This document proposes a method to visualize the fluid relationship between lectures and laboratories using semi-supervised non-negative matrix factorization (SSNMF). It collects data on lectures and graduation theses from laboratories, represents them as multidimensional vectors, and applies SSNMF to output a relationship matrix showing which combination of lectures constitutes specialized fields in laboratories. The method is intended to help students explore lecture and laboratory options by providing quantitative evidence on potential relationships based on each element's characteristics, beyond simple one-to-one comparisons. It is shown to capture the many-to-many relationships between lectures and laboratories when applied to different lecture sets.

1. Visualization of the Relationship
Between Lectures and Laboratories Using SSNMF
Kansai university
Kyoka Yamamoto
Ryosuke Yamanishi
Mitsunori Matsushita
Which lectures should I take to
learn for that laboratory?
Which laboratory should be good
for using the knowledge I have
learned in the lectures?
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2. Background
[How students should behave]
l Select a laboratory to specialize knowledge and skills
in the lectures they have taken
l Select lectures to acquire the knowledge and skills necessary
for the laboratory they wish to join
[How students actually behave]
l Lectures and laboratories are carelessly selected
In daily circumstances
・what to wear ・what to eat 2

3. Problems
Attending lectures based on their own biases
They donʼt know what they will need in the laboratory at the time
when they have joined
Chose a laboratory without knowing their potential options
Not being able to do the research they really were interested in
[Why these problems happen]
Difficulty in understanding relationships between objects
Quantity problem: Difficulty in covering all lectures and labs
Knowledge problem: lacking knowledge of options
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4. The Feature of Selecting Lecture and Labs
The relationships between lectures and laboratories are fluid.
lThe candidates of the laboratory where they offer to join should differ
lThe set of laboratories in the department might change
Based on aggregate information of alternatives rather than one-to-one comparisons
Necessity of understanding many-to-many relationships
Student A Student B
The relationships differ
depending on the situation.

5. Goals and Approach
[Goals]
l Helping students think exploratively
about lecture and laboratory selection
l Providing evidence for choosing lectures and labs
[Approach]
lFocusing on the relationship between elements beyond sets
lQuantitatively evaluating potential relationships based on the
characteristics of each set
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6. A method to visualize the relationships between elements
[Procedures]
STEP1: Data collection and normalization
STEP2: Multidimensional vector representation
STEP3: Application of SSNMF
Representing the knowledge covered in lectures and labs as
multidimensional vectors
Semi-supervised non-negative matrix factorization (SSNMF)
is used for visualizing the relationship between them.
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7. Basic concept of the method
Y H ＋ FG
〜
〜
Proposed method: Application of SSNMF
Y H
U a set of laboratories a set of lectures
SSNMF
A method for feature analysis which is commonly used
in the field of signal processing
(E.g.) sound source separation
Audio data composed of mixed sound sources: Y
How active a certain sound source feature: H is for Y
can be shown as a matrix U.
By decomposing the matrix Y representing laboratories by the matrix H
concerning the lectures, we expect to obtain an activation matrix U showing the
relationship between laboratories and knowledge handled in the lectures.
U
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8. STEP1:Data collection and normalization
[Target data]
Specialty: Graduation Thesis
Defining one laboratory as one field of specialization
The text excluding the name of the supervisor, student ID number, authorʼs name, and references
Lecture : Lecture syllabus
Course outline, plan, and achievement objectives indicating course content
[Normalization]
l Normalization of one-byte alphanumeric characters and symbols
l Remove line breaks and spaces
l Morphological analysis to extract only nouns; the text is separated into part-of-speech in Japanese
STEP1: Data collection and normalization
STEP2: Multidimensional vector representation
STEP3: Application of SSNMF
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9. STEP2: Multidimensional vector representation
[bag of words method]
Labs and Lectures.
Numerical representation by frequency
Lectures
Labs
words
[NMF]
Dimensional compression
Sparsity resolution
（Labs + Lectures） words （ Labs + Lectures） Dimensional variance
STEP1:データ収集・正規化
STEP2:研究室と講義を多次元ベクトルで表現
STEP3:半教師あり⾮負値⾏列因⼦分（SSNMF）の適⽤
Dimensional variance
500-dimensional vector for each object
[Splitting]
Splitting the matrix into two vector
sets representing the matrix
concerning lectures and laboratories
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Lectures
Labs
STEP1: Data collection and normalization
STEP2: Multidimensional vector representation
STEP3: Application of SSNMF

10. Y 〜 HU ＋ FG
〜
Matrix representation of what kind and how much knowledge is covered in each lab/lecture
Y : Observed information of lectures
H : A template indicating how each type of knowledge is used/applied/adjusted in a laboratory
U : Activation matrix showing which and how much knowledge in the lecture is
referenced in the laboratory
FG : knowledge unrelated with the target (e.g., basic knowledge commonly needed in all labs)
The Relationship between Lectures and Laboratories
representing which combination of lectures constitutes a specialized field
STEP3: Application of SSNMF
Output：The Relationship of Objects
STEP1:データ収集・正規化
STEP2:講義と研究室を多次元ベクトルで表現
STEP3:半教師あり⾮負値⾏列因⼦分（SSNMF）の適⽤
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STEP1: Data collection and normalization
STEP2: Multidimensional vector representation
STEP3: Application of SSNMF

11. To Analyze The Relationship between Lectures and
Laboratories, Which Has A Fluid Relationship
Target Faculty
The lectures are labeled C, M, and S in a Faculty of Informatics to identify the lectures'
specialties.
・programming and algorithms such as basic theories of informatics: C course
・processing in media and communication: M course
・information processing in various fields including management, economics, psychology,
and politics: S course
Resource
Labs：the graduation thesis outlines from 43 labs (459students)
which is collected from the SJ undergraduate thesis outline collection in 2019
Lectures：192 lectures in total
the syllabus of the SJ faculty for the year 2020
which is collected from the university website.
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12. To Analyze The Relationship between Lectures and
Laboratories, Which Has A Fluid Relationship
[The task]
_To analyze the relationship between lectures and laboratories, which has a fluid relationship
[Comparison]
・The proposed method is applied to the following sets of lectures.
・Comparison of results between sets of lectures
c-series: 31 lectures, m-series: 25 lectures, s-series: 28 lectures, all lectures: 84 Lectures
●A compilation of lectures on estimation accuracy in a laboratory specializing in human media communication desig
Decomposed in S lectures Decomposed in all lectures
Focusing on “Environmental economics”
When C- and M-series lectures are added to the choices,
the activation trend value and the rank changed
Therefore, we confirmed that the proposed method
captured the many-to-many relationships
complying with the input set
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13. Summary
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Background
Selecting a laboratory to specialize knowledge and skills in the lectures they have taken
Problems
Attending lectures based on their own biases
Chose a laboratory without knowing their potential options
Purpose
Representing the knowledge covered in lectures and labs as multidimensional vectors
Method
Focusing on the relationship between elements beyond sets
Quantitatively evaluating potential relationships based on the characteristics of each set

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