Exploring Price Patterns of Vegetables with Recurrence Quantification Analysis
Abstract
:1. Introduction
2. Methodology
2.1. Recurrence Plots
2.2. Recurrence Quantification Analysis
- %Recurrence or RR: the ratio of the number of recurrence points to the total number of points in the plot
- %Determinism or DET: The percentage of recurrence points which form diagonal lines:
- Average Diagonal Line Length, L: The average length of the diagonal line segments in the plot, excluding the main diagonal.
- Laminarity LAM: The percentage of recurrence points which form vertical lines:
- Trapping Time, TT: It shows the average length of the vertical lines. Trapping Time represents the average time that the system has been trapped in the same state.
2.3. Data
3. Results
3.1. Recurrence Plots
- Diagonal lines parallel to the main diagonal, which vary in length and quantity depending on the case.
- White regions, which in some cases constitute a significant part of the plot.
- Small dark regions with a large density of diagonal and horizontal lines.
- G1(vis): {Garlic, Onions, Carrots, Dill—Parsley}
- G2(vis) {Celery, Spring onions, Knossos cucumbers, Beetroots}
- G3(vis) {Coarse peppers. Long-fruited peppers. Zucchini}.
- G4(vis) = {Spinach, Salads, Endives, Lettuce}
- G5(vis): {Tomatoes. cucumbers}
3.2. RQA Results
- G1(clust) = {Garlic-id1}
- G2(clust) = {Onion-id2, Carrots-id3, Dill-Parsley-id4}
- G3(clust) = {Celery-id5, Knossos cucumbers-id6, beetroots-id7, spring onions-id8, coarse peppers-id9}
- G4(clust) = {long-fruited peppers-id10, spinach-id12, zucchini-id11, salads-id12, endives-id14}
- G5(clust) = {tomatoes-id16, cucumbers-id17, lettuce-id15}
- G1(clust)
- G2(clust)
- G3(clust)
- G4(clust)
- G5(clust)
3.3. Recurrence Analysis with Epochs
- G1 (epochs) = {onions, garlic}
- G2(epochs) = {Carrots, Dill-Parsley)
- G3(epochs) = {celery, spinach, beetroots, Long-fruited peppers, Coarse-grained peppers}
- G4(epochs) = {Lettuce, Salads, Spring onions, Knossos Cucumber, Endives}
- G5(epochs) = {Tomatoes, Cucumber, zucchini}
4. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Description |
---|
Cucumbers |
Knossos Cucumbers |
Dill, Parsley bales |
Endives |
Carrots |
Zucchini |
Spring onions, fresh bale |
Onions |
Lettuce |
Beetroot |
Long-fruited peppers |
Coarse peppers |
Salads |
Celery |
Garlic |
Spinach |
Tomatoes |
Product | Delay | Embedding | Threshold |
---|---|---|---|
Cucumber | 15 | 4 | 0.147 |
Knossos cucumbers | 23 | 4 | 0.176 |
Dill—Parsley | 27 | 4 | 0.0435 |
Endives | 22 | 4 | 0.105 |
Carrots | 35 | 4 | 0.046 |
Zucchini | 21 | 4 | 0.25 |
Spring onions | 25 | 3 | 0.029 |
Onions | 35 | 5 | 0.075 |
Lettuce | 25 | 4 | 0.185 |
Beetroot | 29 | 4 | 0.105 |
Long-fruited peppers | 25 | 4 | 0.33 |
Coarse peppers | 27 | 4 | 0.41 |
Salads | 26 | 5 | 0.34 |
Celery | 25 | 4 | 0.18 |
Garlic | 50 | 4 | 0.2235 |
Spinach | 25 | 5 | 0.28 |
Tomatoes | 16 | 4 | 0.2291 |
ID | Vegetable | DET | LAM | L | TT |
---|---|---|---|---|---|
1 | Garlic | 0.991 | 0.997 | 14.886 | 26.723 |
2 | Onions | 0.965 | 0.987 | 9.234 | 15.267 |
3 | Carrots | 0.959 | 0.984 | 8.867 | 15.315 |
4 | Dill-Parsley | 0.958 | 0.983 | 8.104 | 13.960 |
5 | Celery | 0.932 | 0.975 | 6.318 | 10.295 |
6 | Knossos Cucumbers | 0.932 | 0.975 | 5.977 | 9.322 |
7 | Beetroots | 0.928 | 0.975 | 5.612 | 9.003 |
8 | Spring onions | 0.897 | 0.957 | 5.624 | 9.203 |
9 | Coarse Peppers | 0.915 | 0.962 | 6.036 | 8.494 |
10 | Long-fruited peppers | 0.893 | 0.954 | 5.015 | 7.118 |
11 | Zucchini | 0.836 | 0.920 | 4.351 | 6.057 |
12 | Spinach | 0.884 | 0.950 | 4.796 | 7.059 |
13 | Salads | 0.857 | 0.933 | 4.471 | 6.286 |
14 | Endives | 0.851 | 0.939 | 4.305 | 6.466 |
15 | Lettuce | 0.800 | 0.906 | 3.838 | 5.405 |
16 | Tomatoes | 0.716 | 0.850 | 3.209 | 4.194 |
17 | Cucumbers | 0.713 | 0.858 | 3.130 | 4.167 |
RQA Measures | Onions | Garlic |
---|---|---|
DET | 0.869–1 | 0.876–1 |
L | 4.701–21.727 | 3.365–17.050 |
LAM | 0.937–1 | 0.952–1 |
TT | 7.180–39 | 4.507–29 |
RQA Measures | Dill-Parsley | Carrots |
---|---|---|
DET | 0.408–0.999 | 0.418–0.999 |
L | 2.080–50 | 2.214–38 |
LAM | 0.556–1 | 0.627–1 |
TT | 2.229–98 | 2.485–74 |
RQA Measures | Celery | Spinach | Beetroots | Long-Fruited Peppers | Coarse Peppers |
---|---|---|---|---|---|
DET | 0.642–0.998 | 0.714–0.992 | 0.669–0.997 | 0.784–0.996 | 0.777–0.998 |
L | 2.666–29.576 | 2.775–21.480 | 2.685–21.878 | 3.796–26.083 | 2.940–25.652 |
LAM | 0.804–1 | 0.882–1 | 0.815–1 | 0.918–1 | 0.885–1 |
TT | 3.341–53.114 | 2.870–26.440 | 2.794–37.154 | 4.606–29.543 | 3.510–29.085 |
RQA Measure | Lettuce | Salads | Spring Onions | Knossos Cucumber | Endives |
---|---|---|---|---|---|
DET | 0.491–0.992 | 0.640–0.995 | 0.307–0.997 | 0.735–0.999 | 0.523–0.998 |
L | 2.214–11.585 | 2.666–26.875 | 2.181–24.333 | 2.95–34.923 | 2.371–26.895 |
LAM | 0.629–1 | 0.788–1 | 0.515–1 | 0.862–1 | 0.710–1 |
TT | 2.342–19.870 | 2.745–38.459 | 2.264–40 | 3.551–62.745 | 2.718–51 |
RQA Measure | Tomatoes | Cucumber Pair | Zucchini |
---|---|---|---|
DET | 0.567–0.962 | 0.603–0.958 | 0.471–0.986 |
L | 2.626–8.627 | 2.566–6.523 | 2.757–12.363 |
LAM | 0.716–0.984 | 0.794–0.986 | 0.673–0.999 |
TT | 2.735–10.668 | 2.759–8.041 | 2.870–17.175 |
Vegetables | DET | LAM | L | TT | G1 (Vis) | G2 (Vis) | G3 (Vis) | G4 (Vis) | G5 (Vis) | G1 (Clust) | G2 (Clust) | G3 (Clust) | G4 (Clust) | G5 (Clust) | G1 (Epoch) | G2 (Epoch) | G3 (Epoch) | G4 (Epoch) | G5 (Epoch) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Garlic | 0.991 | 0.997 | 14.886 | 26.723 | |||||||||||||||
Onions | 0.965 | 0.987 | 9.234 | 15.267 | |||||||||||||||
Carrots | 0.959 | 0.984 | 8.867 | 15.315 | |||||||||||||||
Dill-Parsley | 0.958 | 0.983 | 8.104 | 13.960 | |||||||||||||||
Celery | 0.932 | 0.975 | 6.318 | 10.295 | |||||||||||||||
Knossos Cucumbers | 0.932 | 0.975 | 5.977 | 9.322 | |||||||||||||||
Beetroots | 0.928 | 0.975 | 5.612 | 9.003 | |||||||||||||||
Spring Onions | 0.897 | 0.957 | 5.624 | 9.203 | |||||||||||||||
Coarse Peppers | 0.915 | 0.962 | 6.036 | 8.494 | |||||||||||||||
Long-fruited Peppers | 0.893 | 0.954 | 5.015 | 7.118 | |||||||||||||||
Zucchini | 0.836 | 0.920 | 4.351 | 6.057 | |||||||||||||||
Spinach | 0.884 | 0.950 | 4.796 | 7.059 | |||||||||||||||
Salads | 0.857 | 0.933 | 4.471 | 6.286 | |||||||||||||||
Endives | 0.851 | 0.939 | 4.305 | 6.466 | |||||||||||||||
Lettuce | 0.800 | 0.906 | 3.838 | 5.405 | |||||||||||||||
Tomatoes | 0.716 | 0.850 | 3.209 | 4.194 | |||||||||||||||
Cucumbers | 0.713 | 0.858 | 3.130 | 4.167 |
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Karakasidou, S.; Fragkou, A.; Zachilas, L.; Karakasidis, T. Exploring Price Patterns of Vegetables with Recurrence Quantification Analysis. AppliedMath 2024, 4, 1012-1046. https://doi.org/10.3390/appliedmath4030055
Karakasidou S, Fragkou A, Zachilas L, Karakasidis T. Exploring Price Patterns of Vegetables with Recurrence Quantification Analysis. AppliedMath. 2024; 4(3):1012-1046. https://doi.org/10.3390/appliedmath4030055
Chicago/Turabian StyleKarakasidou, Sofia, Athanasios Fragkou, Loukas Zachilas, and Theodoros Karakasidis. 2024. "Exploring Price Patterns of Vegetables with Recurrence Quantification Analysis" AppliedMath 4, no. 3: 1012-1046. https://doi.org/10.3390/appliedmath4030055