Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних
The paper is devoted to improving semi-supervised clustering methods and comparing their accuracy and robustness. The proposed approach is based on expanding a clustering algorithm for using an available set of labels by replacing the distance function. Using the distance function considers not only...
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| author | Lyubchyk, Leonid Yamkovyi, Klym |
| author_facet | Lyubchyk, Leonid Yamkovyi, Klym |
| author_institution_txt_mv | [
{
"author": "Leonid Lyubchyk",
"institution": "National Technical University “Kharkiv Polytechnic Institute”, Kharkiv"
},
{
"author": "Klym Yamkovyi",
"institution": "National Technical University “Kharkiv Polytechnic Institute”, Kharkiv"
}
] |
| author_sort | Lyubchyk, Leonid |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
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| datestamp_date | 2023-05-21T20:04:38Z |
| description | The paper is devoted to improving semi-supervised clustering methods and comparing their accuracy and robustness. The proposed approach is based on expanding a clustering algorithm for using an available set of labels by replacing the distance function. Using the distance function considers not only spatial data but also available labels. Moreover, the proposed distance function could be adopted for working with ordinal variables as labels. An extended approach is also considered, based on a combination of unsupervised k-medoids methods, modified for using only labeled data during the medoids calculation step, supervised method of k nearest neighbor, and unsupervised k-means. The learning algorithm uses information about the nearest points and classes’ centers of mass. The results demonstrate that even a small amount of labeled data allows us to use semi-supervised learning, and proposed modifications improve accuracy and algorithm performance, which was found during experiments. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2022.4.03 |
| first_indexed | 2025-07-17T10:27:22Z |
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L.M. Lyubchyk, K.S. Yamkovyi, 2022
34 ISSN 1681–6048 System Research & Information Technologies, 2022, №4
TIДC
ПРОГРЕСИВНІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ,
ВИСОКОПРОДУКТИВНІ КОМП’ЮТЕРНІ
СИСТЕМИ
UDC 519.925.51
DOI: 10.20535/SRIT.2308-8893.2022.4.03
COMPARATIVE ANALYSIS OF MODIFIED SEMI-SUPERVISED
LEARNING ALGORITHMS ON A SMALL AMOUNT OF
LABELED DATA
L.M. LYUBCHYK, K.S. YAMKOVYI
Abstract. The paper is devoted to improving semi-supervised clustering methods
and comparing their accuracy and robustness. The proposed approach is based on
expanding a clustering algorithm for using an available set of labels by replacing the
distance function. Using the distance function considers not only spatial data but
also available labels. Moreover, the proposed distance function could be adopted for
working with ordinal variables as labels. An extended approach is also considered,
based on a combination of unsupervised k-medoids methods, modified for using
only labeled data during the medoids calculation step, supervised method of k nearest
neighbor, and unsupervised k-means. The learning algorithm uses information about
the nearest points and classes’ centers of mass. The results demonstrate that even a
small amount of labeled data allows us to use semi-supervised learning, and pro-
posed modifications improve accuracy and algorithm performance, which was found
during experiments.
Keywords: center of mass, clustering, distance function, medoids, nearest neighbor,
semi-supervised learning.
INTRODUCTION
A large amount of data was produced recently, and nowadays humanity has the
opportunity to store and process all this data. In all spheres of life, people try to
use various data for optimizing business and life-improving using AI and data
mining.
There are several approaches to data processing and analysis problems
within the framework of machine learning (ML) paradigms. One of them is
unsupervised learning when one tries to detect inner structure or patterns without
human supervision. The most efficient approach in ML is supervised learning
when we have some data with labels and try to learn a model function on data
points as pairs of feature vectors and suitable labels. In many cases, there is no
opportunity to label all data from different cases, causes are too complex and
expensive experiments, data streaming with large frequency or just high cost of
data labeling. Therefore, in this case, a satisfactory compromise is semi-
supervised learning [1, 2], when we use datasets with a small amount of label that
Comparative analysis of modified semi-supervised learning algorithms on a small amount …
Системні дослідження та інформаційні технології, 2022, №4 35
allows learning better its inner structure, which is illustrated by (Fig. 1).
Semi-supervised learning includes a variety
of different approaches and can be used for any
popular data analysis problems, such as cluster-
ing, anomaly detection, latent variables models,
and many overs. In this paper, the object of the
study is the process of the data points classifica-
tions, namely, identifying to which of a set of
categories a new observation belongs to using a
training set of data containing observations
whose category membership is known for a piece
of data. The purpose is to develop an improved
combined semi-supervised method using already
existing supervised and unsupervised algorithms
and compare their accuracy and robustness.
PROBLEM STATEMENT
Given a set of l labeled examples { 1 1, , , , }l lx y x y , where ix – feature vec-
tor of i-th example and iy – its label (class), 1 2, , , ,ly y y Y and a set of u
unlabeled data { 1, , }l l ux x 1 2, , , l ux x x X . The goal is to determine
some function using given sets that will give correct mapping of points from X to
Y: jj yxf )( for any point from X .
REVIEW OF LITERATURE
The semi-supervised learning approach described in the literature is not so widely
investigated as unsupervised or supervised, especially algorithms implementation.
In [2] presented an overview of semi-supervised approaches that describe as-
sumptions of semi-supervised learning especially: smoothness, low-density, and
manifold.
In particular, the semi-supervised approach demonstrates high efficiency in
solving clustering problems. The idea of the corresponding improvement of clus-
tering algorithm was described in the review [4]. Majority of these methods are
modifications of the popular k-means clustering method. As the base method
chosen for improvement within the semi-supervised paradigm, the unsupervised
k-medoids approach also known as PAM (Partitioning Around Medoid) algo-
rithm, proposed in [5]. A medoid is a point in the cluster, whose average dissimi-
larities with all the other points in the cluster is minimum. k-medoid is a partition-
ing technique of clustering, which clusters the data set of n objects into k clusters,
with the number k of clusters assumed known a priori. Both the k-means and
k-medoids algorithms are partitional, which breaks the dataset up into groups, and
both attempt to minimize the distance between points labeled to be in a cluster,
and a point designated as the center of that cluster. In contrast to the k-means al-
gorithm, k-medoids choose data points as centers and can be used with arbitrary
Fig. 1. Example of unlabeled
data in semi-supervised
learning (adapted from [3])
L.M. Lyubchyk, K.S. Yamkovyi
ISSN 1681–6048 System Research & Information Technologies, 2022, №4 36
distances, while in k-means the center of a cluster is the average between the
points in the cluster (Fig. 2). Consequently, k-medoids are more robust to noise
and outliers as compared to k-means.
Another clustering method refined within the implementation of semi-
supervised paradigm is DBSCAN – Density-Based Spatial Clustering of Applica-
tions with Noise proposed in [7]. The idea is to find core samples of high density
and expand clusters from them. Such an approach is suitable for data that contains
clusters of similar density. Based on a set of points, DBSCAN groups together
points that are close to each other based on distance measurement, wherein it also
marks as outliers the points that are in low-density regions.
A widespread clustering algorithm is also agglomerative clustering, which is
the typical type of hierarchical clustering used to group objects in clusters based
on their distance to each other. The algorithm starts by treating each object as a
singleton cluster. Next, pairs of clusters are successively merged until all clusters
have been merged into one big cluster containing all objects. The result is a tree-
based representation of the objects – dendrogram (Fig. 3) [8].
The supervised approach for clustering problem is described in [10]. The
nearest neighbor decision rule assigns to an unclassified sample point the classifi-
cation of the nearest of a set of previously classified points. Thus, for any number
Fig. 3. Dendrogram of hierarchical clustering (adapted from [9])
Fig. 2. Mean and medoid difference (adapted from [6]): a —mean; b — medoids
a b
Comparative analysis of modified semi-supervised learning algorithms on a small amount …
Системні дослідження та інформаційні технології, 2022, №4 37
of categories, the probability of error of the nearest neighbor rule is bounded
above by twice the Bayes probability of error. In this sense, it may be said that
half the classification information in an infinite sample set is contained in the
nearest neighbor.
MATERIALS AND METHODS
Distance function extension
As was shown above the major clustering methods form clusters based only on
distance function. So we made the assumption that feature space can be extended
by additional dimensions with information about available labels. We develop
multiple distance functions that take to account that label dimension. The pro-
posed approach allows concentrating attention on distance function creation and
the use of already implemented and optimized clustering algorithms.
As a base distance metric, we use Euclidean distance. If there is additional
data from the label space, it is advisable to use this information. An example is a
naive solution - to reduce the distance between points if they have the same labels
and increase in the opposite case:
),(*)),(*1(),( qpdqpSWqpDlabeled , (1)
where W — weight coefficient, ]1,0[W ; ,1 if ,1{),( qp labellabelqpS
otherwise , 0 and if qp labellabel :distanceeuclidean ),(( qpd
2
1
)( kk
n
k
qp
.
In (1) weight coefficient W is used for tuning influence of labels: 0 — has no
influence, ignoring label information; 1 — the distance between points with the
same label equal to zero.
The suggestions concerning distance function not only decrease the distance
between points with the same labels but also increase if points have different la-
bels and improve robustness in cases with noised data and close clusters.
In real cases, data often occurs with labels as ordinal variables wherein the
labels should be number type (0, 1, 2…). In this case, we can also use the distance
between labels, because rank 1 is closer to rank 2 than rank 3 (for example, “cat”
is closer to “dog” than to “fish”) [11]. However, it required additional data analy-
sis before clustering.
Considering the idea above, one can expand the (1) with the distance between
labesls:
),(*)**),(*1(),( qpdlabellabelqpSKqpD qplabeled .
The methods described above are intuitively understood and easy to imple-
ment, but have one con:
– labeled and unlabeled data have the same influence on cluster formation,
while the labeled point should have more influence;
– only points with labels are considered and do not take neighborhood
points without labels, but in most cases, the neighborhood has the same class.
L.M. Lyubchyk, K.S. Yamkovyi
ISSN 1681–6048 System Research & Information Technologies, 2022, №4 38
Semi-supervised k-medoids algorithm
We will propose some improved techniques that can resolve these issues and use
the k-medoid approach as a base idea. However, unlike k-medoids the proposed
algorithm first calculates medoids using only labeled data and next processes un-
labeled classes – assign labels of nearest medoid. This approach is described by
Algorithm 1.
This algorithm has the following pros:
– reduced processing time, because required only multiple iteration throw
points unlike standard k-medoid;
– more robustness to wrong assigned labels, because the algorithm gives
higher weights to labeled data in the medoids calculation step.
Algorithm 1. Modified k-medoids algorithm
Input:
X — feature matrix n*m, n — number of objects, m — number of features
y — labels vector of length n, y[i] = –1 if no label data for i-th object
Output:
y_predicted – vector of length n with object labels
1: k ← number of clusters, e.g. number of unique labels in y
2: X_l ←labeled point from X
3: X_u ←unlabeled point from X
4: select k random points out of the X_l as the medoids
5: associate each data point to the closest medoid
6: while the cost of the configuration decreases:
7: for each medoid m, and for each non-medoid data point o from X_l:
8: Consider the swap of m and o, and compute the cost change
9: If the cost change is the current best, remember this m and o combination
10: associate each point from X_u with the nearest medoid
11: for each point o in X:
12: fill y_predicted with assigned medoid of point o
13: return y_predicted
Semi-supervised k-nearest neighbors algorithm
Another proposed approach uses the idea of k-nearest neighbors and the k-mean
algorithm, because for classifying we use both information about the nearest
points and classes centers of mass. As a distance metric was used Euclidean dis-
tance but any metric could be used.
Classes’ centers do not recalculate after each assignment, because experi-
ments show that it does not bring benefits but takes more computation time.
Algorithm 2 implements the proposed approach.
Algorithm 2. Object clustering using k-NN based approach
Input:
X – feature matrix n*m, n – number of objects, m – number of features
y – labels vector of length n, y[i] = –1 if no label data for i-th object
Comparative analysis of modified semi-supervised learning algorithms on a small amount …
Системні дослідження та інформаційні технології, 2022, №4 39
K – number of nearest points
C – the weight of the nearest class center
Output:
y_predicted – vector of length n with object labels
1: y_predicted ← empty list of length n
2: unlabeled_idxs ← list of indexes where y = -1
3: labeled_idxs ←list of indexes where y > -1
4: center_coordinates ← list of center coordinates for each class, calculated using
available labels
5: random shuffle unlabeld_idxs
6: for i in unlabeld_idxs do
7: distances_i ← distances from i-th object to each object with indexes in la-
beled_idxs
8: argsort distances_i
9: nearest_idxs ← indexes of first K elements from distances_i
10: classes_dist_i ← distance from i-th object to each classes' center
11: neares_class_idx ← index of nearest class to i-th object
12: cls_counts ← list, where j-th element denote numbers of points belonging to j-th
class among nearest_idxs
13: cls_counts[neares_class_idx] ← cls_counts[neares_class_idx] + C // add addi-
tional value for class with nearest center
14: label ← argmax(cls_counts)
15: y_predicted[i] ← label
16: end for
17: for i in labeled_idxs do
18: y_predicted[i] ← y[i]
19: end for
20: return y_predicted
So, the method described above allows:
– consider information about the nearest point, because in most cases point
has the same label as its neighbors;
– combine a different kind of information;
– tune the weight of different sources using input parameters.
EXPERIMENTS
For experiments purpose was generated synthetic multiple datasets using sklearn
library. Each dataset contains 250 points in 2D space. Available only 10% of la-
bels as default. In addition, datasets have multiple clusters with different distribu-
tions and shapes (Fig. 4).
We will compare different approaches to find the average accuracy score on
all these datasets for each approach with different combinations of base clustering
methods and distance functions. Table included combinations that have improved
compared to the base clustering method.
L.M. Lyubchyk, K.S. Yamkovyi
ISSN 1681–6048 System Research & Information Technologies, 2022, №4 40
Accuracy comparison
Dataset name
Method name
Moons Aniso Varied
Avg accuracy
Agglomerative + custom distance
with ordinal variables (W = 0.8)
1.000 0.824 0.888 0.904
DBSCAN + custom distance (W = 1.0) 1.000 0.488 0.360 0.616
K-Medoids based 0.86 0.864 0.904 0.876
k-NN based (N = 5, С = 2) 0.904 0.900 0.912 0.905
The results shown in Table show that the best-unsupervised method is
k-medoid and the k-NN based algorithm has higher average accuracy.
Fig. 5 illustrates the difference between unsupervised and semi-supervised
methods, which is especially pronounced for non-convex data localization areas
and for clusters with the same variation and located nearest to each other.
Fig. 4. Datasets visualization. The legend shows classes’ labels, -1 – unlabeled point;
a, b – Moons dataset, 2 classes, with non-convex and separable shapes; c, d – Aniso
dataset, 3 classes, convex shape with same class variation, not separable; e, f – Varied
dataset, 3 classes with a convex shape and different class variation, also not separable
a b
e f
c
Comparative analysis of modified semi-supervised learning algorithms on a small amount …
Системні дослідження та інформаційні технології, 2022, №4 41
Another required feature of a semi-supervised algorithm is quality versus
a umber of labels dependency: more labels – higher quality and vice versa. How-
ever, Fig. 6 shows that clustering methods with custom distance functions do not
have this feature. Therefore, this approach can be easy and fast, because it re-
quires implementation only of the distance function. However, on the other hand,
it is necessary to develop and tune the distance function for each case with a dif-
ferent number of available labels.
DISCUSSIONS
In Fig. 6 we can see that with the percentage of available labels increasing the
accuracy of k-NN based and k-medoids based algorithms increased too. In addi-
tion, these algorithms have high accuracy according to Table. At that time,
DBSCAN and Agglomerative methods did not respond to increasing labels. It
means that we need to develop and tune the distance function for each case with a
different number of available labels.
a b
c d
e f
Fig. 5. Predicted labels visualization. a, c, e — unsupervised k-medoids, b, d, f — semi-
supervised k-NN based method
L.M. Lyubchyk, K.S. Yamkovyi
ISSN 1681–6048 System Research & Information Technologies, 2022, №4 42
CONCLUSIONS
In this study, we had shown that even small amounts of labeled data allow the use
of semi-supervised learning and improve accuracy. At that, semi-supervised
learning can improve algorithm performance too. Multiple approaches to semi-
supervised learning were proposed, one of them is using a distance metric that
considers available label information.
Further development of this work was a modification of other methods of classifi-
cation and clustering and a deeper study of the influence of the distance function
on the accuracy of clustering.
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Nonlinear Preference Model,” Recent Developments in Fuzzy Logic and Fuzzy Sets
Studies in Fuzziness and Soft Computing, pp. 81–103, 2020.
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Learning, vol. 109, no. 2, pp. 373–440, 2019.
3. Wikipedia contributors, “Semi-supervised learning”, in Wikipedia, The Free Ency-
clopedia. [Online]. Available: https://en.wikipedia.org/wiki/Semi-supervised_ learning
4. E. Bair, “Semi-supervised clustering methods,” Wiley Interdisciplinary Reviews:
Computational Statistics, vol. 5, no. 5, pp. 349–361, 2013.
5. A.S. Hadi, L. Kaufman, and P.J. Rousseeuw, “Finding Groups in Data: An Introduc-
tion to Cluster Analysis,” Technometrics, vol. 34, no. 1, pp. 111, 1992.
6. X. Jin and J. Han, “K-Medoids Clustering,” in Encyclopedia of Machine Learning.
Boston, MA: Springer, 2011
7. M. Ester, H. Kriegel, J. Sander, and X. Xu, “A density-based algorithm for discover-
ing clusters in large spatial databases with noise,” in Proceedings of the Second In-
ternationalConference on Knowledge Discovery and Data Mining (KDD-96), Port-
land, Oregon, USA, E. Simoudis, J. Han, and U.M. Fayyad, Eds. AAAI Press, 1996,
pp. 226–231. [Online]. Available: http://www.aaai.org/Library/KDD/1996/kdd96-
037.php
8. Daniel Müllner, Modern hierarchical, agglomerative clustering algorithms.
[Online]. Available: https://arxiv.org/pdf/1109.2378.pdf
1
2
4
3
A
cc
ur
ac
y
% of labeled data
1 –
2 –
3 –
4 –
Fig. 6. Accuracy versus the quantity of labeled data comparison plot
Comparative analysis of modified semi-supervised learning algorithms on a small amount …
Системні дослідження та інформаційні технології, 2022, №4 43
9. T. Tullis and A. Bill, Measuring the User Experience: Collecting, Analyzing, and
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Received 09.12.2021
INFORMATION ON THE ARTICLE
Leonid M. Lyubchyk, National Technical University «Kharkiv Polytechnic Institute»,
Ukraine, e-mail: Leonid.Liubchyk@kpi.edu.ua
Klym S. Yamkovyi, National Technical University «Kharkiv Polytechnic Institute»,
Ukraine, e-mail: klym.yamkovyi@cs.khpi.edu.ua
ПОРІВНЯЛЬНИЙ АНАЛІЗ МОДИФІКОВАНИХ АЛГОРИТМІВ НАВЧАННЯ
З ЧАСТКОВИМ ЗАЛУЧЕННЯМ УЧИТЕЛЯ НА МАЛІЙ КІЛЬКОСТІ
РОЗМІЧЕНИХ ДАНИХ / Л.М. Любчик, К.С. Ямковий
Анотація. Присвячено вдосконаленню методів кластеризації з частковим під-
кріпленням, а також порівнянню їх точності та стійкості. Запропонований під-
хід заснований на розширенні алгоритмів кластеризації шляхом використання
доступного набору міток класів за допомогою заміни функції відстані, при
цьому за використання запропонованої функції відстані враховуються не тіль-
ки просторові дані, але й мітки. Більше того, запропонована функція відстані
може бути адаптована для роботи з порядковими змінними як мітки. Також
запропоновано підхід, заснований на методі навчання без вчителя k-медоїдів,
модифікований для використання лише розмічених даних на етапі обчислення
медоїдів кластерів, комбінацію методу навчання з учителем k найближчих су-
сідів та без вчителя – k-середніх. При цьому алгоритм навчання використовує
інформацію як про найближчі точки, так і про центри мас класів. Отримані ре-
зультати демонструють, що навіть невеликий обсяг помічених даних дає змогу
використовувати навчання з частковим підкріпленням, а запропоновані моди-
фікації забезпечують підвищення точності і стійкості алгоритму, що продемо-
нстровано під час експериментів.
Ключові слова: центр мас, кластеризація, функція відстані, найближчий
сусід, навчання з частковим залученням вчителя, медоід.
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| id | journaliasakpiua-article-239726 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:22Z |
| publishDate | 2022 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
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| resource_txt_mv | journaliasakpiua/93/d2c41b4469c1b705a9fec4e7cd67d193.pdf |
| spelling | journaliasakpiua-article-2397262023-05-21T20:04:38Z Comparative analysis of modified semi-supervised learning algorithms on a small amount of labeled data СРАВНИТЕЛЬНЫЙ АНАЛИЗ МОДИФИЦИРОВАННЫХ АЛГОРИТМОВ ОБУЧЕНИЯ С ЧАСТИЧНЫМ ПРИВЛЕЧЕНИЕМ УЧИТЕЛЯ НА МАЛОМ КОЛИЧЕСТВЕ РАЗ-МЕЧЕННЫХ ДАННЫХ Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних Lyubchyk, Leonid Yamkovyi, Klym центр мас кластеризація функція відстані медоід найближчий сусід навчання з частковим залученням вчителя center of mass clustering distance function medoids nearest neighbor semi-supervised learning The paper is devoted to improving semi-supervised clustering methods and comparing their accuracy and robustness. The proposed approach is based on expanding a clustering algorithm for using an available set of labels by replacing the distance function. Using the distance function considers not only spatial data but also available labels. Moreover, the proposed distance function could be adopted for working with ordinal variables as labels. An extended approach is also considered, based on a combination of unsupervised k-medoids methods, modified for using only labeled data during the medoids calculation step, supervised method of k nearest neighbor, and unsupervised k-means. The learning algorithm uses information about the nearest points and classes’ centers of mass. The results demonstrate that even a small amount of labeled data allows us to use semi-supervised learning, and proposed modifications improve accuracy and algorithm performance, which was found during experiments. Статья посвящена совершенствованию методов кластеризации с частичным подкреплением, а также сравнению их точности и устойчивости. Предлагаемый подход основан на расширении алгоритмов кластеризации, путем использования доступного набора меток классов с помощью замены функции расстояния; при этом при использовании предложенной функции расстояния учитываются не только пространственные данные, но и доступные метки. Более того, предложенная функция расстояния может быть адаптирована для работы с порядковыми переменными в качестве меток. Также предложено подход основанный на методе  обучения без учителя K-медоидов, модифицированный для использования только размеченных данных на этапе вычисления медоидов кластеров, а также комбинация метода обучения с учителем K ближайшего соседа и без учителя — K-средних. При этом алгоритм обучения использует информацию как о ближайших точках, так и о центрах масс классов. Полученные результаты демонстрируют, что даже небольшой объем помеченных данных позволяет использовать обучение с частичным подкреплением, а предлагаемые модификации обеспечивают повышение точности и устойчивости алгоритма, что было показано в ходе экспериментов. Присвячено вдосконаленню методів кластеризації з частковим підкріпленням, а також порівнянню їх точності та стійкості. Запропонований підхід заснований на розширенні алгоритмів кластеризації шляхом використання доступного набору міток класів за допомогою заміни функції відстані, при цьому за використання запропонованої функції відстані враховуються не тільки просторові дані, але й мітки. Більше того, запропонована функція відстані може бути адаптована для роботи з порядковими змінними як мітки. Також запропоновано підхід, заснований на методі навчання без вчителя k-медоїдів, модифікований для використання лише розмічених даних на етапі обчислення медоїдів кластерів, комбінацію методу навчання з учителем k найближчих сусідів та без вчителя – k-середніх. При цьому алгоритм навчання використовує інформацію як про найближчі точки, так і про центри мас класів. Отримані результати демонструють, що навіть невеликий обсяг помічених даних дає змогу використовувати навчання з частковим підкріпленням, а запропоновані модифікації забезпечують підвищення точності і стійкості алгоритму, що продемонстровано під час експериментів. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2022-12-27 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/239726 10.20535/SRIT.2308-8893.2022.4.03 System research and information technologies; No. 4 (2022); 34-43 Системные исследования и информационные технологии; № 4 (2022); 34-43 Системні дослідження та інформаційні технології; № 4 (2022); 34-43 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/239726/270396 |
| spellingShingle | центр мас кластеризація функція відстані медоід найближчий сусід навчання з частковим залученням вчителя Lyubchyk, Leonid Yamkovyi, Klym Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| title | Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| title_alt | Comparative analysis of modified semi-supervised learning algorithms on a small amount of labeled data СРАВНИТЕЛЬНЫЙ АНАЛИЗ МОДИФИЦИРОВАННЫХ АЛГОРИТМОВ ОБУЧЕНИЯ С ЧАСТИЧНЫМ ПРИВЛЕЧЕНИЕМ УЧИТЕЛЯ НА МАЛОМ КОЛИЧЕСТВЕ РАЗ-МЕЧЕННЫХ ДАННЫХ |
| title_full | Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| title_fullStr | Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| title_full_unstemmed | Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| title_short | Порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| title_sort | порівняльний аналіз модифікованих алгоритмів навчання з частковим залученням учителя на малій кількості розмічених даних |
| topic | центр мас кластеризація функція відстані медоід найближчий сусід навчання з частковим залученням вчителя |
| topic_facet | центр мас кластеризація функція відстані медоід найближчий сусід навчання з частковим залученням вчителя center of mass clustering distance function medoids nearest neighbor semi-supervised learning |
| url | https://journal.iasa.kpi.ua/article/view/239726 |
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