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How to animate a 2D scatter plot given X, Y coordinates and time with appearing and disappearing points?

I have a data frame like the below:
Every row represents a person. They stay at 3 different locations for some time given on the dataframe. The first few people don't stay at location1 but they "born" at location2. The rest of them stay at every locations (3 locations).
I would like to animate every person at the given X, Y coordinates given on the data frame and represent them as dots or any other shape. Here is the flow:
Every person should appear at the first given location (location1) at the given time. Their color should be blue at this state.
Stay at location1 until location2_time and then appear at location2. Their color should be red at this state.
Stay at location2 until location3_time and then appear at location3. Their color should be red at this state.
Stay at location3 for 3 seconds and disappear forever.
There can be several people on the visual at the same time. How can I do that?
There are some good answers on the below links. However, on these solutions, points don't disappear.
How can i make points of a python plot appear over time?
How to animate a scatter plot?

The following is an implementation with python-ffmpeg, pandas, matplotlib, and seaborn. You can find output video on my YouTube channel (link is unlisted).
Each frame with figures is saved directly to memory. New figures are generated only when the state of the population changes (person appears/moves/disappears).
You should definetely separate this code into smaller chunks if you are using this in a Python package:
from numpy.random import RandomState, SeedSequence
from numpy.random import MT19937
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np
import ffmpeg
RESOLUTION = (12.8, 7.2) # * 100 pixels
NUMBER_OF_FRAMES = 900
class VideoWriter:
# Courtesy of https://github.com/kylemcdonald/python-utils/blob/master/ffmpeg.py
def __init__(
self,
filename,
video_codec="libx265",
fps=15,
in_pix_fmt="rgb24",
out_pix_fmt="yuv420p",
input_args=None,
output_args=None,
):
self.filename = filename
self.process = None
self.input_args = {} if input_args is None else input_args
self.output_args = {} if output_args is None else output_args
self.input_args["r"] = self.input_args["framerate"] = fps
self.input_args["pix_fmt"] = in_pix_fmt
self.output_args["pix_fmt"] = out_pix_fmt
self.output_args["vcodec"] = video_codec
def add(self, frame):
if self.process is None:
height, width = frame.shape[:2]
self.process = (
ffmpeg.input(
"pipe:",
format="rawvideo",
s="{}x{}".format(width, height),
**self.input_args,
)
.filter("crop", "iw-mod(iw,2)", "ih-mod(ih,2)")
.output(self.filename, **self.output_args)
.global_args("-loglevel", "quiet")
.overwrite_output()
.run_async(pipe_stdin=True)
)
conv = frame.astype(np.uint8).tobytes()
self.process.stdin.write(conv)
def close(self):
if self.process is None:
return
self.process.stdin.close()
self.process.wait()
def figure_to_array(figure):
"""adapted from: https://stackoverflow.com/questions/21939658/"""
figure.canvas.draw()
buf = figure.canvas.tostring_rgb()
n_cols, n_rows = figure.canvas.get_width_height()
return np.frombuffer(buf, dtype=np.uint8).reshape(n_rows, n_cols, 3)
# Generate data for the figure
rs1 = RandomState(MT19937(SeedSequence(123456789)))
time_1 = np.round(rs1.rand(232) * NUMBER_OF_FRAMES).astype(np.int16)
time_2 = time_1 + np.round(rs1.rand(232) * (NUMBER_OF_FRAMES - time_1)).astype(np.int16)
time_3 = time_2 + np.round(rs1.rand(232) * (NUMBER_OF_FRAMES - time_2)).astype(np.int16)
loc_1_x, loc_1_y, loc_2_x, loc_2_y, loc_3_x, loc_3_y = np.round(rs1.rand(6, 232) * 100, 1)
df = pd.DataFrame({
"loc_1_time": time_1,
"loc_1_x": loc_1_x,
"loc_1_y": loc_1_y,
"loc_2_time": time_2,
"loc_2_x": loc_2_x,
"loc_2_y": loc_2_y,
"loc_3_time": time_3,
"loc_3_x": loc_3_x,
"loc_3_y": loc_3_y,
})
"""The stack answer starts here"""
# Add extra column for disappear time
df["disappear_time"] = df["loc_3_time"] + 3
all_times = df[["loc_1_time", "loc_2_time", "loc_3_time", "disappear_time"]]
change_times = np.unique(all_times)
# Prepare ticks for plotting the figure across frames
x_values = df[["loc_1_x", "loc_2_x", "loc_3_x"]].values.flatten()
x_ticks = np.array(np.linspace(x_values.min(), x_values.max(), 6), dtype=np.uint8)
y_values = df[["loc_1_y", "loc_2_y", "loc_3_y"]].values.flatten()
y_ticks = np.array(np.round(np.linspace(y_values.min(), y_values.max(), 6)), dtype=np.uint8)
sns.set_theme(style="whitegrid")
video_writer = VideoWriter("endermen.mp4")
if 0 not in change_times:
# Generate empty figure if no person arrive at t=0
fig, ax = plt.subplots(figsize=RESOLUTION)
ax.set_xticklabels(x_ticks)
ax.set_yticklabels(y_ticks)
ax.set_title("People movement. T=0")
video_writer.add(figure_to_array(fig))
loop_range = range(1, NUMBER_OF_FRAMES)
else:
loop_range = range(NUMBER_OF_FRAMES)
palette = sns.color_palette("tab10") # Returns three colors from the palette (we have three groups)
animation_data_df = pd.DataFrame(columns=["x", "y", "location", "index"])
for frame_idx in loop_range:
if frame_idx in change_times:
plt.close("all")
# Get person who appears/moves/disappears
indexes, loc_nums = np.where(all_times == frame_idx)
loc_nums += 1
for i, loc in zip(indexes, loc_nums):
if loc != 4:
x, y = df[[f"loc_{loc}_x", f"loc_{loc}_y"]].iloc[i]
if loc == 1: # location_1
animation_data_df = animation_data_df.append(
{"x": x, "y": y, "location": loc, "index": i},
ignore_index=True
)
else:
data_index = np.where(animation_data_df["index"] == i)[0][0]
if loc in (2, 3): # location_2 or 3
animation_data_df.loc[[data_index], :] = x, y, loc, i
elif loc == 4: # Disappear
animation_data_df.iloc[data_index] = np.nan
current_palette_size = np.sum(~np.isnan(np.unique(animation_data_df["location"])))
fig, ax = plt.subplots(figsize=RESOLUTION)
sns.scatterplot(
x="x", y="y", hue="location", data=animation_data_df, ax=ax, palette=palette[:current_palette_size]
)
ax.set_xticks(x_ticks)
ax.set_xticklabels(x_ticks)
ax.set_yticks(y_ticks)
ax.set_yticklabels(y_ticks)
ax.legend(loc="center left", bbox_to_anchor=(1, 0.5))
ax.set_title(f"People movement. T={frame_idx}")
video_writer.add(figure_to_array(fig))
video_writer.close()
Edit: There was a bug in which location_3 wasn't removed after 3 seconds. Fixed now.

Modifying the code from this question to only include the positions you want automatically removes the old ones if the old position isn't included in the new ones. This doesn't change if you want to animate by time or iterations or anything else. I have opted to use iterations here since it's easier and I don't know how you are handling your dataset. The code does have one bug though, the last point (or points if they last the same amount of time) remaining won't disappear, this can be solved easily if you don't want to draw anything again, if you do though for exaple in case you there is a gap in the data with no people and then the data resumes I haven't found any workarounds
import math
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
#The t0,t1,t2,t3 are the times (in iterations) that the position changes
#If t0 is None then the person will never be displayed
people = [
# t0 x1 y1 t1 x2 y2 t2 x3 y3 t4
[ 0, 1, 0.1, 1, 2, 0.2, 2, 3, 0.3, 3],
[ 2, None, None, None, 2, 1, 3, 4, 1, 7],
[ 2, float("NaN"), float("NaN"), float("NaN"), 2, 0.8, 4, 4, 0.8, 10],
]
fig = plt.figure()
plt.xlim(0, 5)
plt.ylim(0, 1)
graph = plt.scatter([], [])
def animate(i):
points = []
colors = []
for person in people:
if person[0] is None or math.isnan(person[0]) or i < person[0]:
continue
# Position 1
elif person[3] is not None and not (math.isnan(person[3])) and i <= person[3]:
new_point = [person[1], person[2]]
color = "b"
# Position 2
elif person[6] is not None and not (math.isnan(person[6])) and i <= person[6]:
new_point = [person[4], person[5]]
color = "r"
# Position 3
elif person[9] is not None and not (math.isnan(person[9])) and i <= person[9]:
new_point = [person[7], person[8]]
color = "r"
else:
people.remove(person)
new_point = []
if new_point != []:
points.append(new_point)
colors.append(color)
if points != []:
graph.set_offsets(points)
graph.set_facecolors(colors)
else:
# You can use graph.remove() to fix the last point not disappiring but you won't be able to plot anything after that
# graph.remove()
pass
return graph
ani = FuncAnimation(fig, animate, repeat=False, interval=500)
plt.show()

How to Create a Boxplot / Group Boxplot from [Min ,Q1 ,Q2 ,Q3 ,Max] in Python? [duplicate]

From what I can see, boxplot() method expects a sequence of raw values (numbers) as input, from which it then computes percentiles to draw the boxplot(s).
I would like to have a method by which I could pass in the percentiles and get the corresponding boxplot.
For example:
Assume that I have run several benchmarks and for each benchmark I've measured latencies ( floating point values ). Now additionally, I have precomputed the percentiles for these values.
Hence for each benchmark, I have the 25th, 50th, 75th percentile along with the min and max.
Now given these data, I would like to draw the box plots for the benchmarks.

As of 2020, there is a better method than the one in the accepted answer.
The matplotlib.axes.Axes class provides a bxp method, which can be used to draw the boxes and whiskers based on the percentile values. Raw data is only needed for the outliers, and that is optional.
Example:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
boxes = [
{
'label' : "Male height",
'whislo': 162.6, # Bottom whisker position
'q1' : 170.2, # First quartile (25th percentile)
'med' : 175.7, # Median (50th percentile)
'q3' : 180.4, # Third quartile (75th percentile)
'whishi': 187.8, # Top whisker position
'fliers': [] # Outliers
}
]
ax.bxp(boxes, showfliers=False)
ax.set_ylabel("cm")
plt.savefig("boxplot.png")
plt.close()
This produces the following image:

To draw the box plot using just the percentile values and the outliers ( if any ) I made a customized_box_plot function that basically modifies attributes in a basic box plot ( generated from a tiny sample data ) to make it fit according to your percentile values.
The customized_box_plot function
def customized_box_plot(percentiles, axes, redraw = True, *args, **kwargs):
"""
Generates a customized boxplot based on the given percentile values
"""
box_plot = axes.boxplot([[-9, -4, 2, 4, 9],]*n_box, *args, **kwargs)
# Creates len(percentiles) no of box plots
min_y, max_y = float('inf'), -float('inf')
for box_no, (q1_start,
q2_start,
q3_start,
q4_start,
q4_end,
fliers_xy) in enumerate(percentiles):
# Lower cap
box_plot['caps'][2*box_no].set_ydata([q1_start, q1_start])
# xdata is determined by the width of the box plot
# Lower whiskers
box_plot['whiskers'][2*box_no].set_ydata([q1_start, q2_start])
# Higher cap
box_plot['caps'][2*box_no + 1].set_ydata([q4_end, q4_end])
# Higher whiskers
box_plot['whiskers'][2*box_no + 1].set_ydata([q4_start, q4_end])
# Box
box_plot['boxes'][box_no].set_ydata([q2_start,
q2_start,
q4_start,
q4_start,
q2_start])
# Median
box_plot['medians'][box_no].set_ydata([q3_start, q3_start])
# Outliers
if fliers_xy is not None and len(fliers_xy[0]) != 0:
# If outliers exist
box_plot['fliers'][box_no].set(xdata = fliers_xy[0],
ydata = fliers_xy[1])
min_y = min(q1_start, min_y, fliers_xy[1].min())
max_y = max(q4_end, max_y, fliers_xy[1].max())
else:
min_y = min(q1_start, min_y)
max_y = max(q4_end, max_y)
# The y axis is rescaled to fit the new box plot completely with 10%
# of the maximum value at both ends
axes.set_ylim([min_y*1.1, max_y*1.1])
# If redraw is set to true, the canvas is updated.
if redraw:
ax.figure.canvas.draw()
return box_plot
USAGE
Using inverse logic ( code at the very end ) I extracted the percentile values from this example
>>> percentiles
(-1.0597368367634488, 0.3977683984966961, 1.0298955252405229, 1.6693981537742526, 3.4951447843464449)
(-0.90494930553559483, 0.36916539612108634, 1.0303658700697103, 1.6874542731392828, 3.4951447843464449)
(0.13744105279440233, 1.3300645202649739, 2.6131540656339483, 4.8763411136047647, 9.5751914834437937)
(0.22786243898199182, 1.4120860286080519, 2.637650402506837, 4.9067126578493259, 9.4660357513550899)
(0.0064696168078617741, 0.30586770128093388, 0.70774153557312702, 1.5241965711101928, 3.3092932063051976)
(0.007009744579241136, 0.28627373934008982, 0.66039691869500572, 1.4772725266672091, 3.221716765477217)
(-2.2621660374110544, 5.1901313713883352, 7.7178532139979357, 11.277744848353247, 20.155971739152388)
(-2.2621660374110544, 5.1884411864079532, 7.3357079047721054, 10.792299385806913, 18.842012119715388)
(2.5417888074435702, 5.885996170695587, 7.7271286220368598, 8.9207423361593179, 10.846938621419374)
(2.5971767318505856, 5.753551925927133, 7.6569980004033464, 8.8161056254143233, 10.846938621419374)
Note that to keep this short I haven't shown the outliers vectors which will be the 6th element of each of the percentile array.
Also note that all usual additional kwargs / args can be used since they are simply passed to the boxplot method inside it :
>>> fig, ax = plt.subplots()
>>> b = customized_box_plot(percentiles, ax, redraw=True, notch=0, sym='+', vert=1, whis=1.5)
>>> plt.show()
EXPLANATION
The boxplot method returns a dictionary mapping the components of the boxplot to the individual matplotlib.lines.Line2D instances that were created.
Quoting from the matplotlib.pyplot.boxplot documentation :
That dictionary has the following keys (assuming vertical boxplots):
boxes: the main body of the boxplot showing the quartiles and the median’s confidence intervals if enabled.
medians: horizonal lines at the median of each box.
whiskers: the vertical lines extending to the most extreme, n-outlier data points. caps: the horizontal lines at the ends of the whiskers.
fliers: points representing data that extend beyond the whiskers (outliers).
means: points or lines representing the means.
For example observe the boxplot of a tiny sample data of [-9, -4, 2, 4, 9]
>>> b = ax.boxplot([[-9, -4, 2, 4, 9],])
>>> b
{'boxes': [<matplotlib.lines.Line2D at 0x7fe1f5b21350>],
'caps': [<matplotlib.lines.Line2D at 0x7fe1f54d4e50>,
<matplotlib.lines.Line2D at 0x7fe1f54d0e50>],
'fliers': [<matplotlib.lines.Line2D at 0x7fe1f5b317d0>],
'means': [],
'medians': [<matplotlib.lines.Line2D at 0x7fe1f63549d0>],
'whiskers': [<matplotlib.lines.Line2D at 0x7fe1f5b22e10>,
<matplotlib.lines.Line2D at 0x7fe20c54a510>]}
>>> plt.show()
The matplotlib.lines.Line2D objects have two methods that I'll be using in my function extensively. set_xdata ( or set_ydata ) and get_xdata ( or get_ydata ).
Using these methods we can alter the position of the constituent lines of the base box plot to conform to your percentile values ( which is what the customized_box_plot function does ). After altering the constituent lines' position, you can redraw the canvas using figure.canvas.draw()
Summarizing the mappings from percentile to the coordinates of the various Line2D objects.
The Y Coordinates :
The max ( q4_end - end of 4th quartile ) corresponds to the top most cap Line2D object.
The min ( q1_start - start of the 1st quartile ) corresponds to the lowermost most cap Line2D object.
The median corresponds to the ( q3_start ) median Line2D object.
The 2 whiskers lie between the ends of the boxes and extreme caps ( q1_start and q2_start - lower whisker; q4_start and q4_end - upper whisker )
The box is actually an interesting n shaped line bounded by a cap at the lower portion. The extremes of the n shaped line correspond to the q2_start and the q4_start.
The X Coordinates :
The Central x coordinates ( for multiple box plots are usually 1, 2, 3... )
The library automatically calculates the bounding x coordinates based on the width specified.
INVERSE FUNCTION TO RETRIEVE THE PERCENTILES FROM THE boxplot DICT:
def get_percentiles_from_box_plots(bp):
percentiles = []
for i in range(len(bp['boxes'])):
percentiles.append((bp['caps'][2*i].get_ydata()[0],
bp['boxes'][i].get_ydata()[0],
bp['medians'][i].get_ydata()[0],
bp['boxes'][i].get_ydata()[2],
bp['caps'][2*i + 1].get_ydata()[0],
(bp['fliers'][i].get_xdata(),
bp['fliers'][i].get_ydata())))
return percentiles
NOTE:
The reason why I did not make a completely custom boxplot method is because, there are many features offered by the inbuilt box plot that cannot be fully reproduced.
Also excuse me if I may have unnecessarily explained something that may have been too obvious.

Here is an updated version of this useful routine. Setting the vertices directly appears to work for both filled boxes (patchArtist=True) and unfilled ones.
def customized_box_plot(percentiles, axes, redraw = True, *args, **kwargs):
"""
Generates a customized boxplot based on the given percentile values
"""
n_box = len(percentiles)
box_plot = axes.boxplot([[-9, -4, 2, 4, 9],]*n_box, *args, **kwargs)
# Creates len(percentiles) no of box plots
min_y, max_y = float('inf'), -float('inf')
for box_no, pdata in enumerate(percentiles):
if len(pdata) == 6:
(q1_start, q2_start, q3_start, q4_start, q4_end, fliers_xy) = pdata
elif len(pdata) == 5:
(q1_start, q2_start, q3_start, q4_start, q4_end) = pdata
fliers_xy = None
else:
raise ValueError("Percentile arrays for customized_box_plot must have either 5 or 6 values")
# Lower cap
box_plot['caps'][2*box_no].set_ydata([q1_start, q1_start])
# xdata is determined by the width of the box plot
# Lower whiskers
box_plot['whiskers'][2*box_no].set_ydata([q1_start, q2_start])
# Higher cap
box_plot['caps'][2*box_no + 1].set_ydata([q4_end, q4_end])
# Higher whiskers
box_plot['whiskers'][2*box_no + 1].set_ydata([q4_start, q4_end])
# Box
path = box_plot['boxes'][box_no].get_path()
path.vertices[0][1] = q2_start
path.vertices[1][1] = q2_start
path.vertices[2][1] = q4_start
path.vertices[3][1] = q4_start
path.vertices[4][1] = q2_start
# Median
box_plot['medians'][box_no].set_ydata([q3_start, q3_start])
# Outliers
if fliers_xy is not None and len(fliers_xy[0]) != 0:
# If outliers exist
box_plot['fliers'][box_no].set(xdata = fliers_xy[0],
ydata = fliers_xy[1])
min_y = min(q1_start, min_y, fliers_xy[1].min())
max_y = max(q4_end, max_y, fliers_xy[1].max())
else:
min_y = min(q1_start, min_y)
max_y = max(q4_end, max_y)
# The y axis is rescaled to fit the new box plot completely with 10%
# of the maximum value at both ends
axes.set_ylim([min_y*1.1, max_y*1.1])
# If redraw is set to true, the canvas is updated.
if redraw:
ax.figure.canvas.draw()
return box_plot

Here is a bottom-up approach where the box_plot is build up using matplotlib's vline, Rectangle, and normal plot functions
def boxplot(df, ax=None, box_width=0.2, whisker_size=20, mean_size=10, median_size = 10 , line_width=1.5, xoffset=0,
color=0):
"""Plots a boxplot from existing percentiles.
Parameters
----------
df: pandas DataFrame
ax: pandas AxesSubplot
if to plot on en existing axes
box_width: float
whisker_size: float
size of the bar at the end of each whisker
mean_size: float
size of the mean symbol
color: int or rgb(list)
If int particular color of property cycler is taken. Example of rgb: [1,0,0] (red)
Returns
-------
f, a, boxes, vlines, whisker_tips, mean, median
"""
if type(color) == int:
color = plt.rcParams['axes.prop_cycle'].by_key()['color'][color]
if ax:
a = ax
f = a.get_figure()
else:
f, a = plt.subplots()
boxes = []
vlines = []
xn = []
for row in df.iterrows():
x = row[0] + xoffset
xn.append(x)
# box
y = row[1][25]
height = row[1][75] - row[1][25]
box = plt.Rectangle((x - box_width / 2, y), box_width, height)
a.add_patch(box)
boxes.append(box)
# whiskers
y = (row[1][95] + row[1][5]) / 2
vl = a.vlines(x, row[1][5], row[1][95])
vlines.append(vl)
for b in boxes:
b.set_linewidth(line_width)
b.set_facecolor([1, 1, 1, 1])
b.set_edgecolor(color)
b.set_zorder(2)
for vl in vlines:
vl.set_color(color)
vl.set_linewidth(line_width)
vl.set_zorder(1)
whisker_tips = []
if whisker_size:
g, = a.plot(xn, df[5], ls='')
whisker_tips.append(g)
g, = a.plot(xn, df[95], ls='')
whisker_tips.append(g)
for wt in whisker_tips:
wt.set_markeredgewidth(line_width)
wt.set_color(color)
wt.set_markersize(whisker_size)
wt.set_marker('_')
mean = None
if mean_size:
g, = a.plot(xn, df['mean'], ls='')
g.set_marker('o')
g.set_markersize(mean_size)
g.set_zorder(20)
g.set_markerfacecolor('None')
g.set_markeredgewidth(line_width)
g.set_markeredgecolor(color)
mean = g
median = None
if median_size:
g, = a.plot(xn, df['median'], ls='')
g.set_marker('_')
g.set_markersize(median_size)
g.set_zorder(20)
g.set_markeredgewidth(line_width)
g.set_markeredgecolor(color)
median = g
a.set_ylim(np.nanmin(df), np.nanmax(df))
return f, a, boxes, vlines, whisker_tips, mean, median
This is how it looks in action:
import numpy as np
import pandas as pd
import matplotlib.pylab as plt
nopts = 12
df = pd.DataFrame()
df['mean'] = np.random.random(nopts) + 7
df['median'] = np.random.random(nopts) + 7
df[5] = np.random.random(nopts) + 4
df[25] = np.random.random(nopts) + 6
df[75] = np.random.random(nopts) + 8
df[95] = np.random.random(nopts) + 10
out = boxplot(df)

how to visualize high volumn 3 dimensional data

I have a data set like the following:
import numpy as np
from pandas import DataFrame
mypos = np.random.randint(10, size=(100, 2))
mydata = DataFrame(mypos, columns=['x', 'y'])
myres = np.random.rand(100, 1)
mydata['res'] = myres
The res variable is continous, the x and y variables are integers representing
positions (therefore largely repetitive),
and res represents kind of correlations between pairs of positions.
I am wondering what are the best ways of visualizing this data set?
Possible approaches already considered:
Scatter plot, with the res variable visualized by a color gradient.
Parallel coordinates plot.
The first approach is problematic when the number of positions get large,
because high values (which are the values we care about) of the res variable would be drowned in a sea of
small dots.
The second approach could be promising, but I am having trouble producing it.
I have tried the parallel_coordinates function from the pandas module,
but it's not behaving as I would like it to. (see this question here:
parallel coordinates plot for continous data in pandas
)

I hope this helps to find a solution in R. Good luck.
# you need this package for the colour palette
library(RColorBrewer)
# create the random data
dd <- data.frame(
x = round(runif(100, 0, 10), 0),
y = round(runif(100, 0, 10), 0),
res = runif(100)
)
# pick the number of colours (granularity of colour scale)
nColors <- 100
# create the colour pallete
cols <-colorRampPalette(colors=c("white","blue"))(nColors)
# get a zScale for the colours
zScale <- seq(min(dd$res), max(dd$res), length.out = nColors)
# function that returns the nearest colour given a value of res
findNearestColour <- function(x) {
colorIndex <- which(abs(zScale - x) == min(abs(zScale - x)))
return(cols[colorIndex])
}
# the first plot is the scatterplot
### this has problems because points come out on top of eachother
plot(y ~ x, dd, type = "n")
for(i in 1:dim(dd)[1]){
with(dd[i,],
points(y ~ x, col = findNearestColour(res), pch = 19)
)
}
# this is your parallel coordinates plot (a little better)
plot(1, 1, xlim = c(0, 1), ylim = c(min(dd$x, dd$y), max(dd$x, dd$y)),
type = "n", axes = F, ylab = "", xlab = "")
for(i in 1:dim(dd)[1]){
with(dd[i,],
segments(0, x, 1, y, col = findNearestColour(res))
)
}

Obtaining values used in boxplot, using python and matplotlib

I can draw a boxplot from data:
import numpy as np
import matplotlib.pyplot as plt
data = np.random.rand(100)
plt.boxplot(data)
Then, the box will range from the 25th-percentile to 75th-percentile, and the whisker will range from the smallest value to the largest value between (25th-percentile - 1.5*IQR, 75th-percentile + 1.5*IQR), where the IQR denotes the inter-quartile range. (Of course, the value 1.5 is customizable).
Now I want to know the values used in the boxplot, i.e. the median, upper and lower quartile, the upper whisker end point and the lower whisker end point. While the former three are easy to obtain by using np.median() and np.percentile(), the end point of the whiskers will require some verbose coding:
median = np.median(data)
upper_quartile = np.percentile(data, 75)
lower_quartile = np.percentile(data, 25)
iqr = upper_quartile - lower_quartile
upper_whisker = data[data<=upper_quartile+1.5*iqr].max()
lower_whisker = data[data>=lower_quartile-1.5*iqr].min()
I was wondering, while this is acceptable, would there be a neater way to do this? It seems that the values should be ready to pull-out from the boxplot, as it's already drawn.

Why do you want to do so? what you are doing is already pretty direct.
Yeah, if you want to fetch them for the plot, when the plot is already made, simply use the get_ydata() method.
B = plt.boxplot(data)
[item.get_ydata() for item in B['whiskers']]
It returns an array of the shape (2,) for each whiskers, the second element is the value we want:
[item.get_ydata()[1] for item in B['whiskers']]

I've had this recently and have written a function to extract the boxplot values from the boxplot as a pandas dataframe.
The function is:
def get_box_plot_data(labels, bp):
rows_list = []
for i in range(len(labels)):
dict1 = {}
dict1['label'] = labels[i]
dict1['lower_whisker'] = bp['whiskers'][i*2].get_ydata()[1]
dict1['lower_quartile'] = bp['boxes'][i].get_ydata()[1]
dict1['median'] = bp['medians'][i].get_ydata()[1]
dict1['upper_quartile'] = bp['boxes'][i].get_ydata()[2]
dict1['upper_whisker'] = bp['whiskers'][(i*2)+1].get_ydata()[1]
rows_list.append(dict1)
return pd.DataFrame(rows_list)
And is called by passing an array of labels (the ones that you would pass to the boxplot plotting function) and the data returned by the boxplot function itself.
For example:
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
def get_box_plot_data(labels, bp):
rows_list = []
for i in range(len(labels)):
dict1 = {}
dict1['label'] = labels[i]
dict1['lower_whisker'] = bp['whiskers'][i*2].get_ydata()[1]
dict1['lower_quartile'] = bp['boxes'][i].get_ydata()[1]
dict1['median'] = bp['medians'][i].get_ydata()[1]
dict1['upper_quartile'] = bp['boxes'][i].get_ydata()[2]
dict1['upper_whisker'] = bp['whiskers'][(i*2)+1].get_ydata()[1]
rows_list.append(dict1)
return pd.DataFrame(rows_list)
data1 = np.random.normal(loc = 0, scale = 1, size = 1000)
data2 = np.random.normal(loc = 5, scale = 1, size = 1000)
data3 = np.random.normal(loc = 10, scale = 1, size = 1000)
labels = ['data1', 'data2', 'data3']
bp = plt.boxplot([data1, data2, data3], labels=labels)
print(get_box_plot_data(labels, bp))
plt.show()
Outputs the following from get_box_plot_data:
label lower_whisker lower_quartile median upper_quartile upper_whisker
0 data1 -2.491652 -0.587869 0.047543 0.696750 2.559301
1 data2 2.351567 4.310068 4.984103 5.665910 7.489808
2 data3 7.227794 9.278931 9.947674 10.661581 12.733275
And produces the following plot:

upper_whisker = data[data<=upper_quartile+1.5*iqr].max()
lower_whisker = data[data>=lower_quartile-1.5*iqr].min()
equal to
upper_whisker = data.max()
lower_whisker = data.min()
if you just want to get the real data points in the dataset. But statistically speaking, the whisker values are upper_quantile+1.5IQR and lower_quantile-1.5IQR

How to put colours in dendograms of matplotlib - scipy in python?

I have the following code to perform hierarchical clutering on data:
Z = linkage(data,method='weighted')
plt.subplot(2,1,1)
dendro = dendrogram(Z)
leaves = dendro['leaves']
print leaves
plt.show()
How ever at the dendogram all the clusters have the same color (blue). Is there a way to use different colors with respect to similarity in between clusters?

Look at the documentation, Looks like you could pass the link_color_func keyword or color_threshold keyword to have different colors.
Edit:
The default behavior of the dendrogram coloring scheme is, given a color_threshold = 0.7*max(Z[:,2]) to color all the descendent links below a cluster node k the same color if k is the first node below the cut threshold; otherwise, all links connecting nodes with distances greater than or equal to the threshold are colored blue [from the docs].
What the hell does this mean? Well, if you look at a dendrogram, different clusters linked together. The "distance" between two clusters is the height of the link between them. The color_threshold is the height below which new clusters will be different colors. If all your clusters are blue, then you need to raise your color_threshold. For example,
In [48]: mat = np.random.rand(10, 10)
In [49]: z = linkage(mat, method="weighted")
In [52]: d = dendrogram(z)
In [53]: d['color_list']
Out[53]: ['g', 'g', 'b', 'r', 'c', 'c', 'c', 'b', 'b']
In [54]: plt.show()
I can check what the default color_threshold is by
In [56]: 0.7*np.max(z[:,2])
Out[56]: 1.0278719020096947
If I lower the color_threshold, I get more blue because more links have distances greater than the new color_threshold. You can see this visually because all the links above 0.9 are now blue:
In [64]: d = dendrogram(z, color_threshold=.9)
In [65]: d['color_list']
Out[65]: ['g', 'b', 'b', 'r', 'b', 'b', 'b', 'b', 'b']
In [66]: plt.show()
If I increase the color_threshold to 1.2, the links below 1.2 will no longer be blue. Additionally, the cyan and red links will merge into a single color because their parent link is below 1.2:

The following code will produce a dendrogram with a different color for each leaf. If in the process of merging clusters it encounters two clusters with different colors, then it selects the default one dflt_col = tab:blue.
Note: the link_matrix function is a plain-copy of the one from the AgglomerativeClustering example in scikit-learn.
To explain what all it does, it's really time-consuming. Thus, print directly every unclear step.
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import linkage, dendrogram
from scipy.spatial.distance import squareform, pdist
from matplotlib.pyplot import cm
from sklearn.cluster import AgglomerativeClustering
import matplotlib.colors as clrs
def link_matrix(model, **kwargs):
# Create linkage matrix and then plot the dendrogram as in the standard sci-kit learn documentation
counts = np.zeros(model.children_.shape[0])
n_samples = len(model.labels_)
for i, merge in enumerate(model.children_):
current_count = 0
for child_idx in merge:
if child_idx < n_samples:
current_count += 1 # leaf node
else:
current_count += counts[child_idx - n_samples]
counts[i] = current_count
Z = np.column_stack(
[model.children_, model.distances_, counts]
).astype(float)
return Z
def assign_link_colors(model):
n_clusters = len(model.Z)
scl_map_to_hex = mpl.cm.ScalarMappable(cmap = "jet").to_rgba(np.unique(model.labels_), norm = True) #colors.to_hex()
col = [clrs.to_hex(rgb) for rgb in scl_map_to_hex]
dic_labels = {s:[c, idx] for s, c, idx in zip(np.arange(len(model.feature_names_in_), dtype = int), model.feature_names_in_, model.labels_, )}
model.dict_idx_name_cl = {k: v for k, v in sorted(dic_labels.items(), key=lambda item: item[1][1])}
dflt_col = "tab:blue" # Unclustered blue
model.dict_colors = {x:col[model.dict_idx_name_cl[x][1]] for x in model.dict_idx_name_cl}
link_cols = {}
for i, i_cl in enumerate(model.Z[:,:2].astype(int)): # select only 1st two rows
c1, c2 = (link_cols[x] if x > n_clusters else model.dict_colors[x] for x in i_cl)
# Choice of coloring assignment: if same color --> ok; if no leaf, dft ("undefined") color
if c1 == c2:
tmp_cl = c1
elif min(i_cl) <= n_clusters: # select the leaf color
tmp_cl = model.dict_colors[min(i_cl)]
else:
tmp_cl = dflt_col
link_cols[i+1+n_clusters] = tmp_cl
#print(f'-link_cols: {link_cols}',)
return link_cols
def mod_2_dendrogram(model, **kwargs):
plt.style.use('seaborn-whitegrid')
plt.figure(figsize=(int(.5 * len(model.feature_names_in_)), 7))
print(f'-0.7*max(Z[:,2]): {0.7*max(model.Z[:,2])}',)
# Plot the corresponding dendrogram
ddata = dendrogram(model.Z, #count_sort = "descending",
**kwargs)
# Plot distances on the dendrogram
# plot cluster points & distance labels
y_lim = dist_thr
for i, d, c in zip(ddata['icoord'], ddata['dcoord'], ddata['color_list']):
x = sum(i[1:3])/2
y = d[1]
if y > y_lim:
plt.plot(x, y, 'o', c=c, markeredgewidth=0)
plt.annotate(np.round(y,2), (x, y), xytext=(0, -5),
textcoords='offset points',
va='top', ha='center', fontsize=9)
plt.axhline(y=dist_thr, color='orange', alpha = 0.7, linestyle='--', label = f"threshold: {int(model.dist_thr)}")
plt.title(f'Agglomerative Dendrogram with n_clust: {model.n_clusters_}')
plt.xlabel('Clusters')
plt.ylabel('Distance')
plt.legend()
return ddata
Now, the running example:
import string
import pandas as pd
np.random.seed(0)
dist = np.random.randint(1e4, size = (10,10))
np.fill_diagonal(dist, 0)
dist = pd.DataFrame(dist, columns = list(string.ascii_lowercase)[:dist.shape[0]])
dist_thr = 1.5e3
model = AgglomerativeClustering(distance_threshold = dist_thr, n_clusters=None, linkage = "single", metric = "precomputed",)
model.dist_thr = dist_thr
model = model.fit(dist)
model.Z = link_matrix(model)
link_cols = assign_link_colors(model)
_ = mod_2_dendrogram(model, labels = dist.columns,
link_color_func = lambda x: link_cols[x])