Comparing classifiers on the MNIST Data Set
This is a adaptation of a report written in collaboration with Louisa Lee (with some modfications) from my Machine Learning class in Fall 2017.
Introduction
The MNIST data set is a widely popular database of handwritten images of digits 0-9 for use in machine learning applications. More information about the MNIST set can be found here. All the images are stored in a specialized format. A helper file to parse the dataset was provided by the professor.
There are 60,000 total images in the dataset. The table below shows the number of images for each digit 0-9.
One benefit of the MNIST dataset is that strikes a decent balance in terms of the size of the problem. There are only 10 possible classifications and the images are relatively small at 28x28 pixels. However, just because the images are small does not mean that there is not large variance in the digits in the data set. Unsurprisingly, some of the digits are difficult to classify exactly straightforward for a human to correctly classify.
A selection of images that are likely to be very difficult to recognize with a classifier are shown next the composite average of the class the classifier is likely to pick. These images are difficult because they look extremely similar to the average (or another relatively common) image of another number. With a given distance metric in 10-dimensional space, a number that appears very similar to another number will have a relatively low distance to the cluster belonging to another class. Numbers such as these may be easily placed on the incorrect side of the decision boundary depending on the hyperparameters of the model in question.
| Image Likely to be Misclassified | Likely Misclassification |
|---|---|
Table 1: Easily Misclassified images from the MNIST dataset
Both the training and testing sets were chosen as a set number of images for each digit label. For example, 3000 images per digit were used for the training set and 1000 images per digit as the validation set. This would result in 30,000 images in our training set and 10,000 images in our testing set. This method allows for good generalizability because it is predetermined that every digit is encompassed in the training and testing data. The training and testing data has an equal amount of images for each digit, allowing the training data to encompass all the possible labels and the testing data to reflect the classifiers performance on all numbers. Given that the training data set consists of 30,000 images and the testing set consists of 10,000 images, it was decided that N-fold cross-validation of the models was both too expensive in terms of time and not strictly required due to the amount of data available for both training and testing.
Even the relatively small 28x28 images provide lots of room for variance in the location and orientation of the digits drawn in the images. To help normalize the images, the MNIST images are centered. A major advantage of this normalization is that it will reduce the variance of the type of images a classifier may encounter. If all the images are centered and oriented correctly, the classifier does not need to learn how to account for those transofmations in its decision boundary. This also has the effect of reducing the
One major advantage of the taking this subset of the data in this manner is that it will reduce the variance in the images that the classifier sees. For example, if all the images are centered and rotated to appear perfectly vertically, the classifier does not need to learn to account for these transformations itself. If all the images are centered, it reduces the possibility that the classifier has “cheated” and just learned to look in a single area for a defining feature. However, this has the trade-off that the classifier has not really learned to identify the digit in general, it has only learned to classify digits that are close to the perfectly arranged data of the training set.
Suport Vector Machines
A support vector machine (SVM) is a type of supervised learning algorithm. The SVM will try to define an equation for a hyperplane in n-dimensions (where n is the number of dimensions in the data) to separate all the given examples of a class. To determine where this hyperplane should go, SVMs will try to maximize the margin between the data and the hyperplane. To solve non-linear problems, a kernel function can be applied to transform the data into higher dimensional space. Since the end-user need not know about this details of this step, only the points that effectively determine the decision boundary are returned. These points are called the support vectors.
To use an SVM for image classification, the image must be converted into a vector and passed to the SVM function. Given a certain dataset, the training process establishes the support vectors that define the decision boundary. By comparing the distance between an unknown input and these support vectors, the class of the new data point can be determined.
The slack hyperparameter for an SVM changes it from a hard-margin classifier to a soft-margin classifier. With a hard-margin, the hyperplane will adjust exactly to correctly identify all data points in the training set. For datasets that aren’t separable in n-dimsions, this will not terminate. A soft-margin classifier allows for misclassifications within a certain tolerance, otherwise known as slack.
The slack value determines if the occasional outlier is allowed to be on the wrong side of the decision boundary. This technically hurts the performance on the training data, but the hope is that it will lead to a more generalizable model by reducing the overfitting to the training data. This slack parameter is defined as C in sci-kit-learn. As C increases the model is forced to classify more and more of the training examples correctly.
SVMs can also use different kernel functions, some of which have additional hyperparameters. For this project, the radial basis function was used as the SVM’s kernel. This function takes an additional hyperparameter gamma. The impact of the gamma parameter defines a “radius of influence” for each support vector. A small gamma value extends this radius to much of the training set and approximates a linear classifier (see more here). Thus, finding the correct balance of C and gamma is an important task in generating a support vector machine model.
K-Nearest Neighbors
KNN is a method of supervised learning. The way KNN classification works is that it encodes the data into a vector and plots it in some n-dimensional space. Given an unknown data point, a given distance metric can be used to determine what the nearest k classified points are. From this set of k neighbors, the identity of the unknown point will be assigned as the majority opinion of those k neighbors. For the purposes of image classification, the same procedure applies. First, the image is converted into a vector and then compared against the k vectors nearest it. The most common resultant class is the predicted class of the new image.
The hyperparameter K in KNN determines how many neighbors to consider in the classification. When the K value is too small, it will fit the unknown data point to noise in the dataset (overfit), and when the K value is too large, it can make decision boundaries in the classification indistinct (underfit).
Derivation of the experiment
To determine an effective trade-off between training set size and exection time, the model accuracy as a function of the training size was determined.
Determination of the size of the training set
While holding the values of the hyperparameters C and gamma to a constant value, and with a constant testing set size, the size of the training set was varied. For this experiment C was left at default (1.0) and gamma was set to 0.035. The size of the testing set was kept at 1000 images per class, for a total of 10,000 images. The plot below shows the impact of the size of the training data set (per image class) on the error rate (y-axis.)
As the size of the training set increases toward 2000 images per class, there are substantial improvements in the model accuracy. After the 2000-3000 images per class range, the returns diminish rapidly. Thus, it does not make sense to train the SVM on more than a total of 30,000 images especially with the amount of time required to train the model.
The exact values of the hyperparameters for slack and gamma have a signficant impact on the peformance of the model. Initially, an exponential range of values were tried for each parameter independently until an approximate order of magnitude that performed decently was established. It so happened that the best approximate size was the values used to generate the plot in the previous part.
For both hyperparameters C and gamma a list was generated that included approximately +/- 20% of the values tried in the previous part. Since the parameters C and gamma are independent of each other, all \(O(N^2)\) of these combinations will be evaluated. This was achieved with 2 nested loops to iterate through the established trial values of C and gamma. On each loop iteration an SVM was trained and its accuracy on the testing set was computed. The result of this experiment is plotted in the graph below:
From this experiment, the best values of C was 1.15 and gamma=0.04 with an error rate of 3.52%. To accomplish this hyperparameter grid-search in a reasonable amount of time, the size of the training data was reduced to 1000 images per class (10,000) total. This explains the increase in error as compared to the 3000 images per class point in the previous experiment. Trading off 1.5% accuracy in training resulting in significantly less time to perform the entire experiment.
SVM Resuts
The table shown below is a confusion matrix of the SVM classifier with the hyperparameter values of \(C=1.15\) and \(\gamma=0.04\). The overall accuracy of the classifier was 97.18%. The confusion matrix is a useful evaluation tool as it also shows the predicted labels for all images in testing set.
While 2.82% error is fairly good, it would be helpful to know if the testing images that were predicted incorrectly are actually hard for people to determine as well. The image below shows all images from the testing set for which the SVM classifier predicted incorrectly.
As anticipated, a significant proportion of the images that appear in the above plot are relatively similar in appearance to other numbers. There are multiple images that would even be reasonable for a human to misclassify if it were given randomly (for example: some of the 9s in the second to last row.) However, these lists as well as the confusion matrix reveal that there is not a significant trend in the misclassification. With the exception of 4 and 9, it seems that there is not a regular pattern in the predicted class when an image is misclassified.
Determination of KNN Hyperparameter
For the KNN classifier, the same setup of evaluating training set size was used. Initially, 5 neighbors (K=5) and a testing size of 1000 images from each number were used, resulting in a total of 10,000 testing images. The size of the training set was from 100-4000 images for each number 0-9 and the error rate was measured. The result is shown in the graph below.
As with the SVM, 3000 images per class seemed to result in the lowest error rate.
To determine the optimal number of neighbors to consider, the value of K was varried from 1 to 30 neighbors. The results are shown in the graph below:
From the graph, it can be seen that 4 neighbors seems to be the optimal number of neighbors for the KNN classifier. This was found keeping the training size at 3000 images per number and the testing size at 1000 images per number.
Other parameters that were kept constant are the weights and distance measure. The weights were kept uniform so that all points in each neighborhood were weighted equally. The distance measure used was minkowski with p = 2, which is the equivalent to the standard Euclidean metric.
KNN Results
The resulting confusion matrix is shown below. The overall error rate of the model was 3.73%.
The images that were misclassified are shown below:
The images that were misclassified are largely ones where the handwritten digit is very similar to the average images of another number. For example, the 0 written in row 1 column 2 looks very similar to a 6. This shows that the KNN classifier is finding the images already classified from the training data that is most similar to the testing image. By using the nearest neighbor method, you find an already labeled image that is “closest” in terms of some distance measure and use that to label the unknown image. This relates to the section “Exploring the dataset” because the misclassified images are handwritten images that look very similar to another digit. As a result, this image will be nearer to the wrong labeled image than an image with its true label, resulting in the misclassification.
Discussion
Using a KNN resulted in an error of 3.73% with K=4 neighbors and a training size of 30,000 and testing size of 10,000. The support vector machine constructed resulted in an error of 3.52% with C=1.150000 and gamma= 0.040000 using the radial basis function as the kernel. To find an optimal hyperparameter for the KNN is an \(O(N)\) process, whereas finding the combination of both hyperparameters for the SVM is an \(O(N^2)\) process. For this reason even with a training size of 10,000 and a testing size of 1,000 the training process for the SVM takes considerably longer.
While the SVM performed slightly better than the KNN, it comes at the cost of significantly increased training time and the additional complexity of selecting a kernel function. However, once trained this disadvantage is not as much of an issue. By the fact that there were 2 independent parameters to be evaluated for the SVM, there is more granularity in adapting the SVM to solving this problem. Another likely reason for the SVM’s outperformance of the KNN has to do with how the hyperparameters function within the algorithm.
Consider a subset of numbers that are drawn very differently from the “normal” and appear very similarly to another digit: say 1s with a horizontal base for example. The nearest 5 neighbors to these outliers are likely to be the elements of another class (say 2), thus these would be misclassifications. However, depending on the tuning of the slack parameter, an SVM may be more likely to recognize this enclave of digits as belonging to belonging to class 1 instead of identifying them as members of class 2.
Boosted Classifiers
Boosting in a concept in machine learning that combines many cheap, weak, classifiers and uses them in coordination to solve tasks that would typically requrie an expensive strong classifier.
One algorithm for boosting is to use many decision stumps, (single question decision trees) to effectively provide constraints to define a hyperplane. This is the default option for the AdaBoostClassifier provided in scikit-learn.
AdaBoost Results
The results provided by the straightforward boosting implementation were not that impressive. The overall error rate was 27.72%. As shown in the confusion matrix below, there were several classes that were commonly misclassified as another class.
The AdaBoost algorithm is a meta-algorithm, that is it is an algorithm to apply on top of another algorithm. The results of boosting a SVM will be shown in the next section.
Boosting a SVM
The SVM used with Adaboost used the radial basis function with \(C=1.15\) and \(\gamma=0.04\) as found previously. This boosted SVM had an error rate of 16.45%. This boosted classifier does not outperform either the SVM or the KNN as described previously (3.52%) and (3.72%) respectively. It should also be noted that an SVM with the linear kernel and the default C value was also tried. This variation of the classifier took less time to run the experiment and resulted in a very similar error rate of 16.21%. The data shown in the confusion matrix below is from the SVM trained with the radial basis function and \(C=1.15\), \(\gamma=0.04\).
Comparison of Boosted Classifier Results
The boosted classifier built with decision stumps had an error rate of 27.72% on the testing set. The boosted classifier built with a SVM had an error rate of 16.45%. By this metric alone, the Boosted SVM is far better than the boosted decision tree classifier.
Conclusion
The MNIST dataset provides an interesting problem that is both realistic and well constrained. 4 Different classifiers were analyzed in this report: a SVM, KNN, boosted decision trees, and a boosted SVM. The SVM had the lowest error rate of the classifiers tested, but this comes at the cost of an expensive process of hyperparameter tuning. The KNN performed almost as well with a very straightforward tuning process. The boosted classifiers did not perform well in this task. These days, Aritificial Neural Nets are frequently used in this kind of image recognition and classification tasks and many neural nets trained for the MNIST dataset often score in the 99th percentile range for classification accuracy. The SVM and KNN classifiers presented here a little behind this current state of the art, but still perform very well for their respective computational complexity.


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Julia Tips¶
This section is intended to familiarize the user with the tools and features of Julia
Packages¶
Usefull commands for packages are :
Pkg.add(package_name)
to add a package from namePkg.clone(package_url)
to add a package from URL, fx from GithubPkg.rm(package_name)
to uninstall a packagePkg.build(package_name)
to build a package, this may sometimes be necessaryPkg.dir()
to get thepath
to all installed packagesusing "package name"
to import a package into the enviroment, fxUsing Cobra
For more information, see the full documentation for packages
Function names¶
Function names ending with an exclamation point (!) modify their arguments.
Some functions have both modifying (e.g., sort!) and non-modifying (sort) versions.
For Cobra, this means that calling:
change_reaction_bounds!(model, 13, 0, 1000)
will change the bounds for reaction 13 in the original model, whereas calling:
new_model = change_reaction_bounds(model, 13, 0, 1000)
returns a new copy of the model, with bounds changed for reaction 13.
Function argument signature¶
Functions in Julia may have either optional arguments and keyword arguments.
This makes it easier to use functions that may have multiple necessary arguments, where some of them have sensible default values.
In the documentation, optional arguments have a default value assigned to them, for example, the flux balance analysis
function fba()
has the following description
fba(model; [direction = "max"])
Here, "max"
is the default value given to direction
Keyword arguments are those that appear inside brackets [ ]
following a semicolon, ;
so "direction"
is a keyword argument
meaning you can equivalently call:
fba(model)
fba(model, "max")
fba(model, direction = "max")
Getting help¶
To access the help for a function, write a question mark (?) in front of the function name
help?> change_reaction_bounds
search: change_reaction_bounds find_exchange_reactions
change_reaction_bounds(model, reaction, lb, ub)
Return a duplicate of the model with the lower/upper bounds of a reaction changed
change_reaction_bounds(model, reaction, value[, bound])
change_reaction_bounds(model, reaction_index, value[, bound])
Return a duplicate of the model after changing a bound
Optional arguements:
––––––––––––––––––––––
bound:
• 'l' to change the lower bound
• 'u' to change the upper bound
• 'b' to fix lower and upper to the same value (default)
Methods¶
Methods within a module¶
To view every single method (and global variables) from a module, like Cobra
or GLPK
or JSON
, write JSON.
and press the tab
key twice:
julia> JSON.
ARRAY_BEGIN LATIN_E OBJECT_END eval
ARRAY_END LATIN_F PLUS_SIGN json
AssociativeWrapper LATIN_L Parser lower
BACKSLASH LATIN_N RETURN parsefile
BACKSPACE LATIN_R REVERSE_ESCAPES prefix
DECIMAL_POINT LATIN_S SEPARATOR print
DELIMITER LATIN_T SOLIDUS print_escaped
DIGIT_NINE LATIN_U SPACE printsp
DIGIT_ZERO LATIN_UPPER_A STRING_DELIM separator
ESCAPES LATIN_UPPER_E State set_state
FORM_FEED LATIN_UPPER_F TAB start_object
INDENT MINUS_SIGN _print suffix
JSONPrimitive NEWLINE _writejson
LATIN_A NOINDENT end_object
LATIN_B OBJECT_BEGIN escaped
Method variations¶
Julia is implemented with multiple dispatch, which means, that methods can have the same name but take different input arguments
For example, the method change_reaction_bounds
has multiple definitions, two of which are
function change_reaction_bounds(model::Model, reaction::String, lb::Number, ub::Number, bound::String = "both")
function change_reaction_bounds(model::Model, reaction::Number, lb::Number, ub::Number, bound::String = "both")
You will notice that these definitions are a bit different, namely, that in one definition, reaction
must be a String
and in another it should be a Number
. So calling:
change_reaction_bounds!(model, "ACONTa", 0, 1000)
change_reaction_bounds!(model, 4, 0, 1000)
will do the same thing to the model, because “ACONTa” is the 4th reaction in model.rxns
There are sometimes a few different definitions and often there are numerous definitions, to view all definitions, use the methods()
function:
julia> methods(change_reaction_bounds)
# 8 methods for generic function "change_reaction_bounds":
change_reaction_bounds(model::Cobra.Model, reaction::String, value::Number)
change_reaction_bounds(model::Cobra.Model, reaction::String, value::Number, bound::String)
change_reaction_bounds(model::Cobra.Model, reaction::String, lb::Number, ub::Number)
change_reaction_bounds(model::Cobra.Model, reaction::String, lb::Number, ub::Number, bound::String)
change_reaction_bounds(model::Cobra.Model, reaction_index::Number, value::Number)
change_reaction_bounds(model::Cobra.Model, reaction_index::Number, value::Number, bound::String)
change_reaction_bounds(model::Cobra.Model, reaction_index::Number, lb::Number, ub::Number)
change_reaction_bounds(model::Cobra.Model, reaction_index::Number, lb::Number, ub::Number, bound::String)


Const BuiltinColor
BuiltinColor: object
BLACK
BLACK: [number, number, number] = [0, 0, 0] as Color
BLUE
BLUE: [number, number, number] = [0x00, 0x00, 0xff] as Color
CLEAR
CLEAR: [number, number, number] = [0x00, 0x00, 0x00] as Color
CYAN
CYAN: [number, number, number] = [0x00, 0xff, 0xff] as Color
GRAY
GRAY: [number, number, number] = [0x80, 0x80, 0x80] as Color
GREEN
GREEN: [number, number, number] = [0x00, 0x80, 0x00] as Color
MAGENTA
MAGENTA: [number, number, number] = [0xff, 0x00, 0xff] as Color
MAROON
MAROON: [number, number, number] = [0x80, 0x00, 0x00] as Color
NAVY
NAVY: [number, number, number] = [0x00, 0x00, 0x80] as Color
OLIVE
OLIVE: [number, number, number] = [0x80, 0x80, 0x00] as Color
PURPLE
PURPLE: [number, number, number] = [0x80, 0x00, 0x80] as Color
RED
RED: [number, number, number] = [0xff, 0x00, 0x00] as Color
RIME
RIME: [number, number, number] = [0x00, 0xff, 0x00] as Color
SILVER
SILVER: [number, number, number] = [0xc0, 0xc0, 0xc0] as Color
TEAL
TEAL: [number, number, number] = [0x00, 0x80, 0x80] as Color
WHITE
WHITE: [number, number, number] = [31, 31, 31] as Color
YELLOW
YELLOW: [number, number, number] = [0xff, 0xff, 0x00] as Color


Scotty Mikul
About me
Hi! I'm Scotty I'm a full stack developer from Atlanta Georgia. I'm a high energy, good attitude kind of guy who enjoys comedy. I love coding, learning new things and overcomming challenges.
I have quite a bit of coding education and a bit of work experience too. I graduated Georgia Southern with a BS in computer science, got a certificate with teamtreehouse in java web development, and more recently graduated from a Full Stack Development bootcamp with Georgia Tech. I had worked as a developer with Home Depot for about 3 years.
Personal
I grew up in Marietta Georgia and went to a high school here too. I've been pretty interested in all kinds of sports and while I have a huge passion for video games, I've also been camping quite a bit growing up. I spent some time with the Boy Scouts and that's where I learned the most about camping. I even made it to Eagle Scout.
I play quite a bit of video games. Currently my favorite is card game called Hearthstone, but I play quite a bit of others too. Recently I've grown pretty fond of my fitbit and I've been very focused on tracking calories and maintaining a healthy weight. I'm doing a bit of running. I've signed up for the bubble run and the blacklight run this year. However I think that the corona virus might be delaying all races. One of my main goals this year is to get employed with a great company with people I enjoy being with.


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Michelle Obama's Schiaparelli Gown Was Designed to Match Her "Strength and Energy"
- Last night, former First Lady Michelle Obama wore a custom Schiaparelli gown to the American Portrait Gala in Washington, D.C., honoring Hamilton creator Lin-Manuel Miranda.
- The acid-yellow dress was overlaid with an intricate crystal bodice, also featuring crystal spaghetti straps and a sweetheart neckline.
"Legacy. What is a legacy?" an iconic Hamilton song goes. For former First Lady Michelle Obama, it includes wearing a custom Schiaparelli gown to the Smithsonian's American Portrait Gala to honor Hamilton creator Lin-Manuel Miranda.
Of course, the former FLOTUS is known for achievements beyond her haute couture decisions at fancy events (think her Let's Move initiative during her time at the White House). But a fashion legacy is a legacy nonetheless.
Her acid-yellow gown featured a sweetheart neckline, crystal spaghetti straps, and an intricate crystal bodice. She elevated the bold look with drop earrings.
"The inspiration for the shape originally came from the crinoline, which is often found underneath couture gowns, but the real starting point for the overall look was the color," said Creative Director Daniel Roseberry in a statement. "The acidic tone echoes Elsa Schiaparelli's signature shocking pink, and we also felt that it matched the strength and energy of Mrs. Obama. It was such an honor to make this special gown for her."
Obama attended the gala to present Miranda, who has long had the support of the Obama family for his creative endeavors. In 2009, he performed an early rendition of the opening song to his Tony Award–winning musical during an event at the White House, at the invitation of the Obamas.


---
layout: guide
permalink: ve-python
category: Virtual Environments
guide-title: Create a Python Virtual Environment
guide-desc: The steps below will walk you through creating a Python virtual environment and kernel so that it may be used in your notebooks.
guide-image: ve_python_02.png
steps:
- step-hr: hr
- step-heading: 1. Open a Terminal.
- step-instruction: If you're not already logged in, follow the steps found here. In the upper-right corner, click the New button and select Terminal.
- step-image: ve_python_01.png
- step-hr: hr
- step-heading: 2. Create virtual environment
- step-instruction: In the Terminal, enter the command below to create a virtual environment. In this example, myEnv
is the name used for the virtual environment, but you may name this whatever you'd like.
- step-code:
lang: shell
code: conda create -n myEnv python=2.7
- step-instruction: Press return when asked to proceed. All packages needed by the virtual environment will be downloaded and installed.
- step-image: ve_python_02.png
- step-hr: hr
- step-heading: 3. Activate virtual environment
- step-instruction: Run source activate myEnv
to activate your virtual environment. Again, you may have used a different name, so substitute as appropriate. You should now see a prompt with the name of your virtual environment in parenthesis as shown.
- step-code:
lang: shell
code: |
grahamhenke@bacon:~$ source activate myEnv
(myEnv) grahamhenke@bacon:~$
- step-hr: hr
- step-heading: 4. Install packages
- step-instruction: "Now that you are in your virtual environment, you may install packages using conda install
or pip install
. For example, to install the requests
package, run:"
- step-code:
lang: shell
code: conda install requests
- step-note: "Note: We highly recommend trying conda install
first, as it installs low level dependencies that some packages (such as tensorflow) need. If this does not work, then use pip install
."
- step-hr: hr
- step-heading: 5. Install ipykernel
- step-instruction: "To use your virtual environment and the packages installed in it, you will need to create an environment kernel. To do this, you first need to install ipykernel
by running the following:"
- step-code:
lang: shell
code: conda install ipykernel
- step-hr: hr
- step-heading: 6. Create the kernel
- step-instruction: "Now create the kernel for your environment by running:"
- step-code:
lang: shell
code: python -m ipykernel install --user --name myEnv --display-name myEnv
- step-note: "Note: Neither the name or display-name have to be the same as your virtual environment name, but it is recommended to avoid confusion."
- step-hr: hr
- step-heading: 7. Open a notebook with the kernel
- step-instruction: Navigate back to the Home tab. Make sure to first refresh the page. Next, click the New button and select the name of your kernel, which is myEnv in this example.
- step-image: ve_python_03.png
- step-hr: hr
- step-heading: 8. Import packages
- step-instruction: You can now import and use packages from your kernel. Notice the requests
package imports successfully.
- step-note: "Note: Please be aware that common packages you may be used to using (such as pandas) are not installed by default and you will have to explicitly install these using conda install
in your virtual environment."
- step-image: ve_python_04.png
---


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This is page 1!
Next Page
The example uses the Content Linking Component to navigate between the pages in a text file.


The dataset contains career statistics of baseball players. Each dataum has the name of player(name
), handednes
(L for Left and R for Right), height
(in inchs) amd weight
(in lbs), avg
(Career average) and HR
(Total Home runs). Body metrics include height
and weight
while perfomance is given by HR
and avg
.
import csv
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
plt.style.use('ggplot')
baseball_lst=[]
with open("baseball_data.csv") as f:
records = csv.DictReader(f)
for row in records:
baseball_lst.append(row)
baseball = pd.read_csv('baseball_data.csv')
# Checking for missing values in each column
for key in baseball.keys():
if baseball[key].isnull().sum():
print (key)
baseball.head(5)
# 'HR' is home runs
baseball.describe()
# Players with top 5 averages
baseball.sort_values(by ='avg', ascending=False)[0:5]
# top 5 Home Run getters
baseball.sort_values(by ='HR', ascending=False)[0:5]
# Players with top 5 weights
baseball.sort_values(by ='weight', ascending=False)[0:5]
Height in inchs and Weight in lbs.
# Histograms of columns.
fig = plt.figure(figsize=(8,5))
for i,key in enumerate(baseball.keys()[2:]):
ax = fig.add_subplot(2,2,i+1)
ax.set_title(key)
baseball[key].hist(bins=10)
plt.tight_layout()
plt.show()
# count of players based on handedness
baseball['handedness'].value_counts().plot.barh()
plt.show()
bball_B = baseball[baseball['handedness']=='B']
bball_R = baseball[baseball['handedness']=='R']
bball_L = baseball[baseball['handedness']=='L']
# plt.show()
# Paired Plots
# baseball[(baseball["avg"]==0)&(baseball["HR"]==0)]
g = sns.PairGrid(baseball)
g = g.map_diag(plt.hist)
g = g.map_offdiag(plt.scatter)
plt.show()
# Paired Plots by group
g = sns.PairGrid(baseball, hue = "handedness", palette='husl')
g = g.map_diag(plt.hist,histtype="step", linewidth=1)
g = g.map_offdiag(plt.scatter)
plt.legend()
plt.show()
# Height based on handedness
sns.boxplot(y = 'height', x='handedness', data = baseball)
sns.stripplot(y = 'height', x='handedness', data = baseball, color='gray', jitter=True)
plt.show()
# Weight based on handedness
plt.figure()
sns.boxplot(y = 'weight', x='handedness', data = baseball)
plt.show()
# avg based on handedness
sns.boxplot(y = 'avg', x='handedness', data = baseball)
plt.show()
# avg based on handedness with avg>0
sns.lvplot(y = 'avg', x='handedness', data = baseball[baseball['avg']!=0])
plt.show()
# HR based on handedness
plt.figure()
sns.boxplot(y = 'HR', x='handedness', data = baseball)
plt.show()
# HR based on handedness with HR >0
plt.figure()
sns.lvplot(y = 'HR', x='handedness', \
data = baseball[baseball['HR']!=0])
plt.show()
bball_median=baseball.groupby('handedness').median()
bball_median["Count"]=baseball.groupby('handedness')["name"].count()
bball_median.to_csv("baseball_median.csv")
bball_median
weight
¶Exploring the difference in average and home run based on three levels of weight - Low(L
) Medium(M
) and High(H
).
pd.qcut(baseball['weight'], q=3, labels=['Low','Medium','High'])\
.cat.reorder_categories(['Low','Medium','High'],ordered=True)\
.value_counts()
# Defining a new dataframe with height and weight categorized
baseball_new = baseball.copy(deep=True)
baseball_new['weight_cat'] = \
pd.qcut(baseball_new['weight'], q=3, labels=['Low','Medium','High'])\
.cat.reorder_categories(['Low','Medium','High'],ordered=True)
baseball_new['height_cat'] = \
pd.qcut(baseball_new['height'], q=3, labels=['Low','Medium','High'])\
.cat.reorder_categories(['Low','Medium','High'],ordered=True)
baseball_new.head(5)
# Mean avg based on weight category
baseball_new.groupby('height_cat').mean()[['avg']].plot(kind='bar')
plt.show()
# Mean HR based on weight category
baseball_new.groupby('weight_cat').mean()[['HR']].plot(kind='bar')
plt.show()
# Paired Plots by group
g = sns.PairGrid(baseball_new, hue = "weight_cat")
g = g.map_diag(plt.hist,bins=20)
g = g.map_offdiag(plt.scatter,alpha=0.4)
# g = g.map_lower(plt.hexbin,gridsize=100)
plt.legend()
plt.show()
# Seperating into 10 Categories of weight
baseball_new['weight_10cat'] = pd.qcut(baseball['weight'], q=10)
baseball_new.groupby('weight_10cat').median()[['HR']].plot(kind='bar')
plt.show()
baseball_new.groupby('weight_10cat').median()[['avg']].plot(kind='bar')
plt.show()
HR
vs. avg
filtered by weight_cat
¶print(baseball_new.groupby('weight_cat').median())
baseball_new.groupby('weight_cat').mean().plot(x='avg',y='HR',kind='scatter', legend=True)
plt.show()
height
¶bb_height_avg
baseball_new.groupby('height_cat').mean().plot(x='avg',y='HR',\
c='height',kind='scatter', legend=True)
plt.show()
# Paired Plots by group
g = sns.PairGrid(baseball_new, hue = "height_cat")
g = g.map_diag(plt.hist,bins=20)
g = g.map_offdiag(plt.scatter,alpha=0.4)
plt.legend()
plt.show()
# Seperating into 10 Categories of weight
baseball_new['height_5cat'] = pd.qcut(baseball['height'], q=5)
baseball_new.groupby('height_5cat').median()[['HR']].plot(kind='bar')
plt.show()
baseball_new.groupby('height_5cat').median()[['avg']].plot(kind='bar')
plt.show()
def plot_bball_cat(bball,_cat):
COLORMAP ='rgbyo'
for i,l in enumerate(["Low","Medium","High"]):
d=bball[bball[_cat]==l]
# print(bball)
plt.scatter(x = d["avg"],y=d["HR"],alpha=0.4, label = l, color = COLORMAP[i])
plt.scatter(x = d["avg"].median(),y=d["HR"].median(),s=5000,\
color = COLORMAP[i], marker ='s')
plt.xlabel("Average")
plt.ylabel("Home Runs")
plt.legend()
plt.show()
plot_bball_cat(baseball_new,'height_cat')
plot_bball_cat(baseball_new,'weight_cat')
baseball_new.to_csv('baseball_data_modified')


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alpha: This controls the opacity of each diamond.
color: This controls the color of the stroke.
bColor: This controls the color of the background.


Problem: You have problems switching to the Modelica perspective, or have problems with using any of the Modelica views.
Solution: Make sure that you have Java 5.0 (aka 1.5) installed on your system. If you get an error message that says "Unsupported major.minor version 49.0" then that is a strong indication that you have an old version of Java.
Problem:
Solution: Make sure that you have a correct version of OMC installed. See http://www.ida.liu.se/~pelab/modelica/OpenModelica/MDT/ for information about the currently supported OMC version.
Problem: This problem can arise if you have upgraded OMC but an old version of OMC is still running in the background.
Solution: Terminate all OMC processes. They're typically named after the OMC binary, i.e. omc.exe or omc. If the problem persists, as a last resort, restart your computer.
Problem: If you, for example, can choose from two different Modelica perspectives when choosing perspective.
Solution: This probably means that you have two or more versions of MDT installed. To remove any old versions, go into the eclipse/plugins folder and remove all folders labeled with older versions of MDT.


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java.lang.Object
tracer.easings.
Easings
tracer.easings.
Easings.CircEaseIn
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CircEaseInBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CircEaseInOut
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CircEaseInOutBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CircEaseOut
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CircEaseOutBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CubicEaseIn
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CubicEaseInBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CubicEaseInOut
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CubicEaseInOutBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CubicEaseOut
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.CubicEaseOutBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.Linear
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.LinearBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.QuadEaseIn
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.QuadEaseInBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.QuadEaseInOut
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.QuadEaseInOutBackAndForth
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.QuadEaseOut
(implements tracer.easings.
Easing
)
tracer.easings.
Easings.QuadEaseOutBackAndForth
(implements tracer.easings.
Easing
)
Interface Hierarchy
tracer.easings.
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Mr Key is delighted to announce that his global domination schemes continue apace. Now, in addition to this very Hooting Yard you are reading, the radio show and the vast archive of podcasts available from ResonanceFM, he has found another berth on what our Flemish pals call het internet. Very sensibly, the quintet of indefatigable blogpersons who have created The Dabbler : A Culture Blog have invited your favourite impoverished scribbler to occupy his own cupboard there.
Postages will be placed in Key's Cupboard once a week, probably on Fridays, and include a mix of brand new stuff written exclusively for The Dabbler and forgotten items long buried in the Hooting Yard archives.
So hie ye over there right now, and make sure you read all the other interesting dabblings. (I particularly recommend the item about the Cobham Cuckoos.)


Notes:
- Select the patient of interest in the tabs above.
- A dash indicates a fragment that we were unable to sequence.
- Each zip archive contains a single-column text file. The format of this file is specified in the first lines (header).
- Once unzipped and reshaped, the pair counts matrices have dimension 6x6xLxL, where 6 is the length of the nucleotide alphabet, which is ACGT-N, and L is the length of the fragment.
- Each file is around 10MB large.


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| | |
- builtins.object
-
- TextLog
class TextLog(builtins.object) |
| |
TextLog(filepath, console=True, create_ok=True)
The TextLog logger logs per-epoch information in a human-readable way
to a simple text file, and optionally to the command line.
The output has the following form:
"Epoch E (lr=LR, time=T): Train [loss (acc)] Val [loss (acc)] "
where E is the epoch number, LR is the current learning rate, and T is
running time for both training and evaluation.
Args:
filepath (str or Path): Path to the log file.
console (bool): Whether to print log information to the commandline.
Default: True.
create_ok (bool): If True, allows the creation of any missing
folders along the path to logfile. Default: True. |
| |
Methods defined here:
- __init__(self, filepath, console=True, create_ok=True)
- Initialize self. See help(type(self)) for accurate signature.
- log(self, epoch, time, train_loss=0, train_acc=0, test_loss=0, test_acc=0, lr=None)
- Append to the log file, and optionally print to the console.
Accepts the current epoch number, execution time for the epoch,
values for the training and test loss and accuracy, and optionally
the value of the learning rate that was used.
Args:
epoch (int): Epoch number.
time (float): Elapsed time over the epoch.
train_loss (float): Loss measured across the training set.
train_acc (float): Accuracy measured across the training set.
test_loss (float): Loss measured across the test/validation set.
test_acc (float): Accuracy measured across the test/validation set.
lr (float): The learning rate.
- text(self, text)
- Append arbitrary text to the log file. Useful for keeping notes
when starting a new run or resuming a stopped run.
Args:
text (str): Text to add to the log file.
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
| |


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|
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| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Object Map
public class Map
Map class keeps track objects on the playing grid, helper methods to make movement decisions, and export/import methods for the editor
| Field Summary | |
|---|---|
private java.util.ArrayList<Actor> |
actorList
|
int |
CELL_SIZE
|
private byte[][] |
collideMap
|
private int |
dotsRemaining
|
private Item[][] |
itemMap
|
private int |
mapHeight
|
private int |
mapWidth
|
| Constructor Summary | |
|---|---|
Map(int w,
int h,
int cs)
Class constructor, inits a blank map based on a width, height, and cell size Used in the editor |
|
Map(java.lang.String filename,
int cs)
Class Constructor that reads the map data from filename |
| Method Summary | |
|---|---|
boolean |
addActor(Actor act)
Put a new actor in the map (actorList ArrayList) |
boolean |
addCollidable(int x,
int y,
byte t)
Add a collidable (by type) to the collideMap |
boolean |
addItem(Item item)
Put a new item to the item map |
boolean |
canMove(Actor act,
int x,
int y)
Move attempt method. |
int |
findDistance(GameObject start,
GameObject end)
Find the distance (Manhattan) between two objects |
Actor |
getActor(int idx)
Return an actor at index in the actorList ArrayList |
Actor |
getActor(int x,
int y,
boolean notPlayer)
Return an actor at coordinate (x,y) |
byte |
getCollidable(int x,
int y)
Return a value at (x,y) in the collision map |
byte[][] |
getCollidableMap()
Return the collidable map (a 2d array of bytes which correspond to the collidable types defined in GameObject) |
float |
getCost(Actor mover,
int sx,
int sy,
int tx,
int ty)
Get the cost of moving through the given tile. |
int |
getDotsRemaining()
Return the number of dots remaining on the map. |
int |
getHeight()
The height of the map originally set in the constructor |
Item |
getItem(int x,
int y)
Return an item at coordinate (x,y) from within the item map (itemMap) |
Item[][] |
getItemMap()
Return the item map (a 2D array of Item objects) |
int |
getNumActors()
Get the number of actorList on the map (the size of the actorList ArrayList) |
Player |
getPlayer()
Find and return the player object within the local actorList ArrayList |
int |
getWidth()
The width of the map originally set in the constructor |
boolean |
isEmpty(int x,
int y)
Check if a coordinate is completely empty (void of actorList, items, and collissions) Used by the editor |
private void |
read(java.lang.String filename)
Read a file with map contents and set the properties in this map Called by the constructor. |
void |
removeActor(int idx)
Remove an actor from actorList based on index. |
boolean |
removeAnyAt(int x,
int y)
Remove everything at coordiante (x,y) Used by the editor only |
void |
removeItem(int x,
int y)
Remove an item from the item array by coordinate (x, y) |
void |
write(java.lang.String filename)
Write the contents of this map to a file in the correct format |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Field Detail |
|---|
private int mapWidth
private int mapHeight
public final int CELL_SIZE
private byte[][] collideMap
private Item[][] itemMap
private java.util.ArrayList<Actor> actorList
private int dotsRemaining
| Constructor Detail |
|---|
public Map(int w, int h, int cs)
w
- Width of the maph
- Height of the mapcs
- Size of individual cells in pixelspublic Map(java.lang.String filename, int cs)
filename
- The file name of the map to read contents fromcs
- Size of individual cells in pixels. This is something that should be deteremined by graphics, not the mapfile| Method Detail |
|---|
public int getWidth()
public int getHeight()
public int getNumActors()
public byte[][] getCollidableMap()
public Item[][] getItemMap()
public int getDotsRemaining()
public boolean addCollidable(int x, int y, byte t)
x
- X coordinatey
- Y coordinatet
- Type of collidable
public boolean addItem(Item item)
item
- Item
public boolean addActor(Actor act)
act
- Actor
public byte getCollidable(int x, int y)
x
- X Coordinatey
- Y Coordinate
public Item getItem(int x, int y)
x
- X Coordinatey
- Y Coordinate
public Actor getActor(int idx)
idx
- Index in actorList
public Player getPlayer()
public Actor getActor(int x, int y, boolean notPlayer)
x
- X Coordinatey
- Y CoordinatenotPlayer
- If true, ignore a "Player" actor at (x,y)
public void removeActor(int idx)
idx
- Index of the actorpublic void removeItem(int x, int y)
x
- X coordinate of the itemy
- Y coordinate of the itempublic boolean removeAnyAt(int x, int y)
x
- X coordinatey
- Y coordinate
public int findDistance(GameObject start, GameObject end)
start
- GameObject at the initial positionend
- GameObject at the end position
public boolean isEmpty(int x, int y)
x
- A x coordinate to move toy
- A y coordinate to move to
public boolean canMove(Actor act, int x, int y)
act
- The actor object trying to movex
- A x coordinate to move toy
- A y coordinate to move to
public float getCost(Actor mover, int sx, int sy, int tx, int ty)
mover
- The mover that is trying to move across the tilesx
- The x coordinate of the tile we're moving fromsy
- The y coordinate of the tile we're moving fromtx
- The x coordinate of the tile we're moving toty
- The y coordinate of the tile we're moving to
public void write(java.lang.String filename)
filename
- File name of the mapprivate void read(java.lang.String filename)
filename
- File name of the map
|
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