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Simple moving average for time data - Python

I need to calculate the SMA for a time serie data.
In particular, I want to plot in x-axis that mean function and in y-axis another array.
At the beginning, when I didn't do the SMA, these 2 arrays have the same lenght.
Then I found this example online to calculate the SMA:
# Python program to calculate
# simple moving averages using pandas
import pandas as pd
arr = [1, 2, 3, 7, 9]
window_size = 3
# Convert array of integers to pandas series
numbers_series = pd.Series(arr)
# Get the window of series
# of observations of specified window size
windows = numbers_series.rolling(window_size)
# Create a series of moving
# averages of each window
moving_averages = windows.mean()
# Convert pandas series back to list
moving_averages_list = moving_averages.tolist()
# Remove null entries from the list
final_list = moving_averages_list[window_size - 1:]
print(final_list)
I tried to replay that in my case, but I obtain this error:
"ValueError: x and y must have same first dimension, but have shapes
(261228,) and (261237,)"
I paste a bit of my code, maybe it can be useful to understand better:
y_Int_40_dmRe=pd.Series(y_Int_40_dmRe)
windows_40_dmRe = y_Int_40_dmRe.rolling(window_size)
moving_averages_40_dmRe = windows_40_dmRe.mean()
moving_averages_40_dmRe_list = moving_averages_40_dmRe.tolist()
final_list_40_dmRe = moving_averages_40_dmRe_list[window_size - 1:]
plt.plot(final_list_40_dmRe,y_TotEn_40_dmRe, linewidth=2, label="40° - dmRe")
I'm here if you need more informations, thank you in advance for your help
Chiara

How to make a data frame combining different regression results in python?

I am running some regression models to predict performance.
After running the models I created a variable to see the predictions (y_pred_* are lists with 2567 values):
y_pred_LR = regressor.predict(X_test)
y_pred_SVR = regressor2.predict(X_test)
y_pred_RF = regressor3.predict(X_test)
the types of these prediction lists are Array of float64, while the y_test is a DataFrame.
I wanted to create a table with the results, I tried some different ways, calling as list, trying to convert, trying to select as values, and I did not succeed so far, any one could help?
My last trial was like below:
comparison = pd.DataFrame({'Real': y_test, LR':y_pred_LR,'RF':y_pred_RF,'SVM':y_pred_SVM})
In this case the DataFrame is created but the values don´t appear.
Additionally, I would like to create two new rows with the mean and standard deviation of results and this row should be located at beginning (or first row) of the Data Frame.
Thanks

import pandas as pd
import numpy as np
real = np.array([2] * 10).reshape(-1,1)
y_pred_LR = np.array([0] * 10)
y_pred_SVR = np.array([1] * 10)
y_pred_RF = np.array([5] * 10)
real = real.flatten()
comparison = pd.DataFrame({'real':real,'y_pred_LR':y_pred_LR,'y_pred_SVR':y_pred_SVR,"y_pred_RF":y_pred_RF})
Mean = comparison.mean(axis=0)
StD = comparison.std(axis=0)
Mean_StD = pd.concat([Mean,StD],axis=1).T
result = pd.concat([Mean_StD,comparison],ignore_index=True)
print(result)

Normalizing all numeric columns in my dataset and compare before and after

I want to normalize all the numeric values in my dataset.
I have taken my whole dataset into a pandas dataframe.
My code to do this so far:
for column in numeric: #numeric=df._get_numeric_data()
x_array=np.array(df[column])
normalized_X=preprocessing.normalize([x_array])
But how do i verify this is correct though?
I tried plotting a histogram for one of the columns before normalizing and after adding this piece of code before and after my for loop:
x=df['Below.Primary'] #Below.Primary is one of my column names
plt.hist(x, bins=45)
The blue histogram was before the for loop and the orange, after.
My total code looked like this:
ln[21] plt.hist(df['Below.Primary'], bins=45)
ln[22] for column in numeric:
x_array=np.array(df[column])
normalized_X=preprocessing.normalize([x_array])
x=df['Below.Primary']
plt.hist(x, bins=45)
I don't see any reduction in scale. What have i done wrong? If not correct, can someone point out the correct way to do what i wanted to do?

Try use this:
scaler = preprocessing.StandardScaler()
df[col] = scaler.fit_transform(df[col])

A couple general things first.
If numeric is a list of column names (looks like this is the case), the for loop is not necessary.
A Pandas series using an ndarray under the hood so you can just request the ndarray with Series.values instead of calling np.array(). See this page on the Pandas Series.
I am assuming you are using preprocessing from sklearn.
I recommend using sklearn.preprocessing.Normalizer for this.
import pandas as pd
from sklearn.preprocessing import Normalizer
### Without the for loop (recommended)
# this version returns array
normalizer = Normalizer()
normalized_values = normalizer.fit_transform(df[numeric])
# normalized_values is a 2D array which is useful
# for many applications
# to convert back to DataFrame
df = pd.DataFrame(normalized_values, columns = numeric)
### with the for-loop (not recommended)
for column in numeric:
x_array = df[column].values.reshape(-1,1)
df[column] = normalizer.fit_transform(x_array)

You have to set normalized_X to the respective column while iterating.
for column in numeric:
x_array=np.array(df[column])
normalized_X=preprocessing.normalize([x_array])
df[column]= normalized_X #Setting normalized value in the column
x=df['Below.Primary']
plt.hist(x, bins=45)

Pandas: How to detect the peak points (outliers) in a dataframe?

I am having a pandas dataframe with several of speed values which is continuously moving values, but its a sensor data, so we often get the errors in the middle at some points the moving average seems to be not helping also, so what methods can I use to remove these outliers or peak points from the data?
Example:
data points = {0.5,0.5,0.7,0.6,0.5,0.7,0.5,0.4,0.6,4,0.5,0.5,4,5,6,0.4,0.7,0.8,0.9}
in this data If I see the points 4, 4, 5, 6 are completely outlier values,
before I have used the rolling mean with 5 min of window frame to smooth these values but still I am getting these type of a lot of blip points, which I want to remove, can any one suggest me any technique to get rid of these points.
I have an image which is more clear view of data:
if you see here how the data is showing some outlier points which I have to remove?
any Idea whats the possible way to get rid of these points?

I really think z-score using scipy.stats.zscore() is the way to go here. Have a look at the related issue in this post. There they are focusing on which method to use before removing potential outliers. As I see it, your challenge is a bit simpler, since judging by the data provided, it would be pretty straight forward to identify potential outliers without having to transform the data. Below is a code snippet that does just that. Just remember though, that what does and does not look like outliers will depend entirely on your dataset. And after removing some outliers, what has not looked like an outlier before, suddenly will do so now. Have a look:
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
# your data (as a list)
data = [0.5,0.5,0.7,0.6,0.5,0.7,0.5,0.4,0.6,4,0.5,0.5,4,5,6,0.4,0.7,0.8,0.9]
# initial plot
df1 = pd.DataFrame(data = data)
df1.columns = ['data']
df1.plot(style = 'o')
# Function to identify and remove outliers
def outliers(df, level):
# 1. temporary dataframe
df = df1.copy(deep = True)
# 2. Select a level for a Z-score to identify and remove outliers
df_Z = df[(np.abs(stats.zscore(df)) < level).all(axis=1)]
ix_keep = df_Z.index
# 3. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df.loc[ix_keep]
return(df_keep)
Originial data:
Test run 1 : Z-score = 4:
As you can see, no data has been removed because the level was set too high.
Test run 2 : Z-score = 2:
Now we're getting somewhere. Two outliers have been removed, but there is still some dubious data left.
Test run 3 : Z-score = 1.2:
This is looking really good. The remaining data now seems to be a bit more evenly distributed than before. But now the data point highlighted by the original datapoint is starting to look a bit like a potential outlier. So where to stop? That's going to be entirely up to you!
EDIT: Here's the whole thing for an easy copy&paste:
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
# your data (as a list)
data = [0.5,0.5,0.7,0.6,0.5,0.7,0.5,0.4,0.6,4,0.5,0.5,4,5,6,0.4,0.7,0.8,0.9]
# initial plot
df1 = pd.DataFrame(data = data)
df1.columns = ['data']
df1.plot(style = 'o')
# Function to identify and remove outliers
def outliers(df, level):
# 1. temporary dataframe
df = df1.copy(deep = True)
# 2. Select a level for a Z-score to identify and remove outliers
df_Z = df[(np.abs(stats.zscore(df)) < level).all(axis=1)]
ix_keep = df_Z.index
# 3. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df.loc[ix_keep]
return(df_keep)
# remove outliers
level = 1.2
print("df_clean = outliers(df = df1, level = " + str(level)+')')
df_clean = outliers(df = df1, level = level)
# final plot
df_clean.plot(style = 'o')

You might cut values above a certain quantile as follows:
import numpy as np
clean_data=np.array(data_points)[(data_points<=np.percentile(data_points, 95))]
In pandas you would use df.quantile, you can find it here
Or you may use the Q3+1.5*IQR approach to eliminate the outliers, like you would do through a boxplot

How can I remove sharp jumps in data?

I have some skin temperature data (collected at 1Hz) which I intend to analyse.
However, the sensors were not always in contact with the skin. So I have a challenge of removing this non-skin temperature data, whilst preserving the actual skin temperature data. I have about 100 files to analyse, so I need to make this automated.
I'm aware that there is already this similar post, however I've not been able to use that to solve my problem.
My data roughly looks like this:
df =
timeStamp Temp
2018-05-04 10:08:00 28.63
. .
. .
2018-05-04 21:00:00 31.63
The first step I've taken is to simply apply a minimum threshold- this has got rid of the majority of the non-skin data. However, I'm left with the sharp jumps where the sensor was either removed or attached:
To remove these jumps, I was thinking about taking an approach where I use the first order differential of the temp and then use another set of thresholds to get rid of the data I'm not interested in.
e.g.
df_diff = df.diff(60) # period of about 60 makes jumps stick out
filter_index = np.nonzero((df.Temp <-1) | (df.Temp>0.5)) # when diff is less than -1 and greater than 0.5, most likely data jumps.
However, I find myself stuck here. The main problem is that:
1) I don't know how to now use this index list to delete the non-skin data in df. How is best to do this?
The more minor problem is that
2) I think I will still be left with some residual artefacts from the data jumps near the edges (e.g. where a tighter threshold would start to chuck away good data). Is there either a better filtering strategy or a way to then get rid of these artefacts?
*Edit as suggested I've also calculated the second order diff, but to be honest, I think the first order diff would allow for tighter thresholds (see below):
*Edit 2: Link to sample data

Try the code below (I used a tangent function to generate data). I used the second order difference idea from Mad Physicist in the comments.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
df = pd.DataFrame()
df[0] = np.arange(0,10,0.005)
df[1] = np.tan(df[0])
#the following line calculates the absolute value of a second order finite
#difference (derivative)
df[2] = 0.5*(df[1].diff()+df[1].diff(periods=-1)).abs()
df.loc[df[2] < .05][1].plot() #select out regions of a high rate-of-change
df[1].plot() #plot original data
plt.show()
Following is a zoom of the output showing what got filtered. Matplotlib plots a line from beginning to end of the removed data.
Your first question I believe is answered with the .loc selection above.
You second question will take some experimentation with your dataset. The code above only selects out high-derivative data. You'll also need your threshold selection to remove zeroes or the like. You can experiment with where to make the derivative selection. You can also plot a histogram of the derivative to give you a hint as to what to select out.
Also, higher order difference equations are possible to help with smoothing. This should help remove artifacts without having to trim around the cuts.
Edit:
A fourth-order finite difference can be applied using this:
df[2] = (df[1].diff(periods=1)-df[1].diff(periods=-1))*8/12 - \
(df[1].diff(periods=2)-df[1].diff(periods=-2))*1/12
df[2] = df[2].abs()
It's reasonable to think that it may help. The coefficients above can be worked out or derived from the following link for higher orders.
Finite Difference Coefficients Calculator
Note: The above second and fourth order central difference equations are not proper first derivatives. One must divide by the interval length (in this case 0.005) to get the actual derivative.

Here's a suggestion that targets your issues regarding
[...]an approach where I use the first order differential of the temp and then use another set of thresholds to get rid of the data I'm not interested in.
[..]I don't know how to now use this index list to delete the non-skin data in df. How is best to do this?
using stats.zscore() and pandas.merge()
As it is, it will still have a minor issue with your concerns regarding
[...]left with some residual artefacts from the data jumps near the edges[...]
But we'll get to that later.
First, here's a snippet to produce a dataframe that shares some of the challenges with your dataset:
# Imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
np.random.seed(22)
# A function for noisy data with a trend element
def sample():
base = 100
nsample = 50
sigma = 10
# Basic df with trend and sinus seasonality
trend1 = np.linspace(0,1, nsample)
y1 = np.sin(trend1)
dates = pd.date_range(pd.datetime(2016, 1, 1).strftime('%Y-%m-%d'), periods=nsample).tolist()
df = pd.DataFrame({'dates':dates, 'trend1':trend1, 'y1':y1})
df = df.set_index(['dates'])
df.index = pd.to_datetime(df.index)
# Gaussian Noise with amplitude sigma
df['y2'] = sigma * np.random.normal(size=nsample)
df['y3'] = df['y2'] + base + (np.sin(trend1))
df['trend2'] = 1/(np.cos(trend1)/1.05)
df['y4'] = df['y3'] * df['trend2']
df=df['y4'].to_frame()
df.columns = ['Temp']
df['Temp'][20:31] = np.nan
# Insert spikes and missing values
df['Temp'][19] = df['Temp'][39]/4000
df['Temp'][31] = df['Temp'][15]/4000
return(df)
# Dataframe with random data
df_raw = sample()
df_raw.plot()
As you can see, there are two distinct spikes with missing numbers between them. And it's really the missing numbers that are causing the problems here if you prefer to isolate values where the differences are large. The first spike is not a problem since you'll find the difference between a very small number and a number that is more similar to the rest of the data:
But for the second spike, you're going to get the (nonexisting) difference between a very small number and a non-existing number, so that the extreme data-point you'll end up removing is the difference between your outlier and the next observation:
This is not a huge problem for one single observation. You could just fill it right back in there. But for larger data sets that would not be a very viable soution. Anyway, if you can manage without that particular value, the below code should solve your problem. You will also have a similar problem with your very first observation, but I think it would be far more trivial to decide whether or not to keep that one value.
The steps:
# 1. Get some info about the original data:
firstVal = df_raw[:1]
colName = df_raw.columns
# 2. Take the first difference and
df_diff = df_raw.diff()
# 3. Remove missing values
df_clean = df_diff.dropna()
# 4. Select a level for a Z-score to identify and remove outliers
level = 3
df_Z = df_clean[(np.abs(stats.zscore(df_clean)) < level).all(axis=1)]
ix_keep = df_Z.index
# 5. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df_raw.loc[ix_keep]
# 6.
# df_keep will be missing some indexes.
# Do the following if you'd like to keep those indexes
# and, for example, fill missing values with the previous values
df_out = pd.merge(df_keep, df_raw, how='outer', left_index=True, right_index=True)
# 7. Keep only the first column
df_out = df_out.ix[:,0].to_frame()
# 8. Fill missing values
df_complete = df_out.fillna(axis=0, method='ffill')
# 9. Replace first value
df_complete.iloc[0] = firstVal.iloc[0]
# 10. Reset column names
df_complete.columns = colName
# Result
df_complete.plot()
Here's the whole thing for an easy copy-paste:
# Imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
np.random.seed(22)
# A function for noisy data with a trend element
def sample():
base = 100
nsample = 50
sigma = 10
# Basic df with trend and sinus seasonality
trend1 = np.linspace(0,1, nsample)
y1 = np.sin(trend1)
dates = pd.date_range(pd.datetime(2016, 1, 1).strftime('%Y-%m-%d'), periods=nsample).tolist()
df = pd.DataFrame({'dates':dates, 'trend1':trend1, 'y1':y1})
df = df.set_index(['dates'])
df.index = pd.to_datetime(df.index)
# Gaussian Noise with amplitude sigma
df['y2'] = sigma * np.random.normal(size=nsample)
df['y3'] = df['y2'] + base + (np.sin(trend1))
df['trend2'] = 1/(np.cos(trend1)/1.05)
df['y4'] = df['y3'] * df['trend2']
df=df['y4'].to_frame()
df.columns = ['Temp']
df['Temp'][20:31] = np.nan
# Insert spikes and missing values
df['Temp'][19] = df['Temp'][39]/4000
df['Temp'][31] = df['Temp'][15]/4000
return(df)
# A function for removing outliers
def noSpikes(df, level, keepFirst):
# 1. Get some info about the original data:
firstVal = df[:1]
colName = df.columns
# 2. Take the first difference and
df_diff = df.diff()
# 3. Remove missing values
df_clean = df_diff.dropna()
# 4. Select a level for a Z-score to identify and remove outliers
df_Z = df_clean[(np.abs(stats.zscore(df_clean)) < level).all(axis=1)]
ix_keep = df_Z.index
# 5. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df_raw.loc[ix_keep]
# 6.
# df_keep will be missing some indexes.
# Do the following if you'd like to keep those indexes
# and, for example, fill missing values with the previous values
df_out = pd.merge(df_keep, df_raw, how='outer', left_index=True, right_index=True)
# 7. Keep only the first column
df_out = df_out.ix[:,0].to_frame()
# 8. Fill missing values
df_complete = df_out.fillna(axis=0, method='ffill')
# 9. Reset column names
df_complete.columns = colName
# Keep the first value
if keepFirst:
df_complete.iloc[0] = firstVal.iloc[0]
return(df_complete)
# Dataframe with random data
df_raw = sample()
df_raw.plot()
# Remove outliers
df_cleaned = noSpikes(df=df_raw, level = 3, keepFirst = True)
df_cleaned.plot()