How i plot statistics, an example

This is an example of how i plot statistics using plotly, pandas and numpy.

The data i’m plotting

I’m plotting a table that contains the evaluation of a LLM called Kosmos 2, i used it to find the bounding boxes of certain objects in computer generated images. What i found, computing statistics, is that there’s a correlation between the dimension of the object and the precision of my model: namely my model is more precise when the object is big, and way less precise when the object is small.

entity_type	Average BBox Dimensions (All)	Percentage of Matches
Total	0.0222	22.2700
Painting	0.0355	40.3462
Cell Phone	0.0011	2.0701
Remote Control	0.0010	1.7375
Book	0.0043	8.8660
Chair	0.0196	25.0564
Pen	0.0004	0.0000
Dining Table	0.0549	58.6751
Box	0.0062	10.2804
Key Chain	0.0004	0.4831
Counter Top	0.1126	37.7451
Bowl	0.0033	5.6701
Bottle	0.0023	6.7708
House Plant	0.0172	46.3542
Television	0.0716	63.7838
Statue	0.0059	20.7101
Plate	0.0018	4.2424
Sofa	0.0772	65.8385
Laptop	0.0084	16.7702
Fridge	0.1582	66.2420
Knife	0.0018	2.6667
Bed	0.0869	52.4823
Dresser	0.0830	61.7021
Wine Bottle	0.0059	13.7681
Garbage Can	0.0217	66.6667
Fork	0.0007	0.0000
Spoon	0.0004	0.0000
Pillow	0.0054	15.2000
Mug	0.0019	4.2017
Arm Chair	0.0419	54.3860
Bread	0.0029	7.8947
Spray Bottle	0.0027	15.0442
Vase	0.0031	8.1818
Soap Bottle	0.0030	6.6038
Spatula	0.0020	0.0000
Pencil	0.0003	1.0989
Toaster	0.0060	12.3596
Shelving Unit	0.1030	61.3636
Toilet	0.0598	66.2791
Kettle	0.0044	5.9524
TV Stand	0.0538	35.7143
Butter Knife	0.0002	0.0000
Newspaper	0.0024	5.2632
Apple	0.0019	2.6667
Cup	0.0017	4.1096
Washing Machine	0.0764	69.8630
Side Table	0.0327	40.2778
Candle	0.0008	1.4286
Sink	0.0604	71.8750
Floor Lamp	0.0830	59.3750
Credit Card	0.0003	0.0000
Pepper Shaker	0.0019	0.0000
Potato	0.0021	5.2632
Salt Shaker	0.0005	0.0000
Tomato	0.0008	8.9286
Stool	0.0181	56.3636
Pan	0.0048	7.4074
Garbage Bag	0.0167	68.5185
Faucet	0.0120	11.1111
Dish Sponge	0.0006	0.0000
Lettuce	0.0019	11.7647
Microwave	0.0133	13.0435
Toilet Paper	0.0013	4.3478
Watch	0.0003	0.0000
Teddy Bear	0.0088	48.8372
Paper Towel Roll	0.0025	7.8947
Desk Lamp	0.0056	8.1081
Plunger	0.0061	24.3243
Basket Ball	0.0038	31.4286
Pot	0.0049	8.5714
Dog Bed	0.0273	44.1176
Ladle	0.0013	2.9412
Baseball Bat	0.0065	15.1515
Cart	0.0559	46.8750
Tissue Box	0.0026	3.8462
Egg	0.0005	0.0000
Alarm Clock	0.0046	18.1818
Desk	0.0876	47.0588
Coffee Machine	0.0151	35.7143
Soap Bar	0.0005	0.0000
Tennis Racket	0.0052	9.0909
Safe	0.0094	36.3636
Cloth	0.0026	0.0000
Laundry Hamper	0.0352	44.4444
Vacuum Cleaner	0.0250	57.1429
Boots	0.0011	0.0000
Desktop	0.0316	0.0000
Room Decor	0.0130	0.0000
Table Top Decor	0.0027	0.0000
Ottoman	0.1021	100.0000
So i plotted it to find out if there actually was a correlation between those values

Transclude of plot-1

And there obviously is. To view a more in depth analysis of this correlation see: Progetto WMIR completo

The code

First of all we read the csv file and we exclude the total from the plot (we want to know the correlation for each entity type we don’t really care about the total)

```python
import pandas as pd
import plotly.graph_objects as go
import numpy as np
 
# Read the CSV file into a DataFrame
df = pd.read_csv("entity_statistics_with_std_rounded.csv")
 
# Exclude the 'Total' row from the DataFrame
df = df[df['entity_type'] != 'Total']

now we extract the required columns to compute these statistics: these are

number of Occurrences	Average BBox Dimensions (All)	Percentage of Matches

# Extract required columns
percentage_matches = df['Percentage of Matches']
avg_bbox_dimensions = df['Average BBox Dimensions (All)']
num_occurrences = df['Number of Occurrences']
 

Now one cool thing i did was to scale the color of the points: a green dot means that there are a lot of occurrences and that the dot is “trusted” red is the opposite. If i just use a raw scale where dark green is a dot that represented an entity that occurred 700 times (which is the max) then there would be very few green dots (since there are only a bunch of entities that occur around 700 times) and many red dots. So the gradient needs to concentrate around the mean value of “number of Occurrences”

# Calculate the mean of the values of "Number of Occurrences"
mean_num_occurrences = num_occurrences.mean()
 
# Create normalized values based on the mean
normalized_values = 0.5 + (num_occurrences - mean_num_occurrences) / (2 * mean_num_occurrences)
normalized_values = np.clip(normalized_values, 0, 1)  # Clip values to [0, 1] range
 

This gives us a range [0,1] that can be used as a scale for the color parameter in a plotly figure

# Create scatter plot using Plotly
fig = go.Figure(data=go.Scatter(
    x=avg_bbox_dimensions,
    y=percentage_matches,
    mode='markers',
    marker=dict(
        color=normalized_values,
        colorscale='RdYlGn',  # Red-Yellow-Green colormap
        line_width=1
    )
))

The scale is Red Yellow Green and uses the normalized values. Then it just exports the plot as an html file:

# Update layout
fig.update_layout(
    title='Correlation between BBox Dimensions and Percentage of Matches',
    xaxis_title='Average BBox Dimensions (All)',
    yaxis_title='Percentage of Matches',
    plot_bgcolor='rgba(0,0,0,0)'
)
 
# Export the plot to an HTML file
fig.write_html("plot.html")

This is the whole file:

import pandas as pd
import plotly.graph_objects as go
import numpy as np
 
# Read the CSV file into a DataFrame
df = pd.read_csv("entity_statistics_with_std_rounded.csv")
 
# Exclude the 'Total' row from the DataFrame
df = df[df['entity_type'] != 'Total']
 
# Extract required columns
percentage_matches = df['Percentage of Matches']
avg_bbox_dimensions = df['Average BBox Dimensions (All)']
num_occurrences = df['Number of Occurrences']
 
# Calculate the mean of the values of "Number of Occurrences"
mean_num_occurrences = num_occurrences.mean()
 
# Create normalized values based on the mean
normalized_values = 0.5 + (num_occurrences - mean_num_occurrences) / (2 * mean_num_occurrences)
normalized_values = np.clip(normalized_values, 0, 1)  # Clip values to [0, 1] range
 
# Create scatter plot using Plotly
fig = go.Figure(data=go.Scatter(
    x=avg_bbox_dimensions,
    y=percentage_matches,
    mode='markers',
    marker=dict(
        color=normalized_values,
        colorscale='RdYlGn',  # Red-Yellow-Green colormap
        line_width=1
    )
))
 
# Update layout
fig.update_layout(
    title='Correlation between BBox Dimensions and Percentage of Matches',
    xaxis_title='Average BBox Dimensions (All)',
    yaxis_title='Percentage of Matches',
    plot_bgcolor='rgba(0,0,0,0)'
)
 
# Export the plot to an HTML file
fig.write_html("plot.html")