How Many Dimensions?
A teacher asks students to write an essay on one of three topics: modern art, soccer, or zebras. The teacher feeds the essays to a plagiarism detector to compare the essays to one another. It plots 32 points in a 1023-dimensional space.
1 What does the number 32 tell us?
2 What does the number 1023 tell us?
3 The teacher knows, of course, that students don’t merely copy one another’s writing; instead, they copy/paste text from the internet! The teacher opens her plagiarism detection software and tells it to consume a large training corpus of internet text about modern art, soccer, and zebras. How many dimensions will the space contain, now?
Circle one: more dimensions the same number of dimensions fewer dimensions
4 Explain your choice.
Assessing the Output
On the left is a description of the output of a plagiarism detector. On the right is an interpretation of what each output means. Match the description of each output with the correct interpretation.
The 32 points are evenly scatter all over the 1023-dimensional space, with no apparent clustering. |
1 |
A |
Essays about one topic are likely to use similar words, but essays about different topics likely use different words. The three clusters probably represent the three different topics (modern art, zebras, and soccer). |
|
The points are clustered into three groups, but two of the points are almost on top of one another. |
2 |
B |
Two of the essays use almost the same words, in almost the same frequencies. This look suspicious, and the teacher should take a closer look at those essays for potential plagiarism. |
|
The points are clustered into three groups. |
3 |
C |
Only one student opted to write about a particular topic, while the rest of the class wrote essays on the other two. There is no evidence of plagiarism. |
|
Almost all the points are clustered into two groups, but one point is positioned very far away from both clusters. |
4 |
D |
Every student appears to have written essays about entirely different topics! The teacher has no reason to suspect plagiarism, but they should probably worry about their students not following the assignment! |
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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