MAG Depth Uniqueness & Interdisciplinarity

Table of Contents

• Overview
• Files
• Metrics
  • 1. Uniqueness
  • 2. Interdisciplinarity
  • 3. Depth
• Algorithm
• Data Sample
• Usage

Overview

In this repository you can find the algorithm for the Depth Uniqueness & Interdisciplinarity metrics calculation for Microsoft Academic Graph (MAG).

The metrics are calculated at 26GB /scratch/aal544/AndriyMetrics/AndriyMetrics.csv. The table includes the metrics for 152M papers. bka3 has root permissions to the directory / file. Expect the code re-runs to run 10-12 hours.

Files

You will need these files from the MAG for the calculation.

• 46G PaperFieldsOfStudy.txt

• 71G Papers.txt

• 59M FieldsOfStudy.txt

• 18M FieldOfStudyChildren.txt

Metrics

We are dealing with the following metrics:

1. Uniqueness

The metric is a tuple: (new_field_2combinations, field_count). The field_count is how many fields in total this paper has. The new_field_2combinations is a counter of how many unique 2-pairs of fields this paper introduces comparing to all the papers that were published up to the field's piublication year.

This way the first combination of feild1+field2 will increment the new_field_2combinations value. If a paper has 5 fileds {f1,f2,f3,f4,f5}, it's the first time f5 is introduced and the other 4 fields had been published together, the value of new_field_2combinations would be nCr(5,2). In other case, for instance, if all fields except for field2 and field5 had appeared together, the value of new_field_2combinations would be 1 because it only introduces 1 new unseen combination.

P.S. We cannot interpret “counter” as “innovation” or “novelty”. This is because one may argue that p can be innovative or novel compared to other papers that preceded it, even if all of them had the same vector as p and were published before p (e.g., if p is novel in the way it solved a particular problem, rather than being novel in the topics it studies). In contrast, interpreting “counter” as “uniqueness” is harder to argue against.

2. Interdisciplinarity

Measure interdisciplinarity in a way similar to lexicographic ordering.

In MAG there are 6 levels of fields: 19 parent fields (Math, Physics, Biology, etc.), 100+ first children (AI, Astronomy, ML, etc), and so on. We can find the vector of counts of field levels per paper v = [l0,l1,l2,l3,l4,l5].

• The most interdisciplinary papers are those whose 1st value in vector is greatest.

  • Out of those, the most interdisciplinary are those whose 2nd value is greatest

  • Out of those, the most interdisciplinary are those whose 3rd value is greatest

  • And so on…

• Then, we have those whose 2nd value in vector is greatest.

  • Out of those, the most interdisciplinary are those whose 3rd value is greatest

  • Out of those, the most interdisciplinary are those whose 4th value is greatest

  • And so on…

3. Depth

This is the index of the last non-zero value in the counts of field levels per paper v = [l0,l1,l2,l3,l4,l5] vector.

Since the field levels are hierarchical in MAG, the lower the field is — the more specific in relation to the science it is.

Algorithm

The code for computing the metrics is available here in the repository. It is well commented and segmented.

Synopsis:

1. Global Vars

   • ENV can be set to test or HPC for local and production execution.
   • FIELD_CONFIDENCE is the threshold for the MAG certainty of the field per paper. It is >50% by default.

2. Paths

   • Set the path to the parent folder of MAG (it will be the place where data is saved)
   • Set the name of the MAG folder

3. Get the Paper-Field associations

   • Group papers and paper fields by PID
   • Drop all fields that are below the threshold of certainty

4. Get the Paper Publication Years

   • Merge each paper with its publication year

5. Extend Fields with the Parent Fields

   • Run BFS on fields that we have to propagate up and note all parent fields. For instance, if Eigen Decomposition is a field we add its parent Linear Algebra and its parent Math to the fields of the paper.

6. Count Fields per Level

   • Calculate the v vector of field counts per level per paper.

7. Calculate Uniqueness

   • Run a linear scan and update the tuple counts every year.
   • For every field set per paper, find all the 2 combinations of the fields and keep track of which ones appear for the first time.

8. Get Depth and Interdisciplinarity

   • Convert the v vector into a scaled value, and standardize the distribution to keep it in bounds.
   • Save the index of the last non-zero value of the v vector.

9. Save the Metrics

   • save the file to path

Data Sample

PID	PaperFields	PubYear	LevelCounts	New_Tuples	Field_Count	Depth	Interdisciplinarity
3483532	{199539241, 190136086, 111472728, 17744445, 138885662}	1825	[2, 2, 1, 0, 0, 0]	10	5	2	-0.6337096715235878
152588939	{71924100, 141071460, 2780401607, 86803240, 151730666, 127313418, 105702510, 2780193326, 2779777117}	1884	[3, 3, 2, 1, 0, 0]	36	9	3	0.05073388992405839
134480136	{111472728, 2780349523, 138885662}	1893	[1, 1, 1, 0, 0, 0]	2	3	2	-1.3179426349523269
76015792	{71924100, 2778536324, 141071460, 86803240, 2778722699, 105702510}	1904	[2, 2, 2, 0, 0, 0]	9	6	2	-0.6335027045050068
118077477	{54355233, 24107716, 185592680, 86803240, 55493867}	1906	[2, 2, 1, 0, 0, 0]	10	5	2	-0.6337096715235878
173670722	{2780550144, 50522688, 199539241, 162324750, 17744445}	1914	[2, 2, 1, 0, 0, 0]	9	5	2	-0.6337096715235878
114636826	{185592680, 178790620, 2777517455}	1918	[1, 1, 1, 0, 0, 0]	3	3	2	-1.3179426349523269
58810875	{2524010, 2781425163, 33923547}	1919	[1, 1, 1, 0, 0, 0]	3	3	2	-1.3179426349523269

Usage

If you intend on using the PaperFields set, use {'PaperFields':literal_eval}, but it is slow. Otherwise, just read it in as a string.

pd.read_csv(path + filename, usecols=['PID','PaperFields', 'PubYear'], converters={'PaperFields':literal_eval})