<( Collecting the gold-standard data for benchmarking )
This Python notebook shows the process of benchmarking the search result ranking for the Charles Explorer application. It is a part of my diploma thesis at the Faculty of Mathematics and Physics, Charles University, Prague.
Find out more about the thesis in the GitHub repository.
Made by Jindřich Bär, 2024.
In the previous posts, we have established a methodology for benchmarking the different search result ranking algorithms. We have also collected the relevance scores for the benchmark, since the Charles Explorer application does not provide enough usage data to use for the benchmarking yet.
In this post, we will measure the current search result ranking of the Charles Explorer application to establish the baseline for the benchmarking.
We start by comparing the results from both search engines (Charles Explorer and Elsevier Scopus).
import pandas as pd
queries = pd.read_csv('./best_queries.csv')
scopus = pd.read_csv('./scopus_results.csv')
explorer = pd.read_csv('./filtered_search_results.csv')
original_queries = set(queries['0'].to_list())
scopus_queries = set(scopus['query'].unique())
print(f"Scopus missing queries: {len(original_queries.difference(scopus_queries))}")Scopus missing queries: 25
For 25 queries out of the original query set of 174 queries, Scopus does not return any results. We will exclude these queries from the benchmarking.
We proceed by calculating the prceision, recall and F1 score for the search results of the Charles Explorer application - considering the Scopus search results as the ground truth.
from utils.calc.precision_recall import get_precision, get_recall
queries = scopus['query'].unique()
precision = pd.Series(queries).map(
lambda query: get_precision(
explorer[explorer['query'] == query]['name'].to_list(),
scopus[scopus['query'] == query]['title'].to_list(),
lambda x: x.lower()
)
)
recall = pd.Series(queries).map(
lambda query: get_recall(
explorer[explorer['query'] == query]['name'].to_list(),
scopus[scopus['query'] == query]['title'].to_list(),
lambda x: x.lower()
)
)
f1 = 2 * (precision * recall) / (precision + recall)
metrics = pd.DataFrame({
'query': queries,
'precision': precision,
'recall': recall,
'f1': f1
})
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| query | precision | recall | f1 | |
|---|---|---|---|---|
| 0 | physics | 0.043011 | 0.040000 | 0.041451 |
| 1 | bolus | 0.125000 | 0.121212 | 0.123077 |
| 2 | Plavix | 0.000000 | 0.000000 | NaN |
| 3 | draft | 0.010870 | 0.010753 | 0.010811 |
| 4 | block | 0.144330 | 0.141414 | 0.142857 |
| ... | ... | ... | ... | ... |
| 144 | metaphysics | 0.020833 | 0.037736 | 0.026846 |
| 145 | angiogenesis inhibitor | 0.187500 | 0.044118 | 0.071429 |
| 146 | sports medicine | 0.109589 | 0.163265 | 0.131148 |
| 147 | clinical neurology | 0.088889 | 0.666667 | 0.156863 |
| 148 | specific | 0.000000 | 0.000000 | NaN |
149 rows × 4 columns
metrics['f1'].describe()count 114.000000
mean 0.208727
std 0.211699
min 0.010101
25% 0.074786
50% 0.137028
75% 0.265263
max 1.000000
Name: f1, dtype: float64
These calculations show us that the mean f1 score over all available queries is 0.21. This shows that the current Charles Explorer search results differ quite a lot from the Scopus search results. This can be caused by mutiple reasons - either the publications are not present in the Scopus database, or the queries are not specific enough - and the search results are returning partially disjoint sets of publications.
This is an issue that cannot be solved by simply re-ranking the Charles Explorer search results. Changing the ordering of the search results will not help if the search results themselves are not relevant. Moreover, this also limits our ability to use the Scopus search results ranking as the proxy for the relevance feedback.
We are already trying to mitigate the issue of the broad queries by evaluating the benchmark on a larger-than-usual sets of results. By collecting data for the top 100 search results (Charles Explorer only shows the first 30 results by default), we could see if the missing publications are just ranked lower or if they are not present at all.
Since this thesis is focused on the search result ranking algorithms, we will proceed with the benchmarking as planned. However, to improve the relevance score assignment, we try adding a similarity search step. Currently, we are only matching the Charles Explorer search results with the Scopus search results by the publication title (case-insensitive). This matching criterion is prone to even the slightest variations in the publication titles, which can lead to false negatives.
In the proposed similarity search step, we use the similarity of LLM (Large Language Model) embeddings to match the publication titles. This should help us to relate the publications missing from the Scopus search results to the ones present there and assign them a relevance score.
The similarity search step works as follows:
- By the means of a LLM embedding model, we calculate the embeddings for the publication titles of the Elsevier Scopus search results. We store these embeddings in a vector database.
- For each publication title in the Charles Explorer search results, we calculate its embedding. In the database, we search for the nearest embedding among Scopus search results embeddings. Futhermore, we require the retrieved document to be a result of the same query (in Elsevier Scopus) as the Charles Explorer search result.
- We calculate original document's relevance from the retrieved document's attributes - e.g. its position in Scopus search.
The LLM embeddings are vector representations of the publication titles. While those can be arbitrary vectors, they are usually optimized to capture the semantic meaning of the text. This means that texts with similar meanings should have similar embeddings - i.e. the (cosine) similarity of the embedding vectors should be high.
For the purpose of this thesis, we are embedding the documents using the all-MiniLM-L6-v2 sentence-transformer model. This model is a general-purpose English embedding model designed for running on consumer-grade hardware. Due to its small size and competitive performance, it's often used for the real-time use-cases, like semantic search or RAG (Retrieval-Augmented Generation).
https://www.sbert.net/docs/sentence_transformer/pretrained_models.html
from utils.llm.get_vector_db import vectorstore, embedder
import time
import warnings
warnings.filterwarnings("ignore")
KNN = 1
def get_similarity_position(records: list[str], query: str):
embedding_start = time.time()
vectors = embedder.embed_documents(records)
embedding_end = time.time()
results = []
for vector in vectors:
vector_db_start = time.time()
result = vectorstore.similarity_search_by_vector(vector, KNN, filter={'query': query})
vector_db_end = time.time()
if(len(result) == 0):
results.append(None)
else:
results.append({
'ranking': result[0].metadata.get('ranking'),
'embedding_duration': (embedding_end - embedding_start) / len(records),
'vector_db_roundtrip': vector_db_end - vector_db_start
})
return results
def get_positions():
new_df = pd.DataFrame()
done=0
total=len(explorer)
for query in explorer['query'].unique():
records = explorer[explorer['query'] == query]
records.reset_index(inplace=True)
similarities = get_similarity_position(records['name'].to_list(), query)
records['ranking'] = [similarity['ranking'] if similarity is not None else None for similarity in similarities]
records['embedding_duration'] = [similarity['embedding_duration'] if similarity is not None else None for similarity in similarities]
records['vector_db_roundtrip'] = [similarity['vector_db_roundtrip'] if similarity is not None else None for similarity in similarities]
new_df = pd.concat([new_df, records])
done += len(records)
print(f"Done {done} out of {total}")
return new_df
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This expands the table with the Charles Explorer search results with the rankings of the most similar publications from the Scopus database for the given queries.
As a reminder - we are trying to use these values as a proxy for the relevance of the search results. In a way, this replaces a manual relevance score assignment, which would require us to conduct a user survey to get the relevance scores for the search results.
We can now plot the distribution of the positions of the most similar publications in the Scopus search results for the Charles Explorer search results. This will help us to see whether the similarity search step helps with the missing publications problem.
import pandas as pd
import matplotlib.pyplot as plt
df = pd.read_csv('./similarity_ranking.csv')
df.rename(columns={'ranking': 'similarity_scopus_ranking'}, inplace=True)
c = df['similarity_scopus_ranking'].hist(bins=100)
c.set_title('Similarity-based ranking prediction for Charles Explorer documents')
c.set_xlabel('Predicted position in the Scopus search results')
c.set_ylabel('Number of documents')
plt.show()
While the distribution of the predicted rankings might seem skewed, this does not pose a serious problem to our benchmark.
Firstly, we are not trying to predict the exact ranking of the search results, but rather to assign a relevance score to each search result. The peak of the distribution is at the top of the rankings, which simulates the human behaviour of having clearer opinions about the few top search results.
Secondly, the left-skewed distribution might be caused by non-uniform lengths of the search result lists. Since for some of the queries, Scopus returns only a few relevant search results (100 is only the maximum limit), the resulting predicted rankings will be skewed towards the top of the list for these queries.
h = scopus.groupby('query')['ranking'].max().hist(bins=100)
h.set_title('Histogram of lengths of the Scopus search results')
h.set_xlabel('Number of documents in the result list')
h.set_ylabel('Query count')Text(0, 0.5, 'Query count')
We now set the target value for the search ranking benchmark. We add the original positions of the search results as a separate column.
rankings = pd.DataFrame()
for query in df['query'].unique():
x = df[df['query'] == query].reset_index()
x['charles_explorer_ranking'] = x.index
rankings = pd.concat([
rankings,
x
])
rankings.drop(columns=['index'], inplace=True)
rankings.reset_index(inplace=True)
rankings.drop(columns=['index'], inplace=True)
rankings.rename(columns={'ranking': 'scopus_similarity_ranking'}, inplace=True)
rankings.to_csv('./rankings.csv', index=False)
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| id | year | name | faculty | faculty_name | query | similarity_scopus_ranking | embedding_duration | vector_db_roundtrip | charles_explorer_ranking | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 491147 | 2014.0 | Lexical semantic conversions in a valency lexicon | 11320 | Faculty of Mathematics and Physics | lexical semantics | 0.0 | 0.021093 | 0.019749 | 0 |
| 1 | 592464 | 2020.0 | Dirk Geeraerts:Theories of Lexical Semantics | 11210 | Faculty of Arts | lexical semantics | 0.0 | 0.021093 | 0.019631 | 1 |
| 2 | 594640 | NaN | DIACR-Ita @ EVALITA2020: Overview of the EVALI... | -1 | Unknown faculty | lexical semantics | 0.0 | 0.021093 | 0.015370 | 2 |
| 3 | 588808 | 2020.0 | Dual semantics of intransitive verbs: lexical ... | 11210 | Faculty of Arts | lexical semantics | 5.0 | 0.021093 | 0.015556 | 3 |
| 4 | 268937 | 2000.0 | Manfred Stede: Lexical Semantics and Knowledge... | 11320 | Faculty of Mathematics and Physics | lexical semantics | 2.0 | 0.021093 | 0.015275 | 4 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 9264 | 73261 | 2005.0 | Modern X-ray imaging techniques and their use ... | -1 | Unknown faculty | biology | 94.0 | 0.019262 | 0.016730 | 95 |
| 9265 | 31897 | 2003.0 | Teaching tasks for biology education | 11310 | Faculty of Science | biology | 18.0 | 0.019262 | 0.013611 | 96 |
| 9266 | 566168 | 2019.0 | Hands-on activities in biology: students' opinion | 11310 | Faculty of Science | biology | 18.0 | 0.019262 | 0.012192 | 97 |
| 9267 | 279719 | 2013.0 | One of the Overlooked Themes in High School Pr... | 11310 | Faculty of Science | biology | 1.0 | 0.019262 | 0.013341 | 98 |
| 9268 | 551485 | 2018.0 | Evolutionary biology : In the history, today a... | 11310 | Faculty of Science | biology | 52.0 | 0.019262 | 0.013132 | 99 |
9269 rows × 10 columns
Using the original ranking positions and the predicted ranking positions as the source for the relevance feedback, we can calculate the nDCG (Normalized Discounted Cumulative Gain) score for the search result ranking.
The nDCG score is a measure of the ranking quality of the search results. It is calculated as the ratio of the DCG (Discounted Cumulative Gain) score to the IDCG (Ideal Discounted Cumulative Gain) score. The DCG score is calculated as the sum of the relevance scores of the search results, discounted by their position in the ranking. The IDCG score is the DCG score of the ideal ranking of the search results.
To transform the predicted Scopus rankings into relevance feedback, we introduce a new function nDCG score calculation, which requires more relevant documents to have higher relevance scores.
The inverse proportionality is achieved by the following formula:
where nDCG score. For the purpose of this thesis, we set +1 in the denominator is necessary to avoid division by zero, as our rankings are 0-based.
While it would be possible to achieve the ranking - relevance transformation via e.g. subtracting the predicted ranking from the total number of search results, our proposed method with
from typing import List
import numpy as np
def get_ndcg(gold_rankings: List[int]):
dcg = 0
for i, result in enumerate(gold_rankings):
relevance = 5 / (result + 1)
dcg += relevance / np.log2(i + 2)
return dcgscores = pd.DataFrame()
queries = []
dcgs = []
best_ndcgs = []
for query in rankings['query'].unique():
queries.append(query)
dcgs.append(get_ndcg(rankings[rankings['query'] == query]['similarity_scopus_ranking'].to_list()))
best_ndcgs.append(get_ndcg(rankings[rankings['query'] == query].sort_values('similarity_scopus_ranking')['similarity_scopus_ranking'].to_list()))
scores['query'] = queries
scores['dcg'] = dcgs
scores['idcg'] = best_ndcgs
scores['ndcg'] = scores['dcg'] / scores['idcg']
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| query | dcg | idcg | ndcg | |
|---|---|---|---|---|
| 0 | lexical semantics | 29.482590 | 33.308123 | 0.885147 |
| 1 | booster | 11.771938 | 17.401799 | 0.676478 |
| 2 | logic | 4.557156 | 11.233671 | 0.405669 |
| 3 | gabapentin | 18.529698 | 21.165926 | 0.875449 |
| 4 | thalidomide | 13.151393 | 20.222288 | 0.650341 |
| ... | ... | ... | ... | ... |
| 169 | sports medicine | 27.963706 | 33.238549 | 0.841303 |
| 170 | dendrology | NaN | NaN | NaN |
| 171 | alienism | 88.309044 | 93.423651 | 0.945254 |
| 172 | hedonism | 42.712391 | 47.876866 | 0.892130 |
| 173 | biology | 18.064385 | 31.570575 | 0.572191 |
174 rows × 4 columns
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| dcg | idcg | ndcg | |
|---|---|---|---|
| count | 149.000000 | 149.000000 | 149.000000 |
| mean | 14.919819 | 19.167405 | 0.761607 |
| std | 16.810894 | 17.665142 | 0.180979 |
| min | 0.094340 | 0.094340 | 0.405669 |
| 25% | 5.250473 | 7.704989 | 0.627563 |
| 50% | 9.527864 | 14.840570 | 0.736246 |
| 75% | 18.064385 | 24.112511 | 0.934206 |
| max | 104.693354 | 104.693354 | 1.000000 |
This gives us values for our benchmark - the nDCG values for the original Charles Explorer result ranking act as the baseline value. We see that the mean nDCG score over all queries is 0.76, which is a good starting point for the benchmarking.
We can now proceed to collecting the graph data statistics for the publications in the search results. We will use the Charles Explorer API to get the graph data for the publications in the search results.
The following scripts collects betweenness centrality for 1-hop and 2-hop neighbourhoods of the publications in the search results. The "betweenness centrality" is a graph node measure that quantifies the importance of a node in a graph. It is calculated as the number of shortest paths between all pairs of nodes that pass through the node in question:
where
While this is often calculated for larger graphs, it is an useful measure for ego-networks too, as it can help us quantify the importance of a node in its local neighbourhood. Everett et. al have shown that the betweenness centrality might be strongly correlated with the actual global betweenness of a node in the graph.
In the following cells, we calculate the 1- and 2-hop centrality, node degree, size of the neighborhood node cut and the katz centrality for the publications in the search results. We then store these values in a CSV file for further analysis.
from utils.memgraph import get_centralities
import pandas as pd
local_centrality = pd.DataFrame()
for i, query in enumerate(rankings['query'].unique()):
if i % 10 == 0:
print(f"{i}/{len(rankings['query'].unique())}")
ids = rankings[rankings['query'] == query]['id'].astype(str).to_list()
centralities = get_centralities(ids, 1, 2)
centralities['query'] = query
local_centrality = pd.concat([local_centrality, centralities])
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| id | centrality_1 | centrality_2 | query | |
|---|---|---|---|---|
| 0 | 74651 | 0.000000 | 0.000000 | lexical semantics |
| 1 | 97393 | 0.000000 | 0.000000 | lexical semantics |
| 2 | 117637 | 0.000000 | 0.000000 | lexical semantics |
| 3 | 118521 | 0.002127 | 0.000026 | lexical semantics |
| 4 | 145132 | 0.000491 | 0.002471 | lexical semantics |
| ... | ... | ... | ... | ... |
| 95 | 588322 | 0.000000 | 0.000000 | biology |
| 96 | 592720 | 0.000313 | 0.000168 | biology |
| 97 | 605136 | 0.000000 | 0.000000 | biology |
| 98 | 605641 | 0.001118 | 0.000168 | biology |
| 99 | 621001 | 0.000000 | 0.000000 | biology |
9269 rows × 4 columns
from utils.memgraph import get_neighborhood_node_cut
import pandas as pd
rankings = pd.read_csv('./rankings.csv')
node_cuts = pd.DataFrame()
for i, query in enumerate(rankings['query'].unique()):
if i % 10 == 0:
print(f"{i}/{len(rankings['query'].unique())}")
ids = rankings[rankings['query'] == query]['id'].astype(str).to_list()
current_node_cuts = get_neighborhood_node_cut(ids)
current_node_cuts['query'] = query
node_cuts = pd.concat([node_cuts, current_node_cuts])
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| id | node_cut | query | |
|---|---|---|---|
| 0 | 491147 | 99 | lexical semantics |
| 1 | 592464 | 29 | lexical semantics |
| 2 | 594640 | 0 | lexical semantics |
| 3 | 588808 | 98 | lexical semantics |
| 4 | 268937 | 44 | lexical semantics |
| ... | ... | ... | ... |
| 95 | 73261 | 282 | biology |
| 96 | 31897 | 154 | biology |
| 97 | 566168 | 75 | biology |
| 98 | 279719 | 99 | biology |
| 99 | 551485 | 62 | biology |
9269 rows × 3 columns
from utils.memgraph import get_degrees
import pandas as pd
degrees = pd.DataFrame()
for i, query in enumerate(rankings['query'].unique()):
if i % 10 == 0:
print(f"{i}/{len(rankings['query'].unique())}")
ids = rankings[rankings['query'] == query]['id'].astype(str).to_list()
new_degrees = get_degrees(ids)
new_degrees['query'] = query
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| id | degree | query | |
|---|---|---|---|
| 0 | 74651 | 1 | lexical semantics |
| 1 | 118521 | 2 | lexical semantics |
| 2 | 97393 | 1 | lexical semantics |
| 3 | 117637 | 1 | lexical semantics |
| 4 | 145132 | 4 | lexical semantics |
| ... | ... | ... | ... |
| 95 | 588322 | 1 | biology |
| 96 | 592720 | 2 | biology |
| 97 | 605641 | 2 | biology |
| 98 | 605136 | 1 | biology |
| 99 | 621001 | 1 | biology |
9269 rows × 3 columns
from utils.memgraph import get_katz_centrality
import pandas as pd
katz = pd.DataFrame({'id': [], 'katz_centrality': []})
for i, id in enumerate(rankings['id'].unique()):
if i % 500 == 0:
print(f"{i}/{len(rankings['id'].unique())}")
katz_centrality = get_katz_centrality(id)
katz = pd.concat([katz, pd.DataFrame({'id': [id], 'katz_centrality': [katz_centrality]})])0/9105
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| id | katz_centrality | |
|---|---|---|
| 0 | 491147.0 | 0.200 |
| 1 | 592464.0 | 0.200 |
| 2 | 594640.0 | 1.496 |
| 3 | 588808.0 | 0.200 |
| 4 | 268937.0 | 0.200 |
| ... | ... | ... |
| 9100 | 73261.0 | 0.200 |
| 9101 | 31897.0 | 1.000 |
| 9102 | 566168.0 | 0.400 |
| 9103 | 279719.0 | 0.400 |
| 9104 | 551485.0 | 0.200 |
9105 rows × 2 columns
katz.to_csv('./katz.csv', index=False)
degrees.to_csv('./degrees.csv', index=False)
node_cuts.to_csv('./node_cuts.csv', index=False)
local_centrality.to_csv('./local_centrality.csv', index=False)Once we collect all the graph measures we want to utilize for the reranking, we can proceed to the actual reranking of the search results. We merge all of the collected data into a single dataframe, with separate columns for each of the graph measures.
import pandas as pd
rankings = pd.read_csv('./rankings.csv')
local_centrality = pd.read_csv('./local_centrality.csv')
degrees = pd.read_csv('./degrees.csv')
katz = pd.read_csv('./katz.csv')
node_cuts = pd.read_csv('./node_cuts.csv')
centralities = rankings.join(local_centrality[['id', 'centrality_1', 'centrality_2']].set_index('id'), how='left', on='id', rsuffix='_centrality')
centralities = centralities.join(degrees[['id', 'degree']].set_index('id'), how='left', on='id', rsuffix='_degree')
centralities = centralities.join(katz[['id', 'katz_centrality']].set_index('id'), how='left', on='id', rsuffix='_katz')
centralities = centralities.join(node_cuts[['id', 'node_cut']].set_index('id'), how='left', on='id', rsuffix='_node_cut')
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| id | year | name | faculty | faculty_name | query | similarity_scopus_ranking | embedding_duration | vector_db_roundtrip | charles_explorer_ranking | centrality_1 | centrality_2 | degree | katz_centrality | node_cut | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 491147 | 2014.0 | Lexical semantic conversions in a valency lexicon | 11320 | Faculty of Mathematics and Physics | lexical semantics | 0.0 | 0.021093 | 0.019749 | 0 | 0.000000 | 0.000000 | 1 | 0.200 | 99 |
| 1 | 592464 | 2020.0 | Dirk Geeraerts:Theories of Lexical Semantics | 11210 | Faculty of Arts | lexical semantics | 0.0 | 0.021093 | 0.019631 | 1 | 0.000000 | 0.000000 | 1 | 0.200 | 29 |
| 2 | 594640 | NaN | DIACR-Ita @ EVALITA2020: Overview of the EVALI... | -1 | Unknown faculty | lexical semantics | 0.0 | 0.021093 | 0.015370 | 2 | 0.000545 | 0.000002 | 5 | 1.496 | 0 |
| 3 | 588808 | 2020.0 | Dual semantics of intransitive verbs: lexical ... | 11210 | Faculty of Arts | lexical semantics | 5.0 | 0.021093 | 0.015556 | 3 | 0.000000 | 0.000000 | 1 | 0.200 | 98 |
| 4 | 268937 | 2000.0 | Manfred Stede: Lexical Semantics and Knowledge... | 11320 | Faculty of Mathematics and Physics | lexical semantics | 2.0 | 0.021093 | 0.015275 | 4 | 0.000000 | 0.000000 | 1 | 0.200 | 44 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 9264 | 73261 | 2005.0 | Modern X-ray imaging techniques and their use ... | -1 | Unknown faculty | biology | 94.0 | 0.019262 | 0.016730 | 95 | 0.000000 | 0.000000 | 1 | 0.200 | 282 |
| 9265 | 31897 | 2003.0 | Teaching tasks for biology education | 11310 | Faculty of Science | biology | 18.0 | 0.019262 | 0.013611 | 96 | 0.001878 | 0.000670 | 5 | 1.000 | 154 |
| 9266 | 566168 | 2019.0 | Hands-on activities in biology: students' opinion | 11310 | Faculty of Science | biology | 18.0 | 0.019262 | 0.012192 | 97 | 0.001118 | 0.000084 | 2 | 0.400 | 75 |
| 9267 | 279719 | 2013.0 | One of the Overlooked Themes in High School Pr... | 11310 | Faculty of Science | biology | 1.0 | 0.019262 | 0.013341 | 98 | 0.006841 | 0.057311 | 2 | 0.400 | 99 |
| 9268 | 551485 | 2018.0 | Evolutionary biology : In the history, today a... | 11310 | Faculty of Science | biology | 52.0 | 0.019262 | 0.013132 | 99 | 0.000000 | 0.000000 | 1 | 0.200 | 62 |
11865 rows × 15 columns
To combine all the available measures into the new relevance score for reranking, we try two different approaches:
The first approach is to use (an L2 regularized) linear regression model. Such model learns linear combination coefficients for each of the graph measures, which are then used to calculate the new relevance score. This approach is simple and interpretable, but it might not capture the non-linear relationships between the graph measures and the relevance score.
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import Ridge
from sklearn.model_selection import train_test_split
projection = centralities[['id', 'charles_explorer_ranking', 'centrality_1', 'centrality_2', 'degree', 'katz_centrality', 'node_cut', 'similarity_scopus_ranking']].dropna()
projection['katz_centrality'] = projection['katz_centrality'].replace([float('inf')], projection['katz_centrality'].median())
feature_columns = ['charles_explorer_ranking', 'centrality_1', 'centrality_2', 'degree', 'katz_centrality', 'node_cut']
X = projection[feature_columns]
# We predict the "relevance feedback" calculated from the Scopus ranking, just like in the NDCG calculation
y = 5 / (projection['similarity_scopus_ranking'] + 1)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
linear_model = Ridge(max_iter=1000)
linear_pipeline = Pipeline([
('scaler', StandardScaler()),
('regression', linear_model)
])
linear_pipeline.fit(X_train, y_train)
from sklearn.metrics import mean_squared_error
y_pred = linear_pipeline.predict(X_test)
print(mean_squared_error(y_test, y_pred))
print(list(zip(feature_columns, linear_model.coef_)))2.1015957992306977
[('charles_explorer_ranking', -0.23068435940164658), ('centrality_1', 0.08316576326530806), ('centrality_2', 0.010186983762182704), ('degree', -0.08756245520393091), ('katz_centrality', -0.004918498830738786), ('node_cut', -0.027334632864995427)]
On the test set (
This means that (at least for the linear regression model), the graph measures do not provide much useful information for the reranking of the search results.
While this might be true - and our attempt at improving the search result ranking using the graph measures might have failed - we can try to learn a more complex model that can capture the non-linear relationships between the graph measures and the relevance score.
The second approach is to use a random forest regression model. This model is a non-linear model that can capture the non-linear relationships between the graph measures and the relevance score. It is also more robust to the noise in the data, as it averages over multiple decision trees.
from sklearn.neural_network import MLPRegressor
neural_network = MLPRegressor(hidden_layer_sizes=(100, 100), max_iter=1000, verbose=True)
pipeline = Pipeline([
('scaler', StandardScaler()),
('neural_network', neural_network)
])
pipeline.fit(X_train, y_train)
from sklearn.metrics import mean_squared_error
y_pred = pipeline.predict(X_test)
mean_squared_error(y_test, y_pred)Iteration 1, loss = 1.02231286
Iteration 2, loss = 0.98644778
Iteration 3, loss = 0.98140297
Iteration 4, loss = 0.97746657
Iteration 5, loss = 0.97548573
Iteration 6, loss = 0.97641211
Iteration 7, loss = 0.97256164
Iteration 8, loss = 0.97151457
Iteration 9, loss = 0.97134148
Iteration 10, loss = 0.96817720
Iteration 11, loss = 0.96761415
Iteration 12, loss = 0.96731812
Iteration 13, loss = 0.96578961
Iteration 14, loss = 0.96533688
Iteration 15, loss = 0.96432081
Iteration 16, loss = 0.96331435
Iteration 17, loss = 0.96119211
Iteration 18, loss = 0.96223902
Iteration 19, loss = 0.96258106
Iteration 20, loss = 0.96601726
Iteration 21, loss = 0.96142456
Iteration 22, loss = 0.95834626
Iteration 23, loss = 0.96036677
Iteration 24, loss = 0.95794635
Iteration 25, loss = 0.95848961
Iteration 26, loss = 0.95653644
Iteration 27, loss = 0.95243912
Iteration 28, loss = 0.95186894
Iteration 29, loss = 0.95210193
Iteration 30, loss = 0.95254282
Iteration 31, loss = 0.95328308
Iteration 32, loss = 0.95021622
Iteration 33, loss = 0.95323434
Iteration 34, loss = 0.95002858
Iteration 35, loss = 0.95316751
Iteration 36, loss = 0.95125432
Iteration 37, loss = 0.94835466
Iteration 38, loss = 0.94961246
Iteration 39, loss = 0.94508779
Iteration 40, loss = 0.94339325
Iteration 41, loss = 0.94475526
Iteration 42, loss = 0.94074612
Iteration 43, loss = 0.94203259
Iteration 44, loss = 0.94607752
Iteration 45, loss = 0.94781724
Iteration 46, loss = 0.94040869
Iteration 47, loss = 0.93854604
Iteration 48, loss = 0.94117788
Iteration 49, loss = 0.93691948
Iteration 50, loss = 0.94035281
Iteration 51, loss = 0.93614566
Iteration 52, loss = 0.93492421
Iteration 53, loss = 0.93621770
Iteration 54, loss = 0.93652761
Iteration 55, loss = 0.93773258
Iteration 56, loss = 0.93270883
Iteration 57, loss = 0.93404918
Iteration 58, loss = 0.93495718
Iteration 59, loss = 0.93344590
Iteration 60, loss = 0.93545076
Iteration 61, loss = 0.93380044
Iteration 62, loss = 0.93152079
Iteration 63, loss = 0.93050401
Iteration 64, loss = 0.92739720
Iteration 65, loss = 0.93463387
Iteration 66, loss = 0.92761031
Iteration 67, loss = 0.92317816
Iteration 68, loss = 0.92489747
Iteration 69, loss = 0.92327646
Iteration 70, loss = 0.92326897
Iteration 71, loss = 0.93223231
Iteration 72, loss = 0.92320831
Iteration 73, loss = 0.92300850
Iteration 74, loss = 0.92791904
Iteration 75, loss = 0.92347111
Iteration 76, loss = 0.92055211
Iteration 77, loss = 0.92071812
Iteration 78, loss = 0.91906237
Iteration 79, loss = 0.91893128
Iteration 80, loss = 0.91934245
Iteration 81, loss = 0.91900184
Iteration 82, loss = 0.91879487
Iteration 83, loss = 0.91595051
Iteration 84, loss = 0.91820723
Iteration 85, loss = 0.91322645
Iteration 86, loss = 0.91371769
Iteration 87, loss = 0.91552889
Iteration 88, loss = 0.91291932
Iteration 89, loss = 0.91285456
Iteration 90, loss = 0.91328988
Iteration 91, loss = 0.91185761
Iteration 92, loss = 0.91115108
Iteration 93, loss = 0.91215725
Iteration 94, loss = 0.91422760
Iteration 95, loss = 0.91005531
Iteration 96, loss = 0.90999359
Iteration 97, loss = 0.91183829
Iteration 98, loss = 0.90776120
Iteration 99, loss = 0.91133150
Iteration 100, loss = 0.90595804
Iteration 101, loss = 0.90832610
Iteration 102, loss = 0.91433753
Iteration 103, loss = 0.90366230
Iteration 104, loss = 0.90306604
Iteration 105, loss = 0.90444941
Iteration 106, loss = 0.90652510
Iteration 107, loss = 0.90186100
Iteration 108, loss = 0.90250346
Iteration 109, loss = 0.90321419
Iteration 110, loss = 0.90705455
Iteration 111, loss = 0.90062882
Iteration 112, loss = 0.89881434
Iteration 113, loss = 0.89988572
Iteration 114, loss = 0.90620232
Iteration 115, loss = 0.90023621
Iteration 116, loss = 0.90353988
Iteration 117, loss = 0.89826651
Iteration 118, loss = 0.89579876
Iteration 119, loss = 0.89883197
Iteration 120, loss = 0.89809465
Iteration 121, loss = 0.89804636
Iteration 122, loss = 0.89641157
Iteration 123, loss = 0.89463258
Iteration 124, loss = 0.89474943
Iteration 125, loss = 0.89773291
Iteration 126, loss = 0.89832722
Iteration 127, loss = 0.90165782
Iteration 128, loss = 0.89367484
Iteration 129, loss = 0.89195153
Iteration 130, loss = 0.89007655
Iteration 131, loss = 0.88930204
Iteration 132, loss = 0.88911372
Iteration 133, loss = 0.88859489
Iteration 134, loss = 0.89100618
Iteration 135, loss = 0.89109479
Iteration 136, loss = 0.88916153
Iteration 137, loss = 0.88514613
Iteration 138, loss = 0.88710152
Iteration 139, loss = 0.89005088
Iteration 140, loss = 0.88462308
Iteration 141, loss = 0.88636593
Iteration 142, loss = 0.88389683
Iteration 143, loss = 0.88229623
Iteration 144, loss = 0.88686781
Iteration 145, loss = 0.88770173
Iteration 146, loss = 0.88901551
Iteration 147, loss = 0.88509529
Iteration 148, loss = 0.88058844
Iteration 149, loss = 0.88261315
Iteration 150, loss = 0.88141532
Iteration 151, loss = 0.87877532
Iteration 152, loss = 0.88018106
Iteration 153, loss = 0.88580437
Iteration 154, loss = 0.88216152
Iteration 155, loss = 0.88110478
Iteration 156, loss = 0.88355416
Iteration 157, loss = 0.87749537
Iteration 158, loss = 0.87847931
Iteration 159, loss = 0.87914908
Iteration 160, loss = 0.87741585
Iteration 161, loss = 0.87848044
Iteration 162, loss = 0.87587548
Iteration 163, loss = 0.87523249
Iteration 164, loss = 0.88046574
Iteration 165, loss = 0.87175654
Iteration 166, loss = 0.87855644
Iteration 167, loss = 0.87537240
Iteration 168, loss = 0.87450106
Iteration 169, loss = 0.87996410
Iteration 170, loss = 0.87596864
Iteration 171, loss = 0.87291909
Iteration 172, loss = 0.87485277
Iteration 173, loss = 0.87059811
Iteration 174, loss = 0.87396509
Iteration 175, loss = 0.86761399
Iteration 176, loss = 0.87283183
Iteration 177, loss = 0.87068696
Iteration 178, loss = 0.87077601
Iteration 179, loss = 0.87008127
Iteration 180, loss = 0.87151137
Iteration 181, loss = 0.87403838
Iteration 182, loss = 0.87257197
Iteration 183, loss = 0.87071542
Iteration 184, loss = 0.87366716
Iteration 185, loss = 0.87533898
Iteration 186, loss = 0.87361373
Training loss did not improve more than tol=0.000100 for 10 consecutive epochs. Stopping.
2.0497850932278974
We see that the performance of the neural network model is only marginally better than the linear regression model. The mean squared error on the test set is
While for both models, we have calculated the mean squared error of predicting the relevance scores, this provides only partial information about the actual performance of the model for reranking.
To assess the reranking performance of both models, we calculate the nDCG score for the reranked search results. We use the same formula as for the original search results, but with the new relevance scores assigned by the models.
centralities = centralities.merge(
pd.DataFrame({
'id': projection['id'],
'linear': linear_pipeline.predict(X),
'neural': pipeline.predict(X)
}).set_index('id'),
how='left',
on=('id')
)dcg_centrality_1 = []
dcg_centrality_2 = []
dcg_degree = []
dcg_katz = []
dcg_node_cut = []
linear = []
neural = []
for query in scores['query']:
x = centralities[centralities['query'] == query].drop_duplicates(subset=['id'])
# dcg_centrality_1.append(
# get_ndcg(x.sort_values('centrality_1', ascending=False)['similarity_scopus_ranking'].to_list())
# )
# dcg_centrality_2.append(
# get_ndcg(x.sort_values('centrality_2', ascending=False)['similarity_scopus_ranking'].to_list())
# )
# dcg_degree.append(
# get_ndcg(x.sort_values('degree', ascending=False)['similarity_scopus_ranking'].to_list())
# )
# dcg_katz.append(
# get_ndcg(x.sort_values('katz_centrality', ascending=False)['similarity_scopus_ranking'].to_list())
# )
# dcg_node_cut.append(
# get_ndcg(x.sort_values('node_cut', ascending=False)['similarity_scopus_ranking'].to_list())
# )
linear.append(
get_ndcg(x.sort_values('linear', ascending=False)['similarity_scopus_ranking'].to_list())
)
neural.append(
get_ndcg(x.sort_values('neural', ascending=False)['similarity_scopus_ranking'].to_list())
)
# scores['dcg_1_centrality'] = dcg_centrality_1
# scores['dcg_2_centrality'] = dcg_centrality_2
# scores['dcg_degree'] = dcg_degree
# scores['dcg_katz'] = dcg_katz
# scores['dcg_node_cut'] = dcg_node_cut
scores['dcg_linear'] = linear
scores['dcg_neural'] = neural
# scores['ndcg_1_centrality'] = scores['dcg_1_centrality'] / scores['idcg']
# scores['ndcg_2_centrality'] = scores['dcg_2_centrality'] / scores['idcg']
# scores['ndcg_degree'] = scores['dcg_degree'] / scores['idcg']
# scores['ndcg_katz'] = scores['dcg_katz'] / scores['idcg']
# scores['ndcg_node_cut'] = scores['dcg_node_cut'] / scores['idcg']
scores['ndcg_linear'] = scores['dcg_linear'] / scores['idcg']
scores['ndcg_neural'] = scores['dcg_neural'] / scores['idcg']
scores.drop(columns=['dcg_linear', 'dcg_neural'], inplace=True)
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| dcg | idcg | ndcg | ndcg_linear | ndcg_neural | |
|---|---|---|---|---|---|
| count | 149.000000 | 149.000000 | 149.000000 | 149.000000 | 149.000000 |
| mean | 14.919819 | 19.167405 | 0.761607 | 0.746176 | 0.770519 |
| std | 16.810894 | 17.665142 | 0.180979 | 0.172590 | 0.178775 |
| min | 0.094340 | 0.094340 | 0.405669 | 0.404108 | 0.425830 |
| 25% | 5.250473 | 7.704989 | 0.627563 | 0.618646 | 0.615640 |
| 50% | 9.527864 | 14.840570 | 0.736246 | 0.735163 | 0.759933 |
| 75% | 18.064385 | 24.112511 | 0.934206 | 0.904977 | 0.955842 |
| max | 104.693354 | 104.693354 | 1.000000 | 1.000000 | 1.000000 |
We see that the nDCG score for both the models utilizing the graph measures is lower - or comparable - to the nDCG score of the original search results.
This shows that the graph measures we have collected do not provide much useful information for the reranking of the search results. Note that while the evaluation of the reranking performance is done on the entire set (including the linear regression / neural network training set), the results are still not any better than the original search results. This hints at the high dimensionality of the problem and the lack of generalization of the models.
As mentioned before, the Scopus search result ranking is likely mainly influenced by the relevance of the search results themselves, rather than any other - more global - publication measures. In a way, the fact that the graph measures do not help with the reranking does not come as a surprise. This might be also partially caused by the title similarity search step, which helps with the missing publications problem.
While this concludes the search result ranking benchmarking for the Charles Explorer application (as we do not have better target data to use for the benchmarking), we can still try to get insights on the social network graph structure and the publication popularity.
To perform this experiment, we try to find relationship between the global publication popularity - as captured by the citation count - and the local graph measures as we have defined them before.