QuantStats: Portfolio analytics for quants. And today we're going to be talking about tables, histograms, and box plots for exploratory data analysis. Package ‘mvoutlier’ February 8, 2018 Version 2. Using Mahalanobis Distance to Find Outliers. Multicollinearity is the presence of correlation in independent variables. Here three methods are discussed to detect outliers or anomalous data instances. If bins is a sequence, gives bin edges, including left edge of first bin and right edge of last bin. Vemuri 4 September 2019 In this article we look at an interesting data problem - making decisions about the algorithms used for image segmentation, or separating one qualitatively different part of an image from another. This exciting yet challenging field is commonly referred as Outlier Detection or Anomaly Detection. Let's examine the studentized residuals as a first means for identifying outliers. After you check the distribution of the data by plotting the histogram, the second thing to do is to look for outliers. Guide for Linear Regression using Python – Part 2 This blog is the continuation of guide for linear regression using Python from this post. In the script below, I will plot the data with and without the outliers. Learn how to make a histogram with ggplot2 in R. In this article we will show you, How to Create a ggplot boxplot, Format the colors, changing labels, drawing horizontal boxplots, and plot multiple boxplots using R ggplot2 with an example. Another robust method for labeling outliers is the IQR (interquartile range) method of outlier detection developed by John Tukey, the pioneer of exploratory data analysis. To accomplish this task, we need to create a histogram. These are dumped to stdout. Note: you don't have to sort the data points from smallest to. Pandas includes multiple built in functions such as sum, mean, max, min, etc. If you want to identify them graphically and visualize where your outliers are located compared to rest of your data, you can use Graph > Boxplot. Data cleaning and spotting outliers with UNIVARIATE Michael Auld, Eisai Ltd, London UK ABSTRACT Timely and strategic cleaning of data is crucial for the success of the analysis of a clinical trial. Visualise Categorical Variables in Python using Univariate Analysis. We can also read as a percentage of values under each category. The threshold argument is a two-element row vector containing the lower and upper percentile thresholds, such as [10 90]. Choose a scale for the vertical axis that will accommodate the class with the highest frequency. There are numerous plots which are used in Data Visualization such as Histograms, Pie Chart, Box Plot, Word Cloud, Scatter plot etc. Any valid Python identifier may be used for a fieldname except for names starting with an underscore. Normalizing data over a distribution. This problem is from the following book: goo. Here’s an example using Python programming. You cannot use the WEIGHT statement with the HISTOGRAM statement. Come learn about the. Outliers in a collection of data are the values which are far away from most other points. So first perform a distribution analysis of each variable -- at least look at a histogram and preferably do some kind of goodness of fit test against a normal curve. Visualizing outliers with box plots One of the main purposes of the box plot is to quickly visualize outliers to see if it is necessary to remove them for further analysis. Lately, I’ve been using Jupyter Notebooks for all of my Python and Julia coding. After deleting the outliers, we should be careful not to run the outlier detection test once again. In general, in ML. Close the dataset. To decide which method of finding outliers we should use, we must plot the histogram of the variable and look at its distribution. Data Science Essentials Lab 2 – Working with Summary Statistics Overview In this lab, you will learn how to use either R or Python to compute and understand the basics of descriptive statistics. Box Plot Diagram. Analytics Vidhya is a community discussion portal where beginners and professionals interact with one another in the fields of business analytics, data science, big data, data visualization tools and techniques. The text is released under the CC-BY-NC-ND license, and code is released under the MIT license. Hello Readers, We settle into Part 4 of the Text Analysis Series with Python by examining frequency distributions, word selections, and collocations. Check the distribution of the data. optimize and a wrapper for scipy. Box plot in Python with matplotlib; Create Histogram in Python using matplotlib; Remove Spaces in Python - (strip Leading, Trailing, Duplicate spaces in string) Add Spaces in Python - (Add Leading, Trailing Spaces to string) Add leading zeros in Python pandas (preceding zeros in data frame) Head and tail function in Python pandas (Get First. # Remove outliers will be considered outliers and not. Returns-----H : ndarray, shape(nx, ny) The bi. And today we're going to be talking about tables, histograms, and box plots for exploratory data analysis. Histograms allow for a quick assessment of these parameters: Dataset center. Before you can select and prepare your data for modeling, you need to understand what you’ve got to start with. In other words, if any observation lies outside the range of Q1. Python-Jupyter basics tutorial for ML 2018 course¶ This notebook contains some information and examples for getting started with Jupyter and Python. Everything works nicely, but all the histograms are printed next to each other in one long line. If you are really interested in identifying Outliers (or Novelty detection) I would recommend this paper and a good starting point…. For the rest of the analysis I'll filter out everything longer than 3 hours. With break points in hand, hist counts the values in each bin. How to Detect,Impute or Remove Outliers from a Dataset using Percentile Capping Method in R Percentile Capping Method to Detect, Impute or Remove Outliers from a Data Set in R Sometimes a data set will have one or more observations with unusually large or unusually small values. PointDataSubdivision: vtkLinearSubdivisionFilter vtkButterflySubdivisionFilter: Demonstrates the effect of applying these filters on various sources. Novelty and Outlier Detection¶. If you are mining text in R, what items would you remove to provide the most meaningful analysis? Sparse items When you are mining text in Python you need _____ which is a collection of words that can be used to count things. Details The function can perform three tests given and discussed by Grubbs (1950). 3 ways to remove outliers from your data Mar 16, 2015 According to Google Analytics, my post "Dealing with spiky data" , is by far the most visited on the blog. The ability to develop and submit small snippets of code and create plots inline is just so useful that it has broken the stranglehold of using an IDE while I’m coding. there is a long list of such graphs and most of them we’ll see with examples very soon in this tutorial. Now, after removing outliers we have minimum and maximum value. Let's examine the studentized residuals as a first means for identifying outliers. Again, I will be using the abalone dataset found here. Scatter Plotting is used in Python for Data Visualisation. It offers a variety of functions or. flags cctbx. Note: you don't have to sort the data points from smallest to. Finding and Removing Outliers - simple example in R We look for outliers graphically with a histograms. Note that "plt" here is imported from matplotlib - 'import matplotlib. Although some of these long events may be significant they clearly don't represent the usual behavior. Tuple of (rows, columns) for the layout of the histograms. If some outlier is negative but none of the lower whiskers are negative, then a second y axis is not needed. Visualizing the distribution of a dataset¶ When dealing with a set of data, often the first thing you'll want to do is get a sense for how the variables are distributed. In the former cases, it can be desirable to identify outliers and remove them from data before performing a statistical analysis, because they can throw. Boxplot is probably one of the most common type of graphic. mean , max. Construct histograms, box. For instance, there are numerous ways to identify outliers in a given dataset. Additionally Principal Component Analysis is performed to analyze variability and detect. This problem is from the following book: goo. Every data analyst/data scientist might get these thoughts once in every problem they are. Create a bar plot of the top food producers with a combination of data selection, data grouping, and finally plotting using the Pandas DataFrame plot command. Studentized residuals are a type of standardized residual that can be used to identify outliers. The programming language Python, with its English commands and easy-to-follow syntax, offers an amazingly powerful (and free!) open-source alternative to traditional techniques and applications. In this example the minimum is 5, maximum is 120, and 75% of the values are less than 15. The Scatter Plot and Covariance. First, we are going to find the outliers in the age column. Box plot diagram also termed as Whisker’s plot is a graphical method typically depicted by quartiles and inter quartiles that helps in defining the upper limit and lower limit beyond which any data lying will be considered as outliers. Next, I'll look at the distribution of the variables. Vemuri 4 September 2019 In this article we look at an interesting data problem - making decisions about the algorithms used for image segmentation, or separating one qualitatively different part of an image from another. With Disable Smoothing checked, the unmodified image data are used for creating the background. We requested the studentized residuals in the above regression in the output statement and named them r. The bins parameter represents the number of buckets that your data will be divided into. The dataset is a classic normal distribution but as you can see, there are some values like 10, 20 which will disturb our analysis and ruin the scales on our graphs. Remove Python equivalents of C extensions: Some, but not all C extensions had python equivalents, which calculated equal values but, by using a python-only implementation, are much slower than the C extension. This chapter of the tutorial will give a brief introduction to some of the tools in seaborn for examining univariate and bivariate distributions. Histogram-based Outlier Detection. Also used confidence intervals to remove anomalies using ipython. An extensive list of result statistics are available for each estimator. The bins parameter represents the number of buckets that your data will be divided into. Outliers GroupBy on data frames, Series and Dictionaries Data aggregation/ Data summarization Split, apply, combine Visualisation using matplotlib and seaborn - Histograms and joint plots - Kernel density estimation (KDE) plots - Combining plot styles - Box and violin plots - Heatmaps - Regression plots. With the help of lambda expression, you can create an anonymous function. We can use spreadsheet software such as Excel, Python, or R to create histograms. TF = isoutlier(A,'percentiles',threshold) defines outliers as points outside of the percentiles specified in threshold. The Galton data frame in the UsingR package is one of several data sets used by Galton to study the heights of parents and their children. Multicollinearity is the presence of correlation in independent variables. 9 Date 2018-02-08 Title Multivariate Outlier Detection Based on Robust Methods Author Peter Filzmoser. To discard the outliers, we can compute the Z-score for each attribute and remove those instances containing attributes with abnormally high or low Z-score (e. It is quite easy to spot the median and mode by looking at histograms. GitHub is where people build software. To add data labels when you create a graph, click Labels, then click the Data Labels tab and choose the data element to label and the type of label. The type of histogram to draw. The line that divides the box into 2 parts represents the median. The input arrays and the output array can all have the same or different depths. Line graphs are useful for seeing how values in your data change over time. mp4 and later implement on full project_video. Hello Readers, We settle into Part 4 of the Text Analysis Series with Python by examining frequency distributions, word selections, and collocations. We propose an approach using histograms for outlier detection. If you know how your data are distributed, you can get the ‘critical values’ of the 0. It offers a variety of functions or. Outliers GroupBy on data frames, Series and Dictionaries Data aggregation/ Data summarization Split, apply, combine Visualisation using matplotlib and seaborn - Histograms and joint plots - Kernel density estimation (KDE) plots - Combining plot styles - Box and violin plots - Heatmaps - Regression plots. You can vote up the examples you like or vote down the ones you don't like. To set the minimum and maximum histogram limits, click and hold the minimum or maximum triangle located below the dotted line, and move the breakpoint line along the x-axis to where you want to set the limit. If bins is a sequence, gives bin edges, including left edge of first bin and right edge of last bin. bincount() will be much faster than np. Meet reasonable speed vs accuracy tradeoff Time Increases. Influential Points. Listen Data offers data science tutorials covering a wide range of topics such as SAS, Python, R, SPSS, Advanced Excel, VBA, SQL, Machine Learning. In this situation, it is not legitimate to simply drop the outlier. You can specify alternative aggregations by passing values to the C and reduce_C_function arguments. Then leave the rest of the information to the embedded videos to showcase the. They are also great for detecting outliers and other data problems. I am using it to plot 43 histograms. , K-Nearest Neighbour, mean values, etc. Finally, two functions that aid in efficient processing (with and by) are described. This time we’ll be using Pandas and NumPy, along with the Titanic dataset. This dataset contains a list of US presidents, associated parties,profession and more. Moreover, the Tukey's method ignores the mean and standard deviation, which are influenced by the extreme values (outliers). Description. GitHub Gist: instantly share code, notes, and snippets. I remove the rows containing missing values because dealing with them is not the topic of this blog post. Pandas data analysis functions You now know how to load CSV data into Python as pandas dataframes and you also know how to manipulate a dataframe. If multiple data are given the bars are arranged side by side. In this example, we'll learn step-by-step how to select the variables, paramaters and desired values for outlier elimination. Remove Outliers and Clean Missing Data 1. Cross Validate & Grid Search. Motivation. With careful experimental design, a digital camera or a flatbed scanner, in conjunction with some Python code, can be a powerful instrument in answering many different kinds of problems. Line graphs are useful for seeing how values in your data change over time. This problem is from the following book: goo. The Galton data frame in the UsingR package is one of several data sets used by Galton to study the heights of parents and their children. Novelty and Outlier Detection¶. Package ‘mvoutlier’ February 8, 2018 Version 2. However, you can remove outlier noise and smooth an image using a median filter. Data Visualization with Matplotlib and Python; Matplotlib. Try to identify the cause of any outliers. Linear Programming Boosting via Column Generation. Tuple of (rows, columns) for the layout of the histograms. outliers on opposite tails, 20 is test for two outliers in one tail. Data sets with low kurtosis tend to have light tails, or lack of outliers. 'step' generates a lineplot that is by default unfilled. Now I can have my cake and eat it too. Often, outliers are easiest to identify on a boxplot. Using Mahalanobis Distance to Find Outliers. adp_restraints. to make your histograms in native Python,. Outlier removal in Python using IQR rule. 1 DATA SAMPLING 6. Machine Learning with Python. The Python interface is essentially a one-to-one copy of the underlying C/C++ API, and thus image processing pipelines have to follow an imperative programming style. flags cctbx. 8 Million Haul For A Sloan MBA?. Remember you can use the raserio context manager to import the raster object into Python. 3 UNSUPERVISED LEARNING Cluster Analysis Association Rules 6. Vehicle Detection and Tracking. Disable Smoothing For calculating the background (‘rolling the ball’), images are maximum-filtered (3 × 3 pixels) to remove outliers such as dust and then smoothed to reduce noise (average over (3 × 3 pixels). After learning to read formhub datasets into R, you may want to take a few steps in cleaning your data. This dataset contains a list of US presidents, associated parties,profession and more. Following is the syntax for count() method −. The box-and-whisker plot doesn't show frequency, and it doesn't display each individual statistic, but it clearly shows where the middle of the data lies. Box Plot Diagram. Today, we'll discuss the impact of data cleansing in a Machine Learning model and how it can be achieved in Azure Machine Learning (Azure ML) studio. Input data can be passed in a variety of formats, including:. Here's an example using Python programming. The dataset. Often your first step after. def rveph (self, jd): """Compute the most recently elapsed RV emphemeris of a given planet at a given JD. At the end we will see out to remove outliers. pyplot as plt'. Data outliers…. Finally, two functions that aid in efficient processing (with and by) are described. Remove all; Disconnect; The next Outlier values so Outlier values is big challenge for any data scientist in this video we will see how to handle Outlier values in Python with very simple. Now, I've always been a fan of histograms. The line that divides the box into 2 parts represents the median. The analysis identi es all three outliers correctly, with P i;out ’ 1. If a value is higher than the 1. This post is a summary of 3 different posts about outlier detection methods. Why outliers detection is important? Treating or altering the outlier/extreme values in genuine observations is not a standard operating procedure. Credit Scoring: Data Preparation and Exploratory Data Analysis As much as we all may despise credit scores, the way that they are calculated is actually pretty fascinating. Find Outliers¶ IQR = Q3 - Q1; Outlier < Q1 - 1. a character. Welcome to Statsmodels’s Documentation¶ statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. The lines are positioned at the midpoints of the histogram bins. # Remove outliers will be considered outliers and not. I developed a script to identify, describe, plot and remove the outliers if it is necessary. 7%) accordingly for a normally distributed data (central limit theorem and sampling distribution. The interquartile range rule is useful in detecting the presence of outliers. Auditors, accountants and data analysts are increasingly leveraging Python scripts to create repeatable tests and perform even more advanced analysis. It's always important to look at more than just the mean of a dataset like this since a few outliers can have a large effect on its value. py to load two of your bias frames and calculated their difference. Since 2017, PyOD has been successfully used in various academic researches and commercial products. csv" Get the summary of the balance variable; Do you suspect any outliers in balance ? Get relevant percentiles and see their distribution. If you know how your data are distributed, you can get the ‘critical values’ of the 0. We can use relatively simple image processing and computer vision techniques in Python, using the OpenCV library. There are already tons of tutorials on how to make basic plots in matplotlib. The bins parameter represents the number of buckets that your data will be divided into. We see three residuals that stick out, -3. Outliers, which are data values that are far away from other data values, can strongly affect your results. Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area provided the breaks are equally-spaced. Then leave the rest of the information to the embedded videos to showcase the. Histograms / Distributions Dimension Reduction Feature Selection Remove Outliers Sampling Massive Dataset Better to start with as much data as possible and explore / preprocess toscale to performance needs. You could go cross eyed trying to check the distribution of all 40 features. However, it easily gets messed up by outliers. Python is a data scientist's friend. The identification of multivariate outliers is also considered. Then Alexander Mou demonstrated a way of creating overlapping box and whisker with a histogram. The best tool to identify the outliers is the box plot. Outliers in a collection of data are the values which are far away from most other points. Robust Regression | Stata Data Analysis Examples Version info : Code for this page was tested in Stata 12. Create a histogram showing the distribution of latitude values in the dataset. We also interpret a standard. Outliers They can be natural, provided by the same process as the rest of the data, but sometimes they can be just plain mistakes. Data Cleaning - How to remove outliers & duplicates. Outliers, which are data values that are far away from other data values, can strongly affect your results. Finding Outliers in a Graph. $\begingroup$ Histograms have many failings, but this one is doing a good job at telling you that you have precisely one outlier at about 10. Let's take a look at a velocity time-series with some bad data. This app works best with JavaScript enabled. However, there is an outlier that show a high ISI value for a small area; which again seems unusual, and may indicate some issues with the ISI data. Returns-----H : ndarray, shape(nx, ny) The bi. We will use plt scatter to draw a scatter plot of simple example data in matplotlib. py to load two of your bias frames and calculated their difference. Here three methods are discussed to detect outliers or anomalous data instances. These are dumped to stdout. You can also make histograms by using ggplot2 , “a plotting system for R, based on the grammar of graphics” that was created by Hadley Wickham. Today we are going to be talking about visualizing data in Python and about exploratory data analysis using tables, histograms, box plots, and other grouping methods with the Seaborn package. adp_restraints. In this post you will discover some quick and dirty. Create a bar plot of the top food producers with a combination of data selection, data grouping, and finally plotting using the Pandas DataFrame plot command. Visualize data with Pandas Get the xls data for this tutorial from: depaul. Scatter Plot - Python. Spotting outliers with Isolation Forest using sklearn Isolation Forest is an algorithm to detect outliers. The difference between a good and an average machine learning model is often its ability to clean data. IDEA includes a Python interpreter and key packages so that you can utilize the power of this tool – all without requiring IT skills. 5 times of Interquartile Range (IQR) above the upper quartile (Q3), the value will be considered as mild-outlier. Drawing the Histogram. $\begingroup$ Histograms have many failings, but this one is doing a good job at telling you that you have precisely one outlier at about 10. Installing Python Choosing an editor or IDE Python Basics Building Hello World Variables and expressions Python functions Conditional structures Loops Working with Dates and Time The date, time, and datetime classes Formatting time output Using timedelta objects Working with calendars. Code: The following code shows the results of standardizing the columns of the data. CHAPTER 6 DATA MINING CONTENTS 6. Last revised 13 Jan 2013. Pandas data analysis functions You now know how to load CSV data into Python as pandas dataframes and you also know how to manipulate a dataframe. A boxplot is usually used to visualize a dataset for spotting unusual data points. The analysis identi es all three outliers correctly, with P i;out ’ 1. Systems, Rensselaer. This time we'll be using Pandas and NumPy, along with the Titanic dataset. I then sort the array and now want to be able to plot a CDF of the data using matplotlib. Scatterplot matrices show core relations between variables…and box plots show variable spread…and are useful for outlier detection. The best tool to identify the outliers is the box plot. Python is a high-level interpreted general programming language. Chapter 8 Lists 8. But just to simply we are excluding this step now. Values are very similar to the Freedman-Diaconis estimator in the absence of outliers. Note that you will still want to remove outliers. There are several ways to create a new list; the simplest is to enclose the elements in square brackets ([and ]):. If bins is a string from the list below, histogram will use the method chosen to calculate the optimal bin width and consequently the number of bins (see Notes for more detail on the estimators) from the data that falls within the requested range. Python programming is an extremely versatile language used for a variety of tasks including: Web development, data analytics, game development – even controlling robots! Get up to speed on all the essential Python skills, and learn it all at your own pace with this detailed course. Show Code. Median filter of kernel size 3. In this last lesson, we learned to create graphical visualizations with Python from T-SQL and data stored in SQL Server to complete the analytics cycle. Though, you will not know about the outliers at all in the collection phase. Showing the histogram as a stepped line. One of the challenges in data analysis in general and predictive modeling in particular is dealing with outliers. Related course. Although some of these long events may be significant they clearly don't represent the usual behavior. This is used to visualize the relationship between the X and Y along with the univariate distribution of the X and the Y individually. These histograms are more informative than the initial ones including the outliers, especially the histogram that was constructed using the. We can also read as a percentage of values under each category. Profile histograms are in many cases an elegant replacement of two-dimensional histograms : the inter-relation of two measured quantities X and Y can always be visualized by a two-dimensional histogram or scatter-plot; If Y is an unknown. However, the power (and therefore complexity) of Pandas can often be quite overwhelming, given the myriad of functions, methods, and capabilities the library provides. Histograms show the distribution of the data and can show skewness or unusual dispersion. A median filter replaces the outliers with the median (within a kernel of a given size). 5 IQR) it will be defined as potential. In this work we consider the multi-image object matching problem, extend a centralized solution of the problem to a distributed solution, and present an experimental app. To decide which method of finding outliers we should use, we must plot the histogram of the variable and look at its distribution. The Ultimate Python Seaborn Tutorial: Gotta Catch 'Em All Share Google Linkedin Tweet In this step-by-step Seaborn tutorial, you'll learn how to use one of Python's most convenient libraries for data visualization. TF = isoutlier(A,'percentiles',threshold) defines outliers as points outside of the percentiles specified in threshold. Package 'mvoutlier' February 8, 2018 Version 2. This app works best with JavaScript enabled. It offers a variety of functions or. , [5, 95]) to set the whiskers at specific percentiles of the data. Any valid Python identifier may be used for a fieldname except for names starting with an underscore. Details The function can perform three tests given and discussed by Grubbs (1950). Join Barton Poulson for an in-depth discussion in this video, Solution: Transforming skewed data to pull in outliers, part of R Statistics Essential Training. For most data sets i put into the code, there are no such outliers. sided Logical value indicating if there is a need to treat this test as two-sided. We will use plt scatter to draw a scatter plot of simple example data in matplotlib. Another robust method for labeling outliers is the IQR (interquartile range) method of outlier detection developed by John Tukey, the pioneer of exploratory data analysis. Effect of Outliers on Slope, Intercept and R2 An outlier impacts the slope intercept and R2 in different ways. Thus the researchers prove that the Box-. In this post we will discuss univariate and multivariate outliers. a character. First, do the univariate outlier checks and with those findings in mind (and with no immediate remedial action), follow some, or all of these bivariate or multivariate outlier identifications depending on the type of analysis you are planning. The histogram reveals some interesting aspects of the distribution, indeed we can see that data is slightly skewed to the right and that on average the server takes 20 seconds. If bins is a string from the list below, histogram will use the method chosen to calculate the optimal bin width and consequently the number of bins (see Notes for more detail on the estimators) from the data that falls within the requested range. I wrote a python program that basically takes a text file with 86400 lines containing web server ping responses. 5xIQR rule If you're seeing this message, it means we're having trouble loading external resources on our website. How to Find or Calculate High Median in Python using median_high() Function How to Find or Calculate Low Median in Python using low median_low() Function Following is the statistical formula to calculate the median. Scatterplot matrices show core relations between variables…and box plots show variable spread…and are useful for outlier detection. After you check the distribution of the data by plotting the histogram, the second thing to do is to look for outliers. The dataset is a classic normal distribution but as you can see, there are some values like 10, 20 which will disturb our analysis and ruin the scales on our graphs. Finding Outliers in a Graph. The slope can be pulled up or down based on the direction of the outlier. Matplotlib can be used to create histograms. When reviewing a boxplot, an outlier is defined as a data point that is located outside the fences (“whiskers”) of the boxplot (e. Thus sometimes we want to have these values in the dataset, since they may carry some important information, while other times we want to remove those samples, because of the wrong information that they may carry. Boxplots are another type of plot for showing data distribution. To test this we can simulate a sinusoid and add some Gaussian noise. In this article, we will use z score and IQR -interquartile range to identify any outliers using python. Try to identify the cause of any outliers. However, is an outlier abnormal or normal? It needs to be decided by data analysts. The ability to take counts and visualize them graphically using frequency plots (histograms) enables the analyst to easily recognize patterns and relationships within the data. This was in the days of calculation and plotting by hand, so the datasets involved were typically small, and the emphasis was on understanding the story the data told. Something I talk about with friends when planning and sharing our projects & media we like is titles - and specifically my disdain for one-word titles. Finally, two functions that aid in efficient processing (with and by) are described.