Aligning two data sets in Python - python

I want to develop some python code to align datasets obtained by different instruments recording the same event.
As an example, say I have two sets of measurements:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# Define some data
data1 = pd.DataFrame({'TIME':[1.1, 2.4, 3.2, 4.1, 5.3],\
'VALUE':[10.3, 10.5, 11.0, 10.9, 10.7],\
'ERROR':[0.2, 0.1, 0.4, 0.3, 0.2]})
data2 = pd.DataFrame({'TIME':[0.9, 2.1, 2.9, 4.2],\
'VALUE':[18.4, 18.7, 18.9, 18.8],\
'ERROR':[0.3, 0.2, 0.5, 0.4]})
# Plot the data
plt.errorbar(data1.TIME, data1.VALUE, yerr=data1.ERROR, fmt='ro')
plt.errorbar(data2.TIME, data2.VALUE, yerr=data2.ERROR, fmt='bo')
plt.show()
The result is plotted here:
What I would like to do now is to align the second dataset (data2) to the first one (data1). i.e. to get this:
The second dataset must be shifted to match the first one by subtracting a constant (to be determined) from all its values. All I know is that the datasets are correlated since the two instruments are measuring the same event but with different sampling rates.
At this stage I do not want to make any assumptions about what function best describes the data (fitting will be done after alignment).
I am cautious about using means to perform shifts since it may produce bad results, depending on how the data is sampled. I was considering taking each data2[TIME_i] and working out the shortest distance to data1[~TIME_i]. Then minimizing the sum of those. But I am not sure that would work well either.
Does anyone have any suggestions on a good method to use? I looked at mlpy but it seems to only work on 1D arrays.
Thanks.

You can substract the mean of the difference: data2.VALUE-(data2.VALUE - data1.VALUE).mean()
import pandas as pd
import matplotlib.pyplot as plt
# Define some data
data1 = pd.DataFrame({
'TIME': [1.1, 2.4, 3.2, 4.1, 5.3],
'VALUE': [10.3, 10.5, 11.0, 10.9, 10.7],
'ERROR': [0.2, 0.1, 0.4, 0.3, 0.2],
})
data2 = pd.DataFrame({
'TIME': [0.9, 2.1, 2.9, 4.2],
'VALUE': [18.4, 18.7, 18.9, 18.8],
'ERROR': [0.3, 0.2, 0.5, 0.4],
})
# Plot the data
plt.errorbar(data1.TIME, data1.VALUE, yerr=data1.ERROR, fmt='ro')
plt.errorbar(data2.TIME, data2.VALUE-(data2.VALUE - data1.VALUE).mean(),
yerr=data2.ERROR, fmt='bo')
plt.show()
Another possibility is to subtract the mean of each series

You can calculate the offset of the average and subtract that from every value. If you do this for every value they should align relatively well. This would assume both dataset look relatively similar, so it might not work the best.
Although this question is not Matlab related, you might still be interested in this:
Remove unknown DC Offset from a non-periodic discrete time signal

Related

Python: Trouble running any additional queries on Geopy output?

have encountered the following - Struggling to wrap my head around it.
Have some data that looks like this:
I've written the following Python that works out the distance between the 2 sets of coordinates:
from geopy import distance
# Calculate distance between 2 sets of coordinates
# Result is float64
data['Distance'] = data[['Start_Lat', 'Start_Lng', 'End_Lat', 'End_Lng']].apply(lambda x: distance.distance((x[0],x[1]), (x[2],x[3])).km, axis=1)
print(data['Distance'])
# Create quantiles
data["DisBucket"] = pd.qcut(df_nyc.Aftermath, q=[0, 0.3, 0.7, 1.0], labels=['LOW', 'MEDIUM', 'HIGH'])
The first bit works fine and returns the following as a float64:
The second bit however fails and returns the following:
It doesn't seem to like the output from Geopy for whatever reason. I haven't been able to work out away around this. Is there potentially a way to copy across the values without the association to Geopy?
Any advice would be greatly appreciated :)
#Create sample data
dat = [[43.11944,-75.2932, 40.12029, -74.2935],[40.83488,-75.8662, 40.83377, -73.8633],[40.81212,-73.9165, 40.80491, -73.9112],
[43.07367,-78.9906, 43.07523, -78.9906],
[41.30884,-74.0253, 40.30746, -74.028]]
data = pd.DataFrame(dat, columns=['Start_lat', 'Start_Lng', 'End_Lat', 'End_Lng'])
#Calculate distance between 2 sets of coordinates
data['Distance'] = data.apply(lambda x: distance.distance((x['Start_lat'], x['Start_Lng']), (x['End_Lat'], x['End_Lng'])).km, axis=1)
#Create quantile
data['DisBucket'] = pd.qcut(data.Distance, q=[0, 0.3, 0.7, 1.0], labels=['LOW', 'MEDIUM', 'HIGH'])

Is there a python package that allows you to model a time series of compositional data?

I have a 2 time series that look like this:
import pandas as pd
series_1 = pd.DataFrame({'time': [0,1,2,3,4], 'value_1': [0.3, 0.5, 0.4, 0.8, 0.7]})
series_2 = pd.DataFrame({'time': [0,1,2,3,4], 'value_2': [0.7, 0.5, 0.6, 0.2, 0.3]})
As you can notice, at each point in time the sum of value_ is equal to 1.
From what I read this type of time series is called "compositional".
My question is, is there a python package that can help me model this type of time series ?
I have tried using prophet to model each series_ separately, and later scale the forecasting values so that they sum to 1, but I am not sure if this approach is appropriate for this type of time series data, any thoughts on that ?

plotting data from a list in python

I need to plot the velocities of some objects(cars).
Each velocity are being calculated through a routine and written in a file, roughly through this ( I have deleted some lines to simplify):
thefile_v= open('vels.txt','w')
for car in cars:
velocities.append(new_velocity)
if len(car.velocities) > 4:
try:
thefile_v.write("%s\n" %car.velocities) #write vels once we get 5 values
thefile_v.close
except:
print "Unexpected error:", sys.exc_info()[0]
raise
The result of this is a text file with list of velocities for each car.
something like this:
[0.0, 3.8, 4.5, 4.3, 2.1, 2.2, 0.0]
[0.0, 2.8, 4.0, 4.2, 2.2, 2.1, 0.0]
[0.0, 1.8, 4.2, 4.1, 2.3, 2.2, 0.0]
[0.0, 3.8, 4.4, 4.2, 2.4, 2.4, 0.0]
Then I wanted to plot each velocity
with open('vels.txt') as f:
lst = [line.rstrip() for line in f]
plt.plot(lst[1]) #lets plot the second line
plt.show()
This is what I found. The values are taken as a string and put them as yLabel.
I got it working through this:
from numpy import array
y = np.fromstring( str(lst[1])[1:-1], dtype=np.float, sep=',' )
plt.plot(y)
plt.show()
What I learnt is that, the set of velocity lists I built previously were treated as lines of data.
I had to convert them to arrays to be able to plot them. However the brackets [] were getting into the way. By converting the line of data to string and removing the brackets through this (i.e. [1:-1]).
It is working now, but I'm sure there is a better way of doing this.
Any comments?
Just say you had the array [0.0, 3.8, 4.5, 4.3, 2.1, 2.2, 0.0], to graph this the code would look something like:
import matplotlib.pyplot as plt
ys = [0.0, 3.8, 4.5, 4.3, 2.1, 2.2, 0.0]
xs = [x for x in range(len(ys))]
plt.plot(xs, ys)
plt.show()
# Make sure to close the plt object once done
plt.close()
if you wanted to have different intervals for the x axis then:
interval_size = 2.4 #example interval size
xs = [x * interval_size for x in range(len(ys))]
Also when reading your values from the text file make sure that you have converted your values from strings back to integers. This maybe why your code is assuming your input is the y label.
The example is not complete, so some assumptions must be made here. In general, use numpy or pandas to store your data.
Suppose car is an object, with a velocity attribute, you can write all velocities in a list, save this list as text file with numpy, read it again with numpy and plot it.
import numpy as np
import matplotlib.pyplot as plt
class Car():
def __init__(self):
self.velocity = np.random.rand(5)
cars = [Car() for _ in range(5)]
velocities = [car.velocity for car in cars]
np.savetxt("vels.txt", np.array(velocities))
####
vels = np.loadtxt("vels.txt")
plt.plot(vels.T)
## or plot only the first velocity
#plt.plot(vels[0]
plt.show()
Just one possible easy solution. Use the map function. Say in your file, you have the data stored like, without any [ and ] non-convertible letters.
#file_name: test_example.txt
0.0, 3.8, 4.5, 4.3, 2.1, 2.2, 0.0
0.0, 2.8, 4.0, 4.2, 2.2, 2.1, 0.0
0.0, 1.8, 4.2, 4.1, 2.3, 2.2, 0.0
0.0, 3.8, 4.4, 4.2, 2.4, 2.4, 0.0
Then the next step is;
import matplotlib.pyplot as plt
path = r'VAR_DIRECTORY/test_example.txt' #the full path of the file
with open(path,'rt') as f:
ltmp = [list(map(float,line.split(','))) for line in f]
plt.plot(ltmp[1],'r-')
plt.show()
In top, I just assume you want to plot the second line, 0.0, 2.8, 4.0, 4.2, 2.2, 2.1, 0.0. Then here is the result.

Display more attributes in the decision tree

I am currently viewing the decision tree using the following code. Is there a way that we can export some calculated fields as output too?
For example, is it possible to display the sum of an input attribute at each node, i.e. sum of feature 1 from 'X' data array in the leafs of the tree.
from sklearn import datasets
iris = datasets.load_iris()
X = iris.data[:]
y = iris.target
#%%
from sklearn.tree import DecisionTreeClassifier
alg=DecisionTreeClassifier( max_depth=5,min_samples_leaf=2, max_leaf_nodes = 10)
alg.fit(X,y)
#%%
## View tree
import graphviz
from sklearn import tree
dot_data = tree.export_graphviz(alg,out_file=None, node_ids = True, proportion = True, class_names = True, filled = True, rounded = True)
graph = graphviz.Source(dot_data)
graph
There is plenty of discussion about decision trees in scikit-learn on the github page. There are answers on this SO question and this scikit-learn documentation page that provide the framework to get you started. With all the links out of the way, here are some functions that allow a user to address the question in a generalizable manner. The functions could be easily modified since I don't know if you mean all the leaves or each leaf individually. My approach is the latter.
The first function uses apply as a cheap way to find the indices of the leaf nodes. It's not necessary to achieve what you're asking, but I included it as a convenience since you mentioned you want to investigate leaf nodes and leaf node indices may be unknown a priori.
def find_leaves(X, clf):
"""A cheap function to find leaves of a DecisionTreeClassifier
clf must be a fitted DecisionTreeClassifier
"""
return set(clf.apply(X))
Result on the example:
find_leaves(X, alg)
{1, 7, 8, 9, 10, 11, 12}
The following function will return an array of values that satisfy the conditions of node and feature, where node is the index of the node from the tree that you want values for and feature is the column (or feature) that you want from X.
def node_feature_values(X, clf, node=0, feature=0, require_leaf=False):
"""this function will return an array of values
from the input array X. Array values will be limited to
1. samples that passed through <node>
2. and from the feature <feature>.
clf must be a fitted DecisionTreeClassifier
"""
leaf_ids = find_leaves(X, clf)
if (require_leaf and
node not in leaf_ids):
print("<require_leaf> is set, "
"select one of these nodes:\n{}".format(leaf_ids))
return
# a sparse array that contains node assignment by sample
node_indicator = clf.decision_path(X)
node_array = node_indicator.toarray()
# which samples at least passed through the node
samples_in_node_mask = node_array[:,node]==1
return X[samples_in_node_mask, feature]
Applied to the example:
values_arr = node_feature_values(X, alg, node=12, feature=0, require_leaf=True)
array([6.3, 5.8, 7.1, 6.3, 6.5, 7.6, 7.3, 6.7, 7.2, 6.5, 6.4, 6.8, 5.7,
5.8, 6.4, 6.5, 7.7, 7.7, 6.9, 5.6, 7.7, 6.3, 6.7, 7.2, 6.1, 6.4,
7.4, 7.9, 6.4, 7.7, 6.3, 6.4, 6.9, 6.7, 6.9, 5.8, 6.8, 6.7, 6.7,
6.3, 6.5, 6.2, 5.9])
Now the user can perform whatever mathematical operation is desired on the subset of samples for a given feature.
i.e. sum of feature 1 from 'X' data array in the leafs of the tree.
print("There are {} total samples in this node, "
"{}% of the total".format(len(values_arr), len(values_arr) / float(len(X))*100))
print("Feature Sum: {}".format(values_arr.sum()))
There are 43 total samples in this node,28.666666666666668% of the total
Feature Sum: 286.69999999999993
Update
After re-reading the question, this is the only solution I can put together quickly that doesn't involve modifying scikit source code for export.py. Code below still relies on previously defined functions. This code modifies the dotstring via pydot and networkx.
# Load the data from `dot_data` variable, which you defined.
import pydot
dot_graph = pydot.graph_from_dot_data(dot_data)[0]
import networkx as nx
MG = nx.nx_pydot.from_pydot(dot_graph)
# Select a `feature` and edit the `dot` string in `networkx`.
feature = 0
for n in find_leaves(X, alg):
nfv = node_feature_values(X, alg, node=n, feature=feature)
MG.node[str(n)]['label'] = MG.node[str(n)]['label'] + "\nfeature_{} sum: {}".format(feature, nfv.sum())
# Export the `networkx` graph then plot using `graphviz.Source()`
new_dot_data = nx.nx_pydot.to_pydot(MG)
graph = graphviz.Source(new_dot_data.create_dot())
graph
Notice all the leaves have the sum of values from X for feature 0.
I think the best way to accomplish what you're asking would be to modify tree.py and/or export.py to natively support this feature.

Interpolating a data point on a curve with a negative slope

Hi I have two numpy arrays (in this case representing depth and percentage depth dose data) as follows:
depth = np.array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ,
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. , 2.2,
2.4, 2.6, 2.8, 3. , 3.5, 4. , 4.5, 5. , 5.5])
pdd = np.array([ 80.40649399, 80.35692155, 81.94323956, 83.78981286,
85.58681373, 87.47056637, 89.39149833, 91.33721651,
93.35729334, 95.25343909, 97.06283306, 98.53761309,
99.56624117, 100. , 99.62820672, 98.47564754,
96.33163961, 93.12182427, 89.0940637 , 83.82699219,
77.75436857, 63.15528566, 46.62287768, 29.9665386 ,
16.11104226, 6.92774817, 0.69401413, 0.58247614,
0.55768992, 0.53290371, 0.5205106 ])
which when plotted give the following curve:
I need to find the depth at which the pdd falls to a given value (initially 50%). I have tried slicing the arrays at the point where the pdd reaches 100% as I'm only interested in the points after this.
Unfortunately np.interp only appears to work where both x and y values are incresing.
Could anyone suggest where I should go next?
If I understand you correctly, you want to interpolate the function depth = f(pdd) at pdd = 50.0. For the purposes of the interpolation, it might help for you to think of pdd as corresponding to your "x" values, and depth as corresponding to your "y" values.
You can use np.argsort to sort your "x" and "y" by ascending order of "x" (i.e. ascending pdd), then use np.interp as usual:
# `idx` is an an array of integer indices that sorts `pdd` in ascending order
idx = np.argsort(pdd)
depth_itp = np.interp([50.0], pdd[idx], depth[idx])
plt.plot(depth, pdd)
plt.plot(depth_itp, 50, 'xr', ms=20, mew=2)
This isn't really a programming solution, but it's how you can find the depth. I'm taking the liberty of renaming your variables, so x(i) = depth(i) and y(i) = pdd(i).
In a given interval [x(i),x(i+1)], your linear interpolant is
p_1(X) = y(i) + (X - x(i))*(y(i+1) - y(i))/(x(i+1) - x(i))
You want to find X such that p_1(X) = 50. First find i such that x(i)>50 and x(i+1), then the above equation can be rearranged to give
X = x(i) + (50 - y(i))*((x(i+1) - x(i))/(y(i+1) - y(i)))
For your data (with MATLAB; sorry, no python code) I make it approximately 2.359. This can then be verified with np.interp(X, depth, pdd)
There are several methods to carry out interpolation. For your case, you are basically looking for the depth at 50% which is not available in your data. The simplest interpolation is the linear case. I'm using numerical recipes library in C++ for acquiring the interpolated value via several techniques, therefore,
Linear Interpolation: see page 117
interpolated value depth(50%): 2.35915
Polynomial Interpolation: see page 117
interpolated value depth(50%): 2.36017
Cubic Spline Interpolation: see page 120
interpolated value depth(50%): 2.19401
Rational Function Interpolation: see page 124
interpolated value depth(50%): 2.35986

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