal func) ... Y50 (ideal func) x1 y11 y21 ... ym1 ... y50_1 ... ... ... ... ... ... ... xn y1n y2n ... ymn ... y50_n The database table of the test-data, with mapping and y-deviation X (test func) Y (test func) Delta Y (test func) No. of ideal func x1 y11 y21 N1 ... ... ... ... xn y1n y2n y3n 1.3 Additional Task Assume that your successfully created project is on the Version Control System Git and has a Branch called develop. On this Branch, all operations of the developer team are combined. Write the Git-commands necessary to clone the branch and? develop on your local PC. Imagine that you have added a new function. Write all necessary Git-commands to introduce this project to the team’s develop Branch. Please note: You need the commands for commit, push. Afterwards, you would make a Pull-request and your contribution would be added “merged” to the develop Branch after one or several of your team has reviewed your changes. 1.4 Remarks The Dataset for this task will be made available on request for each particular student. Therefore, a ticket for the tutor should be opened, whereupon the access to the data will be granted. A copy will be sent to the responsible persons – thus a later manipulation by the students is prevented. Your entire source code is expected to be contained in the appendix of your written assignment, so that we are able to test your entire program, including the outputs. Your input data is not required. The aim is to fully reconstruct your work, your decisions and your assessment of the task result through your assignment. Seite 5 von 5 EXAMINATION OFFICE IU.ORG 2. ADDITIONAL INFORMATION FOR THE EVALUATION OF THE WRITTEN ASSIGNMENT When conceptualizing and writing the written assignment, the evaluation criteria and explanations given in the writing guidelines should be considered. 3. TUTORIAL SUPPORT In this written assignment task, several support channels are open; as the student, it is your responsibility to select your preferred support channel. The tutor is available for technical consultations and for formal and general questions regarding the procedure for processing the research essay. However, the tutor is not required to approve outlines or parts of texts and drafts. Independent preparation is part of the examination work and is included in the overall evaluation. However, general editing tips and instructions are given in order to help you get started with the written assignment.
Answered 6 days AfterJul 04, 2022

Answer To: 1. TASK The starting point for your term paper will be the course book, the contents of which will...

Swapnil answered on Jul 11 2022
68 Votes
Application of
An
Error Metric
Table of contents
1 Symbols and abbreviations ----------------------------------------------------------------------------3
2 Introduction ---------------------------------------------------------------------------------------------4
2.1 Measurement vs. ideality -------------------------------------------------------------------4
2.2 Error metrics ---------------------------------------------------------------------------------5
3 Measu
rements -------------------------------------------------------------------------------------------6
3.1 In two dimensions ---------------------------------------------------------------------------6
3.2 In three dimensions -------------------------------------------------------------------------6
4 Quadric Error Metric -----------------------------------------------------------------------------------7
4.1 Modelling -------------------------------------------------------------------------------------7
4.2 Application in mesh simplification -------------------------------------------------------7
4.2.1 New ideal vertex position -------------------------------------------------------8
4.2.2 Noninvertible error metric matrix ----------------------------------------------9
4.2.3 Result-------------------------------------------------------------------------------9
4.2.3 Limitation -------------------------------------------------------------------------9
4.3 Further possibilities ------------------------------------------------------------------------10
4.4 Final words ---------------------------------------------------------------------------------10
5 Reference -----------------------------------------------------------------------------------------------11
    
1. Symbols and abbreviations:
Symbols and abbreviations:
    Label
    Name
    Symbol
    Abbreviation
    Mean Squared Error
    MSE
    
    Root Mean Square Error
    RMSR
    
    Mean Absolute Error
    MAE
    
    Mean Absolute Scaled Error
    MASE
    
    Mean Absolute Percentage Error
    MAPE
    
    Symmetric Mean Absolute Error
    SMAE
    
    Quadric Error Metric
    QEM
    
    Quadric Error Collapse Decimation
    QWCD
    
    Discrete Differential Error Metric
    DDEM
    Mathematical object
    Quadric error metric matrix
    Q
    
    Vertex coordinates
    v
    
    Plane
    P
    
    Error metric
    ∆
    
    Tangential error metric matrix
    T
    
    Discrete curvature error matrix
    C
    Miscellaneous
    matrix transpose
    T
2. Introduction:
2.1 Measurement vs. ideality:
Nothing is without flaw in reality. There is always some uncertainty, some errors that can and will occur. Every scientific experiment, regardless of high technology, has its limits. When measurements are made, scientists can approach them two different ways: they either already know what to expect to some certain extent, and they need certainty by making a theory practice, or they try to explain their results by building a hypothesis around the experiment. In the first scenario, the measured data set has to be fitted to a presumed relation between events, in other words, to an already existing function. This is a more likely approach, since experiments are very demanding, and without proper reasoning, they do not materialise. The second approach ends up having a bunch of data where scientists have to guess what kind of pattern they follow. The function that was at least assumed in the other case, is missing here, which complicates things.
Figure 1: The two cases of experiments. The measured data points (red dots) are the same on both plots, but with the assumption of a pre-existing relation it is easy to check the validity and correctness of the experiment via examination of the errors of the data set. After introducing the mathematical background, it turns to one specific error metric. The main goal is to find a good error metric to define the quality of a data set, but on a 3D surface. Let us go back to Figure 1a. The dots are clearly not perfect. They do not lie on the blue line which is caused by measurement errors. These errors in real practice can come from equipment, environment, human limitations or human negligence. In this current study, the origins of errors are irrelevant and their discussions are omitted. What matters is that they are present and their extension should be somehow qualified.
2.2 Error metrics:
A way to measure the error of a model is the error metric. There are several types, such as
Mean Squared Error (MSE): is probably the most well-known metric. It measures the mean of the squares of the deviations.
MSE = 1/n Σ (yi – y˜i) ^2
where n is the number of data points, yi is the measured value (or vector of measured values), and y˜i is the predicted value (vector of values). In later section, matrix notation will be used. In order to make...
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