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Let's say I have a dataset with the following format:

  • customerid
  • product
  • orders_in_last7days
  • orders_in_last6days
  • orders_in_last5days
  • orders_in_last4days
  • orders_in_last3days
  • orders_in_last2days
  • orders_in_last1days
  • orders_currentday

This dataset could have multiple customers and some customers could place $n$ numbers of orders on different days. How can I flag customers that have unusual number of purchases on the current day, by looking at the distribution of orders on the previous day for that specific customer?

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The definition of an outlier per si is already quite dubious, but we can define them as those values that surpass the limit of +- 1.5 * IQR. In this case, either the standard deviation method or the Tukey method are valid options. We just need to try and see which gives better results.

# Tukey Method

n = 2 #In this case, we considered outliers as rows that have at least two outlied numerical values. The optimal value for this parameter can be later determined through the cross-validation
indexes = []

for col in df.columns[0:14]:
    Q1 = np.percentile(df[col], 25)
    Q3 = np.percentile(df[col],75)
    IQR = Q3 - Q1

    limit = 1.5 * IQR

    list_outliers = df[(df[col] < Q1 - limit) | (df[col] > Q3 + limit )].index # Determine a list of indices of outliers for feature col

    indexes.extend(list_outliers) # append the found outlier indices for col to the list of outlier indices

indexes = Counter(indexes)
multiple_outliers = list( k for k, v in indexes.items() if v > n )

Once you detect the outliers, you can either remove them or replace them with max/min limit values. In the first case, you just need to do this:

df.drop(multiple_outliers, axis = 0)

df = df.drop(multiple_outliers, axis = 0).reset_index(drop=True)

But for the second case, you should do this:

#Setting the min/max to outliers using standard deviation
for col in df.columns[0:14]:
    factor = 3 #The optimal value for this parameter can be later determined though the cross-validation
    upper_lim = df[col].mean () + df[col].std () * factor
    lower_lim = df[col].mean () - df[col].std () * factor

    df = df[(df[col] < upper_lim) & (df[col] > lower_lim)]

Finally, you can also use Isolation Forest or LocalOutlierFactor (more appropriate for Anomaly/Fraud Detection Problems).

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