Clustering of Latvian Pension Funds Using Convolutional Neural Network Extracted Features
Abstract
:1. Introduction
2. Literature Review
2.1. Pension Funds
- The first pillar is a state-based pension scheme that emphasizes poverty prevention;
- Second-tier pension consists of occupational pension schemes that involve regular employer contributions and have a goal of ensuring adequate income;
- The third pillar is made of voluntary funded plans that supplement the income from the first two tiers.
- In DC-type plans, the employee decides where the money is invested, taking responsibility for the risks associated with investment and potential loss. A pensioner can outlive the investment, and it is not protected from inflation. Its return depends on the contributions made and investment performance.
- In the DB type of pension plans, the employer guarantees lifetime pension income regardless of funds’ performance, thus committing to covering the remainder of the underperforming fund. The plan provides lifetime income for retirees, which depends on the salary and years spent working. In addition, DB pension plans protect investment against inflation and are managed by pension fund supervisors.
2.2. Machine Learning Models and Their Application to the Real-World Tasks
2.3. The Application of Machine Learning in Pension Funds
3. Materials and Methods
3.1. Datasets and Preprocessing
- Column ID.
- Pension fund name.
- Date in force.
- Calculation date.
- NAV value in Latvian lats and euros.
- Amount of units.
- Total asset value in Latvian lats and euros.
- The number of participants.
3.2. Training the Neural Networks
3.2.1. Artificial Neural Networks
3.2.2. Convolutional Neural Networks
3.2.3. Classifier Performance Evaluation
- True positive (TP)—the model correctly predicted a positive label;
- False positive (FP)—the model predicted a positive label when the actual label was negative;
- True negative (TN)—the model correctly predicted a negative label;
- False negative (FN)—the model predicted a negative label when the actual label was positive.
3.3. Clustering
- Partition based: K-means, mini batch K-means;
- Hierarchy based: BIRCH, agglomerative clustering;
- Density based: DBSCAN, OPTICS, mean shift;
- Graph based: affinity propagation.
- Number of clusters—indicates to how many clusters the algorithm should group data;
- Random state—the seed to use for the pseudo-random number generator responsible for randomness;
- Min samples—the number of data points surrounding the point required to become a core of a cluster;
- Algorithm—the algorithm used for pointwise distance computation and nearest-neighbor calculation;
- Distance—the distance metric used by the algorithm.
3.3.1. Initial Clustering and Feature Extractor Performance
3.3.2. Pension Fund Clustering
3.4. Post Hoc Testing
3.5. Summary of Research Methods
4. Results
4.1. Pension Fund Analysis
4.2. Convolutional Neural Network Training
- 15 binary classifiers;
- Eight multiclass classifiers;
- Four sector classifiers;
- Three sector top five classifiers;
- One industry classifier; and
- One industry top 10 classifier.
4.3. Cluster Analysis
4.3.1. Initial Clustering Methods
- Seven out of 15 binary models;
- One out of eight multiclass classifiers;
- Two out of four sector classifiers;
- One out of three sector top 5 classifiers;
- One out of one industry top 10 classifier.
4.3.2. Clustering Methods of Pension Funds
4.4. The Interpretation of Results and Discussions
5. Conclusions
- Conservative, balanced, and active Luminor pension fund grouping.
- Grouping of two active and one conservative SEB pension funds.
- A consistent subgroup of CBL active and balanced pension funds.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations and Terms
EU | European union; |
DC | defined contribution; |
DB | defined benefit; |
AI | artificial intelligence; |
ANN | artificial neural networks. |
CNN | convolutional neural network. |
OECD | organization for economic co-operation and development; |
BIRCH | balanced iterative reducing and clustering using hierarchies; |
DBSCAN | density-based spatial clustering of applications with noise; |
OPTICS | ordering points to identify the clustering structure. |
Appendix A. Trained Model Architectures, Clustering Algorithms, and Parameters
Model Name and Classifier Type | Feature Extractor | Neural Network and Neurons |
---|---|---|
X1_6 (binary price classifier) | 16 kernels with size 2 | Dropout 896 |
32 kernels with size 3 | Dense 64 | |
Max pooling | Dense 1 | |
64 kernels with size 5 | ||
128 kernels with size 5 | ||
Max pooling | ||
X1_15 (binary price classifier) | 16 kernels with size 2 | Dropout 896 |
32 kernels with size 3 | Dense 64 | |
Max pooling | Dense 1 | |
64 kernels with size 5 | ||
128 kernels with size 5 | ||
Max pooling | ||
X2_1 (multiclass price classifier) | 32 kernels with size 2 | Dropout 1736 |
64 kernels with size 3 | Dense 256 | |
Max pooling | Dropout | |
124 kernels with size 5 | Dense 64 | |
Max pooling | Dense 3 | |
X2_4 (multiclass price classifier) X2_3 (multiclass price classifier) | 32 kernels with size 2 | Dropout 3072 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 3 | Dense 3 | |
Max pooling | ||
128 kernels with size 5 | ||
256 kernels with size 3 | ||
Max pooling | ||
Y1_1 (sector classifier) | 16 kernels with size 2 | Flatten 320 |
Max pooling | Dense 64 | |
32 kernels with size 2 | Dense 12 | |
Max pooling | ||
64 kernels with size 2 | ||
Max pooling | ||
Y1_2 (sector classifier) | 32 kernels with size 2 | Dropout 256 |
Max pooling stride 3 | Dense 64 | |
64 kernels with size 2 | Dense 12 | |
Max pooling stride 3 | ||
X1_4 (binary price classifier) | 32 kernels with size 2 | Dropout 512 |
Max pooling stride 2 | Dense 32 | |
32 kernels with size 2 | Dense 1 | |
Max pooling stride 2 | ||
Y2_1 (industry classifier) | 32 kernels with size 2 | Dropout 2304 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 2 | Dense 128 | |
Max pooling | ||
128 kernels with size 2 | ||
256 kernels with size 3 | ||
Max pooling | ||
256 kernels with size 3 | ||
256 kernels with size 3 | ||
Max pooling | ||
X2_2 (multiclass price classifier) | 64 kernels with size 2 | Dropout 2304 |
128 kernels with size 3 | Dense 256 | |
Max pooling | Dense 64 | |
128 kernels with size 5 | Dense 3 | |
256 kernels with size 2 | ||
Max pooling | ||
X2_7 (multiclass price classifier) X2_6 (multiclass price classifier) | 32 kernels with size 2 | Dropout 2560 |
64 kernels with size 2 | Dense 256 | |
64 kernels with size 3 | Dense 64 | |
Max pooling | Dense 3 (used range 5) | |
128 kernels with size 2 | ||
256 kernels with size 3 | ||
Max pooling | ||
256 kernels with size 2 | ||
256 kernels with size 2 | ||
Max pooling | ||
X1_14 (binary price classifier) X1_13 (binary price classifier) | 32 kernels with size 2 | Dropout 1265, 2530 |
64 kernels with size 3 | Dense 256 | |
64 kernels with size 5 | Dense 64 | |
Max pooling | Dense 1 | |
128 kernels with size 2 | ||
256 kernels with size 3 | ||
Max pooling | ||
253 kernels with size 3 | ||
Max pooling | ||
X1_8 (binary price classifier) X1_7 (binary price classifier) | 64 kernels with size 2 | Dropout 4096, 2304 |
128 kernels with size 3 | Dense 256 | |
Max pooling | Dense 64 | |
128 kernels with size 5 | Dense 1 | |
256 kernels with size 2 | ||
Max pooling | ||
X1_9 (binary price classifier) X1_10 (binary price classifier) X1_11 (binary price classifier) | 32 kernels with size 2 | Dropout 1280, 2560 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 3 | Dense 1 | |
Max pooling | ||
128 kernels with size 5 | ||
256 kernels with size 3 | ||
Max pooling | ||
X1_12 (binary price classifier) | 64 kernels with size 2 | Dropout 1024 |
64 kernels with size 3 | Dense 256 | |
Max pooling | Dense 64 | |
128 kernels with size 2 | Dense 1 | |
Max pooling | ||
128 kernels with size 6 | ||
256 kernels with size 3 | ||
Max pooling | ||
Y3_1 (sector classifier taking top 5 most frequent sectors) | 32 kernels with size 2 | Dropout 288 |
Max pooling | Dense 32 | |
32 kernels with size 2 | Dense 5 | |
Max pooling | ||
Y3_2 (sector classifier taking top 5 most frequent sectors) Y3_3 (sector classifier taking top 5 most frequent sectors) | 32 kernels with size 2 | Dropout 512 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 2 | Dense 5 | |
Max pooling | ||
128 kernels with size 2 | ||
256 kernels with size 3 | ||
Max pooling | ||
256 kernels with size 3 | ||
256 kernels with size 3 | ||
Max pooling | ||
Y1_3 (sector classifier) | 32 kernels with size 2 | Dropout 1265 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 2 | Dense 12 | |
Max pooling | ||
128 kernels with size 2 | ||
256 kernels with size 3 | ||
Max pooling | ||
253 kernels with size 2 | ||
Y1_4 (sector classifier) X1_2 (binary price classifier) | 32 kernels with size 2 | Dropout 1024, 1408 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 2 | Dense 12, 1 | |
Max pooling | ||
128 kernels with size 2 | ||
256 kernels with size 3 | ||
Max pooling | ||
256 kernels with size 3 | ||
256 kernels with size 3 | ||
X1_3 (binary price classifier) | 16 kernels with size 2 | Dropout 1408 |
32 kernels with size 2 | Dense 64 | |
Max pooling | Dense 1 | |
64 kernels with size 2 | ||
128 kernels with size 2 | ||
Max pooling | ||
X1_1 (binary price classifier) X1_5 (binary price classifier) | 64 kernels with size 2 | Dropout 256 |
128 kernels with size 3 | Dense 64 | |
Max pooling | Dense 1 | |
Y4_1 (industry classifier taking top 100 most frequent industries) | 32 kernels with size 2 | Dropout 288 |
Max pooling | Dense 32 | |
32 kernels with size 2 | Dense 10 | |
Max pooling | ||
X2_5 (multiclass price classifier) | 32 kernels with size 2 | Dropout 768 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 2 | Dense 3 | |
Max pooling | ||
128 kernels with size 5 | ||
128 kernels with size 3 | ||
Max pooling | ||
256 kernels with size 3 | ||
256 kernels with size 5 | ||
Max pooling | ||
X2_8 (multiclass price classifier) | 32 kernels with size 2 | Dropout 256 |
64 kernels with size 3 | Dense 64 | |
64 kernels with size 3 | Dense 3 | |
Max pooling | ||
128 kernels with size 4 | ||
128 kernels with size 5 | ||
Max pooling | ||
256 kernels with size 3 | ||
256 kernels with size 3 | ||
Max pooling |
Model Name | Input Size | Predict Price Timestep | Overlap | Epochs | Accuracy | AUC | Dummy Score |
---|---|---|---|---|---|---|---|
X1_15 | 50 | 5 | 5 | 300 | 0.5916 | 0.6408 | 0.5133 |
X1_6 | 50 | 5 | 5 | 400 | 0.5969 | 0.6472 | 0.5133 |
X1_5 | 50 | 5 | 0 | 400 | 0.5794 | 0.6263 | 0.5133 |
X2_1 | 60 | 5 | 0 | 300 | 0.5176 | 0.6834 | 0.4707 |
X2_5 | 60 | 5 | 0 | 200 | 0.5514 | 0.6741 | 0.5277 |
X2_8 | 60 | 5 | 0 | 200 | 0.5353 | 0.6881 | 0.5277 |
X2_3 | 60 | 5 | 5 | 200 | 0.5611 | 0.7002 | 0.5277 |
X2_4 | 60 | 5 | 10 | 200 | 0.5556 | 0.7012 | 0.5277 |
X1_9 | 30 | 5 | 5 | 100 | 0.5875 | 0.6331 | 0.5076 |
X1_10 | 30 | 5 | 5 | 100 | 0.5841 | 0.6292 | 0.5076 |
X1_11 | 50 | 5 | 5 | 200 | 0.6074 | 0.6590 | 0.5289 |
X1_14 | 60 | 10 | 10 | 100 | 0.5910 | 0.6371 | 0.5175 |
X1_13 | 100 | 80 | 30 | 100 | 0.6067 | 0.6259 | 0.5817 |
X2_7 | 100 | 80 | 30 | 200 | 0.5235 | 0.6160 | 0.5047 |
X2_6 | 100 | 80 | 30 | 100 | 0.5137 | 0.6167 | 0.5047 |
Y1_3 | 60 | - | 0 | 200 | 0.2834 | 0.6516 | 0.1786 |
Y1_4 | 60 | - | 0 | 200 | 0.2965 | 0.6674 | 0.1786 |
Y3_2 | 40 | - | 0 | 200 | 0.3807 | 0.6759 | 0.2601 |
Y3_3 | 40 | - | 0 | 205 | 0.3918 | 0.6756 | 0.2601 |
Y2_1 | 100 | - | 0 | 400 | 0.1556 | 0.7007 | 0.0704 |
X1_12 | 50 | 5 | 5 | 200 | 0.5915 | 0.6405 | 0.5289 |
X2_2 | 50 | 15 | 20 | 200 | 0.5361 | 0.6749 | 0.5136 |
X1_8 | 80 | 15 | 20 | 200 | 0.5800 | 0.6298 | 0.512 |
Y1_1 | 50 | - | 0 | 200 | 0.2320 | - | 0.1786 |
X1_4 | 70 | 7 | 0 | 200 | 0.5118 | - | 0.5 |
Y1_2 | 40 | - | 0 | 150 | 0.2026 | 0.5659 | 0.1786 |
X1_7 | 50 | 15 | 20 | 200 | 0.5800 | 0.6298 | 0.5120 |
Y3_1 | 40 | - | 0 | 180 | 0.3123 | 0.6072 | 0.2601 |
X1_2 | 50 | 5 | 0 | 200 | 0.5388 | - | 0.5168 |
X1_3 | 50 | 10 | 0 | 200 | 0.5265 | - | 0.5168 |
X1_1 | 50 | 5 | 0 | 400 | 0.5532 | 0.5974 | 0.5133 |
Y4_1 | 40 | - | 0 | 200 | 0.3159 | - | 0.26 |
Algorithm Name | Parameter Name | Parameter Value | |
---|---|---|---|
K-means, mini batch K-means | n_clusters | 2 to 10 | |
Birch | n_clusters | 2 to 10 | |
threshold | 0.1 to 1 with 0.1 step | ||
Mean shift | bin_seeding | true, false | |
cluster_all | true, false | ||
Affinity propagation | damping | 0.5 to 1 with 0.05 step | |
DBSCAN | eps | 0.3, 0.5 or 0.8 | |
Optics | leaf_size | 30 | |
DBSCAN, Optics | min_samples | 3, 5 or 10 | |
algorithm, metric | kd_tree | Euclidean, l2, Minkowski, Manhattan, Chebyshev | |
ball_tree | Euclidean, L2, Minkowski, Manhattan, L1, Chebyshev, Wminkowski, Canberra, Bray–Curtis | ||
brute | Euclidean, L2, Minkowski, Manhattan, Chebyshev, Wminkowski, Canberra, Braycurtis, Correlation, Cosine, Squeclidean | ||
Agglomerative | n_clusters | 2 to 10 | |
linkage | Ward, Average, Complete, or single | ||
affinity | Euclidean, L1, L2, Manhattan, Cosine |
Appendix B. Clustering Results
Cluster 0 | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 | Cluster 5 |
---|---|---|---|---|---|
CBL_C_1 INVL_C SEB_C_1 SEB_C_2 Swedbank_C_1 | CBL_A_1 INDEXO_A Luminor_A Luminor_B Luminor_C | ABLV_A INVL_A INVL_B Swedbank_A | SEB_A_1 SEB_A_2 SEB_B | CBL_A_2 CBL_B | CBL_C_2 |
Appendix C. Best Parameters and Models for Each Clustering Algorithm
Algorithm Name | Clusters | Total Combinations | Mean Silhouette Score | Top Taken | Mean Silhouette Score Top | Best Model | Algorithm Parameters |
---|---|---|---|---|---|---|---|
K-means | 2 | 152 | 0.2638 | 10 | 0.6916 | Y1_1, Y1_2, Y3_1 | - |
K-means | 6 | 152 | 0.2184 | 10 | 0.31 | Y1_1 | - |
K-means | 10 | 152 | 0.2064 | 10 | 0.2931 | X1_5, X1_1, Y1_1 | - |
BIRCH | 2 | 1368 | 0.2746 | 10 | 0.7035 | Y1_1 | - |
BIRCH | 6 | 1368 | 0.228 | 10 | 0.3266 | X1_5 | - |
BIRCH | 10 | 1368 | 0.2165 | 10 | 0.314 | X1_5 | - |
Mini batch K-means | 2 | 152 | 0.2556 | 10 | 0.6916 | Y1_1, Y1_2, Y3_1 | - |
Mini batch K-means | 6 | 152 | 0.2017 | 10 | 0.303 | Y1_1, Y1_2, Y3_1 | - |
Mini batch K-means | 10 | 152 | 0.1777 | 10 | 0.2788 | X1_5 | - |
Mean shift | 2 | 117 | 0.1856 | 10 | 0.2859 | Y2_1, X2_7 | - |
Agglomerative clustering | 2 | 400 | 0.421 | 10 | 0.8666 | Y1_1, Y1_2, Y3_1 | Affinity: cosine |
Agglomerative clustering | 6 | 400 | 0.2216 | 10 | 0.4354 | - | Linkage: average or complete; Affinity: cosine |
Agglomerative clustering | 10 | 400 | 0.2125 | 10 | 0.4293 | - | Linkage: average or complete; Affinity: cosine |
OPTICS | 2 | 382 | 0.0813 | 10 | 0.3825 | X1_3 | - |
OPTICS | 10 | 1 | 0.1928 | 1 | 0.1928 | X1_14 | Algorithm: ball_tree; Metric: Bray–Curtis |
DBSCAN | 2 | 321 | 0.4583 | 10 | 0.8349 | Y1_1, Y1_2, Y3_1 | Algorithm: brute; Metric: correlation, Bray-Curtis |
Affinity propagation | 6 | 99 | 0.2052 | 10 | 0.286 | Y1_1, X1_5 | Damping: 0.5, 0.55, 0.6 |
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Pension Fund Name | Encoded Name | Manager | Category |
---|---|---|---|
ABLV active investment plan | ABLV_A | ABLV | Active |
CBL Aktivais ieguldijumu plans | CBL_A_1 | CBL | Active |
Ieguldijumu plans “GAUJA” | CBL_A_2 | CBL | Active |
Ieguldijumu plans “INDEXO Izaugsme 47–57” | INDEXO_A | INDEXO | Active |
Ieguldijumu plans “INVL Ekstra 47+” | INVL_A | INVL | Active |
Luminor Aktivais ieguldijumu plans | Luminor_A | Luminor | Active |
SEB aktivais plans | SEB_A_1 | SEB | Active |
SEB Eiropas plans | SEB_A_2 | SEB | Active |
Swedbank pensiju ieguldijumu plans “Dinamika” | Swedbank_A | Swedbank | Active |
Ieguldijumu plans “VENTA” | CBL_B | CBL | Balanced |
Ieguldijumu plans “INVL Komforts 53+” | INVL_B | INVL | Balanced |
Luminor Sabalansetais ieguldijumu plans | Luminor_B | Luminor | Balanced |
SEB sabalansetais plans | SEB_B | SEB | Balanced |
CBL Universalais ieguldijumu plans | CBL_C_1 | CBL | Conservative |
Ieguldijumu plans “DAUGAVA” | CBL_C_2 | CBL | Conservative |
Ieguldijumu plans “INVL Konservativais 58+” | INVL_C | INVL | Conservative |
Luminor Konservativais ieguldijumu plans | Luminor_C | Luminor | Conservative |
SEB konservativais plans | SEB_C_1 | SEB | Conservative |
SEB Latvijas plans | SEB_C_2 | SEB | Conservative |
Swedbank pensiju ieguldijumu plans “Stabilitate” | Swedbank_C_1 | Swedbank | Conservative |
Encoding | Q1 | Mean | Q3 | Standard Deviation | Kurtosis | Skewness | Sharpe Ratio |
---|---|---|---|---|---|---|---|
ABLV_A | −0.00206 | 0.0002 | 0.00296 | 0.00562 | 16.424 | −1.865 | 0.03596 |
CBL_A_1 | −0.00099 | 0.00016 | 0.00176 | 0.00323 | 14.066 | −1.675 | 0.04872 |
CBL_C_1 | −0.00046 | 9 × 10−5 | 0.00072 | 0.00155 | 58.139 | −4.841 | 0.05972 |
CBL_C_2 | −0.00042 | 2 × 10−5 | 0.00075 | 0.00319 | 51.923 | −4.836 | 0.00675 |
CBL_A_2 | −0.00302 | −0.00015 | 0.00321 | 0.00633 | 6.2933 | −1.33 | −0.02422 |
INDEXO_A | −0.00139 | 0.00026 | 0.00263 | 0.00442 | 10.975 | −1.448 | 0.0582 |
CBL_B | −0.0015 | −6 × 10−5 | 0.00195 | 0.00431 | 16.688 | −2.514 | −0.01394 |
INVL_A | −0.00178 | 0.00022 | 0.00266 | 0.00526 | 14.894 | −1.725 | 0.04239 |
Luminor_A | −0.0015 | 0.00016 | 0.00229 | 0.00457 | 31.072 | −3.096 | 0.03567 |
SEB_A_1 | −0.0013 | 0.00016 | 0.00222 | 0.00463 | 23.401 | −2.522 | 0.03415 |
SEB_A_2 | −0.00163 | 0.00013 | 0.00257 | 0.00517 | 21.512 | −2.329 | 0.02579 |
Swedbank_A | −0.00129 | 0.00013 | 0.00202 | 0.00379 | 15.316 | −1.821 | 0.03432 |
INVL_B | −0.00108 | 0.00016 | 0.00161 | 0.00324 | 21.21 | −2.195 | 0.04849 |
Luminor_B | −0.00081 | 0.00011 | 0.00133 | 0.00302 | 45.314 | −4.171 | 0.03505 |
SEB_B | −0.00079 | 0.0001 | 0.00135 | 0.00283 | 27.892 | −3.011 | 0.03426 |
INVL_C | −0.00012 | 6 × 10−5 | 0.00033 | 0.00104 | 42.75 | −4.118 | 0.05667 |
Luminor_C | −0.00065 | 3 × 10−5 | 0.00087 | 0.00223 | 60.324 | −4.754 | 0.01169 |
SEB_C_1 | −0.00034 | 4 × 10−5 | 0.00059 | 0.00141 | 56.096 | −4.94 | 0.02795 |
SEB_C_2 | −0.00016 | 3 × 10−5 | 0.0003 | 0.00046 | 28.175 | −2.727 | 0.07126 |
Swedbank_C_1 | −0.00032 | 5 × 10−5 | 0.00055 | 0.00123 | 40.703 | −3.78 | 0.04413 |
Cluster 0 | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 | Cluster 5 |
---|---|---|---|---|---|
CBL_C_1 INVL_C SEB_A_1 SEB_C_1 Swedbank_C_1 | CBL_A_1 INDEXO_A Luminor_A Luminor_B Luminor_C | ABLV_A INVL_A INVL_B Swedbank_A | SEB_A_2 SEB_B SEB_C_2 | CBL_A_2 CBL_B | CBL_C_2 |
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Serapinaitė, V.; Kabašinskas, A. Clustering of Latvian Pension Funds Using Convolutional Neural Network Extracted Features. Mathematics 2021, 9, 2086. https://doi.org/10.3390/math9172086
Serapinaitė V, Kabašinskas A. Clustering of Latvian Pension Funds Using Convolutional Neural Network Extracted Features. Mathematics. 2021; 9(17):2086. https://doi.org/10.3390/math9172086
Chicago/Turabian StyleSerapinaitė, Vitalija, and Audrius Kabašinskas. 2021. "Clustering of Latvian Pension Funds Using Convolutional Neural Network Extracted Features" Mathematics 9, no. 17: 2086. https://doi.org/10.3390/math9172086
APA StyleSerapinaitė, V., & Kabašinskas, A. (2021). Clustering of Latvian Pension Funds Using Convolutional Neural Network Extracted Features. Mathematics, 9(17), 2086. https://doi.org/10.3390/math9172086