I was trying to install AmberTools on my macOS Catalina Installation. Running ./configure -macAccelerate clang gave me an error that it could not find X11 libraries, even though locate libXt showed that my installation was correct.

Error:

Could not find the X11 libraries; you may need to edit config.h
   to set the XHOME and XLIBS variables.
Error: The X11 libraries are not in the usual location !
       To search for them try the command: locate libXt
       On new Fedora OS's install the libXt-devel libXext-devel
       libX11-devel libICE-devel libSM-devel packages.
       On old Fedora OS's install the xorg-x11-devel package.
       On RedHat OS's install the XFree86-devel package.
       On Ubuntu OS's install the xorg-dev and xserver-xorg packages.

          ...more info for various linuxes at ambermd.org/ubuntu.html

       To build Amber without XLEaP, re-run configure with '-noX11:
            ./configure -noX11 --with-python /usr/local/bin/python3 -macAccelerate clang
Configure failed due to the errors above!

I searcehd on Google for a solution on their, sadly there was not even a single thread which had a solution about this error.

The Fix

Simply reinstalling XQuartz using homebrew fixed the error brew cask reinstall xquartz

If you do not have xquartz installed, you need to run brew cask install xquartz

This is still a pre-print.

Download paper here

This is still a pre-print.

Download paper here

Recommended citation:

APA

Chauhan, N. (2020, March 15). Is it possible to programmatically generate Vaporwave?. https://doi.org/10.35543/osf.io/9um2r

MLA

Chauhan, Navan. “Is It Possible to Programmatically Generate Vaporwave?.” IndiaRxiv, 15 Mar. 2020. Web.

Chicago

Chauhan, Navan. 2020. “Is It Possible to Programmatically Generate Vaporwave?.” IndiaRxiv. March 15. doi:10.35543/osf.io/9um2r.

Bibtex

@misc{chauhan_2020,
 title={Is it possible to programmatically generate Vaporwave?},
 url={indiarxiv.org/9um2r},
 DOI={10.35543/osf.io/9um2r},
 publisher={IndiaRxiv},
 author={Chauhan, Navan},
 year={2020},
 month={Mar}
}

I finally completed my first quick and dirty vaporwave remix of "I Want It That Way" by the Backstreet Boys

V A P O R W A V E

Vaporwave is all about A E S T H E T I C S. Vaporwave is a type of music genre that emmerged as a parody of Chillwave, shared more as a meme rather than a proper musical genre. Of course this changed as the genre become mature

How to Vaporwave

The first track which is considered to be actual Vaporwave is Ramona Xavier's Macintosh Plus, this unspokenly set the the guidelines for making Vaporwave

• Take a 1980s RnB song
• Slow it down
• Add Bass and Trebble
• Add again
• Add Reverb ( make sure its wet )

There you have your very own Vaporwave track.

( Now, there are some tracks being produced which are not remixes and are original )

My Remix

Where is the Programming?

The fact that there are steps on producing Vaporwave, this gave me the idea that Vaporwave can actually be made using programming, stay tuned for when I publish the program which I am working on ( Generating A E S T H E T I C artwork and remixes)

So I have an Android TV, this posts covers everything I have tried on it

Contents

1. Getting TV's IP Address
2. Enable Developer Settings
3. Enable ADB
4. Connect ADB
5. Manipulating Packages

IP-Address

These steps should be similar for all Android-TVs

• Go To Settings
• Go to Network
• Advanced Settings
• Network Status
• Note Down IP-Address

The other option is to go to your router's server page and get connected devices

Developer-Settings

• Go To Settings
• About
• Continously click on the "Build" option until it says "You are a Developer"

Enable-ADB

• Go to Settings
• Go to Developer Options
• Scroll untill you find ADB Debugging and enable that option

Connect-ADB

• Open Terminal (Make sure you have ADB installed)
• Enter the following command adb connect <IP_ADDRESS>
• To test the connection run adb logcat

Manipulating Apps / Packages

Listing Packages

• adb shell
• pm list packages

Installing Packages

• adb install -r package.apk

Uninstalling Packages

• adb uninstall com.company.yourpackagename

About Open Peeps

Open Peeps is a hand-drawn illustration library to create scenes of people. You can use them in product illustration, marketing, comics, product states, user flows, personas, storyboarding, quinceañera invitations, or whatever you want! - Product Hunt

Some Examples

Standing

This was tested on a Raspberry Pi Zero W

Enter in the Bluetooth Mode

pi@raspberrypi:~ $ bluetoothctl

[bluetooth]# agent on

[bluetooth]# default-agent

[bluetooth]# scan on

To Pair

While being in bluetooth mode

[bluetooth]# pair XX:XX:XX:XX:XX:XX

To Exit out of bluetoothctl anytime, just type exit

For setting up Kaggle with Google Colab, please refer to my previous post

Dataset

Mounting Google Drive

import os
from google.colab import drive
drive.mount('/content/drive')

Downloading Dataset from Kaggle

os.environ['KAGGLE_CONFIG_DIR'] = "/content/drive/My Drive/"
!kaggle datasets download ashutosh69/fire-and-smoke-dataset
!unzip "fire-and-smoke-dataset.zip"

Pre-Processing

!mkdir default smoke fire

!ls data/data/img_data/train/default/*.jpg

img_1002.jpg   img_20.jpg     img_519.jpg     img_604.jpg       img_80.jpg
img_1003.jpg   img_21.jpg     img_51.jpg     img_60.jpg       img_8.jpg
img_1007.jpg   img_22.jpg     img_520.jpg     img_61.jpg       img_900.jpg
img_100.jpg    img_23.jpg     img_521.jpg    'img_62 (2).jpg'   img_920.jpg
img_1014.jpg   img_24.jpg    'img_52 (2).jpg'     img_62.jpg       img_921.jpg
img_1018.jpg   img_29.jpg     img_522.jpg    'img_63 (2).jpg'   img_922.jpg
img_101.jpg    img_3000.jpg   img_523.jpg     img_63.jpg       img_923.jpg
img_1027.jpg   img_335.jpg    img_524.jpg     img_66.jpg       img_924.jpg
img_102.jpg    img_336.jpg    img_52.jpg     img_67.jpg       img_925.jpg
img_1042.jpg   img_337.jpg    img_530.jpg     img_68.jpg       img_926.jpg
img_1043.jpg   img_338.jpg    img_531.jpg     img_700.jpg       img_927.jpg
img_1046.jpg   img_339.jpg   'img_53 (2).jpg'     img_701.jpg       img_928.jpg
img_1052.jpg   img_340.jpg    img_532.jpg     img_702.jpg       img_929.jpg
img_107.jpg    img_341.jpg    img_533.jpg     img_703.jpg       img_930.jpg
img_108.jpg    img_3.jpg      img_537.jpg     img_704.jpg       img_931.jpg
img_109.jpg    img_400.jpg    img_538.jpg     img_705.jpg       img_932.jpg
img_10.jpg     img_471.jpg    img_539.jpg     img_706.jpg       img_933.jpg
img_118.jpg    img_472.jpg    img_53.jpg     img_707.jpg       img_934.jpg
img_12.jpg     img_473.jpg    img_540.jpg     img_708.jpg       img_935.jpg
img_14.jpg     img_488.jpg    img_541.jpg     img_709.jpg       img_938.jpg
img_15.jpg     img_489.jpg   'img_54 (2).jpg'     img_70.jpg       img_958.jpg
img_16.jpg     img_490.jpg    img_542.jpg     img_710.jpg       img_971.jpg
img_17.jpg     img_491.jpg    img_543.jpg    'img_71 (2).jpg'   img_972.jpg
img_18.jpg     img_492.jpg    img_54.jpg     img_71.jpg       img_973.jpg
img_19.jpg     img_493.jpg   'img_55 (2).jpg'     img_72.jpg       img_974.jpg
img_1.jpg      img_494.jpg    img_55.jpg     img_73.jpg       img_975.jpg
img_200.jpg    img_495.jpg    img_56.jpg     img_74.jpg       img_980.jpg
img_201.jpg    img_496.jpg    img_57.jpg     img_75.jpg       img_988.jpg
img_202.jpg    img_497.jpg    img_58.jpg     img_76.jpg       img_9.jpg
img_203.jpg    img_4.jpg      img_59.jpg     img_77.jpg
img_204.jpg    img_501.jpg    img_601.jpg     img_78.jpg
img_205.jpg    img_502.jpg    img_602.jpg     img_79.jpg
img_206.jpg    img_50.jpg     img_603.jpg     img_7.jpg

The image files are not actually JPEG, thus we first need to save them in the correct format for Turicreate

from PIL import Image
import glob


folders = ["default","smoke","fire"]
for folder in folders:
  n = 1
  for file in glob.glob("./data/data/img_data/train/" + folder + "/*.jpg"):
    im = Image.open(file)
    rgb_im = im.convert('RGB')
    rgb_im.save((folder + "/" + str(n) + ".jpg"), quality=100)
    n +=1 
  for file in glob.glob("./data/data/img_data/train/" + folder + "/*.jpg"):
    im = Image.open(file)
    rgb_im = im.convert('RGB')
    rgb_im.save((folder + "/" + str(n) + ".jpg"), quality=100)
    n +=1

!mkdir train
!mv default ./train
!mv smoke ./train
!mv fire ./train

Making the Image Classifier

Making an SFrame

!pip install turicreate

import turicreate as tc
import os

data = tc.image_analysis.load_images("./train", with_path=True)

data["label"] = data["path"].apply(lambda path: os.path.basename(os.path.dirname(path)))

print(data)

data.save('fire-smoke.sframe')

+-------------------------+------------------------+
|           path          |         image          |
+-------------------------+------------------------+
|  ./train/default/1.jpg  | Height: 224 Width: 224 |
|  ./train/default/10.jpg | Height: 224 Width: 224 |
| ./train/default/100.jpg | Height: 224 Width: 224 |
| ./train/default/101.jpg | Height: 224 Width: 224 |
| ./train/default/102.jpg | Height: 224 Width: 224 |
| ./train/default/103.jpg | Height: 224 Width: 224 |
| ./train/default/104.jpg | Height: 224 Width: 224 |
| ./train/default/105.jpg | Height: 224 Width: 224 |
| ./train/default/106.jpg | Height: 224 Width: 224 |
| ./train/default/107.jpg | Height: 224 Width: 224 |
+-------------------------+------------------------+
[2028 rows x 2 columns]
Note: Only the head of the SFrame is printed.
You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.
+-------------------------+------------------------+---------+
|           path          |         image          |  label  |
+-------------------------+------------------------+---------+
|  ./train/default/1.jpg  | Height: 224 Width: 224 | default |
|  ./train/default/10.jpg | Height: 224 Width: 224 | default |
| ./train/default/100.jpg | Height: 224 Width: 224 | default |
| ./train/default/101.jpg | Height: 224 Width: 224 | default |
| ./train/default/102.jpg | Height: 224 Width: 224 | default |
| ./train/default/103.jpg | Height: 224 Width: 224 | default |
| ./train/default/104.jpg | Height: 224 Width: 224 | default |
| ./train/default/105.jpg | Height: 224 Width: 224 | default |
| ./train/default/106.jpg | Height: 224 Width: 224 | default |
| ./train/default/107.jpg | Height: 224 Width: 224 | default |
+-------------------------+------------------------+---------+
[2028 rows x 3 columns]
Note: Only the head of the SFrame is printed.
You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.

Making the Model

import turicreate as tc

# Load the data
data =  tc.SFrame('fire-smoke.sframe')

# Make a train-test split
train_data, test_data = data.random_split(0.8)

# Create the model
model = tc.image_classifier.create(train_data, target='label')

# Save predictions to an SArray
predictions = model.predict(test_data)

# Evaluate the model and print the results
metrics = model.evaluate(test_data)
print(metrics['accuracy'])

# Save the model for later use in Turi Create
model.save('fire-smoke.model')

# Export for use in Core ML
model.export_coreml('fire-smoke.mlmodel')

Performing feature extraction on resized images...
Completed   64/1633
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PROGRESS: Creating a validation set from 5 percent of training data. This may take a while.
          You can set ``validation_set=None`` to disable validation tracking.

Logistic regression:
--------------------------------------------------------
Number of examples          : 1551
Number of classes           : 3
Number of feature columns   : 1
Number of unpacked features : 2048
Number of coefficients      : 4098
Starting L-BFGS
--------------------------------------------------------
+-----------+----------+-----------+--------------+-------------------+---------------------+
| Iteration | Passes   | Step size | Elapsed Time | Training Accuracy | Validation Accuracy |
+-----------+----------+-----------+--------------+-------------------+---------------------+
| 0         | 6        | 0.018611  | 0.891830     | 0.553836          | 0.560976            |
| 1         | 10       | 0.390832  | 1.622383     | 0.744681          | 0.792683            |
| 2         | 11       | 0.488541  | 1.943987     | 0.733075          | 0.804878            |
| 3         | 14       | 2.442703  | 2.512545     | 0.727917          | 0.841463            |
| 4         | 15       | 2.442703  | 2.826964     | 0.861380          | 0.853659            |
| 9         | 28       | 2.340435  | 5.492035     | 0.941328          | 0.975610            |
+-----------+----------+-----------+--------------+-------------------+---------------------+
Performing feature extraction on resized images...
Completed  64/395
Completed 128/395
Completed 192/395
Completed 256/395
Completed 320/395
Completed 384/395
Completed 395/395
0.9316455696202531

We just got an accuracy of 94% on Training Data and 97% on Validation Data!

In order to be able to access Kaggle Datasets, you will need to have an account on Kaggle (which is Free)

Grabbing Our Tokens

Go to Kaggle

Click on your User Profile and Click on My Account

Scroll Down untill you see Create New API Token

This will download your token as a JSON file

Copy the File to the root folder of your Google Drive

Setting up Colab

Mounting Google Drive

import os
from google.colab import drive
drive.mount('/content/drive')

After this click on the URL in the output section, login and then paste the Auth Code

Configuring Kaggle

os.environ['KAGGLE_CONFIG_DIR'] = "/content/drive/My Drive/"

Voila! You can now download kaggel datasets

import numpy
import PIL

# Convert PIL Image to NumPy array
img = PIL.Image.open("foo.jpg")
arr = numpy.array(img)

# Convert array to Image
img = PIL.Image.fromarray(arr)

Saving an Image

try:
    img.save(destination, "JPEG", quality=80, optimize=True, progressive=True)
except IOError:
    PIL.ImageFile.MAXBLOCK = img.size[0] * img.size[1]
    img.save(destination, "JPEG", quality=80, optimize=True, progressive=True)

In this tutorial we will build a fake news detecting app from scratch, using Turicreate for the machine learning model and SwiftUI for building the app

Note: These commands are written as if you are running a jupyter notebook.

Building the Machine Learning Model

Data Gathering

To build a classifier, you need a lot of data. George McIntire (GH: @joolsa) has created a wonderful dataset containing the headline, body and wheter it is fake or real. Whenever you are looking for a dataset, always try searching on Kaggle and GitHub before you start building your own

Dependencies

I used a Google Colab instance for training my model. If you also plan on using Google Colab then I reccomend choosing a GPU Instance (It is Free) This allows you to train the model on the GPU. Turicreat is built on top of Apache's MXNet Framework, for us to use GPU we need to install a CUDA compatible MXNet package.

!pip install turicreate
!pip uninstall -y mxnet
!pip install mxnet-cu100==1.4.0.post0

If you do not wish to train on GPU or are running it on your computer, you can ignore the last two lines

Downloading the Dataset

!wget -q "https://github.com/joolsa/fake_real_news_dataset/raw/master/fake_or_real_news.csv.zip"
!unzip fake_or_real_news.csv.zip

Model Creation

import turicreate as tc
tc.config.set_num_gpus(-1) # If you do not wish to use GPUs, set it to 0

dataSFrame = tc.SFrame('fake_or_real_news.csv')

The dataset contains a column named "X1", which is of no use to us. Therefore, we simply drop it

dataSFrame.remove_column('X1')

Splitting Dataset

train, test = dataSFrame.random_split(.9)

Training

model = tc.text_classifier.create(
    dataset=train,
    target='label',
    features=['title','text']
)

+-----------+----------+-----------+--------------+-------------------+---------------------+
| Iteration | Passes   | Step size | Elapsed Time | Training Accuracy | Validation Accuracy |
+-----------+----------+-----------+--------------+-------------------+---------------------+
| 0         | 2        | 1.000000  | 1.156349     | 0.889680          | 0.790036            |
| 1         | 4        | 1.000000  | 1.359196     | 0.985952          | 0.918149            |
| 2         | 6        | 0.820091  | 1.557205     | 0.990260          | 0.914591            |
| 3         | 7        | 1.000000  | 1.684872     | 0.998689          | 0.925267            |
| 4         | 8        | 1.000000  | 1.814194     | 0.999063          | 0.925267            |
| 9         | 14       | 1.000000  | 2.507072     | 1.000000          | 0.911032            |
+-----------+----------+-----------+--------------+-------------------+---------------------+

Testing the Model

est_predictions = model.predict(test)
accuracy = tc.evaluation.accuracy(test['label'], test_predictions)
print(f'Topic classifier model has a testing accuracy of {accuracy*100}% ', flush=True)

Topic classifier model has a testing accuracy of 92.3076923076923%

We have just created our own Fake News Detection Model which has an accuracy of 92%!

example_text = {"title": ["Middling ‘Rise Of Skywalker’ Review Leaves Fan On Fence About Whether To Threaten To Kill Critic"], "text": ["Expressing ambivalence toward the relatively balanced appraisal of the film, Star Wars fan Miles Ariely admitted Thursday that an online publication’s middling review of The Rise Of Skywalker had left him on the fence about whether he would still threaten to kill the critic who wrote it. “I’m really of two minds about this, because on the one hand, he said the new movie fails to live up to the original trilogy, which makes me at least want to throw a brick through his window with a note telling him to watch his back,” said Ariely, confirming he had already drafted an eight-page-long death threat to Stan Corimer of the website Screen-On Time, but had not yet decided whether to post it to the reviewer’s Facebook page. “On the other hand, though, he commended J.J. Abrams’ skillful pacing and faithfulness to George Lucas’ vision, which makes me wonder if I should just call the whole thing off. Now, I really don’t feel like camping outside his house for hours. Maybe I could go with a response that’s somewhere in between, like, threatening to kill his dog but not everyone in his whole family? I don’t know. This is a tough one.” At press time, sources reported that Ariely had resolved to wear his Ewok costume while he murdered the critic in his sleep."]}
example_prediction = model.classify(tc.SFrame(example_text))
print(example_prediction, flush=True)

+-------+--------------------+
| class |    probability     |
+-------+--------------------+
|  FAKE | 0.9245648658345308 |
+-------+--------------------+
[1 rows x 2 columns]

Exporting the Model

model_name = 'FakeNews'
coreml_model_name = model_name + '.mlmodel'
exportedModel = model.export_coreml(coreml_model_name)

Note: To download files from Google Volab, simply click on the files section in the sidebar, right click on filename and then click on downlaod

Link to Colab Notebook

Building the App using SwiftUI

Initial Setup

First we create a single view app (make sure you check the use SwiftUI button)

Then we copy our .mlmodel file to our project (Just drag and drop the file in the XCode Files Sidebar)

Our ML Model does not take a string directly as an input, rather it takes bag of words as an input. DescriptionThe bag-of-words model is a simplifying representation used in NLP, in this text is represented as a bag of words, without any regatd of grammar or order, but noting multiplicity

We define our bag of words function

func bow(text: String) -> [String: Double] {
        var bagOfWords = [String: Double]()
        
        let tagger = NSLinguisticTagger(tagSchemes: [.tokenType], options: 0)
        let range = NSRange(location: 0, length: text.utf16.count)
        let options: NSLinguisticTagger.Options = [.omitPunctuation, .omitWhitespace]
        tagger.string = text
        
        tagger.enumerateTags(in: range, unit: .word, scheme: .tokenType, options: options) { _, tokenRange, _ in
            let word = (text as NSString).substring(with: tokenRange)
            if bagOfWords[word] != nil {
                bagOfWords[word]! += 1
            } else {
                bagOfWords[word] = 1
            }
        }
        
        return bagOfWords
    }

We also declare our variables

@State private var title: String = ""
@State private var headline: String = ""
@State private var alertTitle = ""
@State private var alertText = ""
@State private var showingAlert = false

Finally, we implement a simple function which reads the two text fields, creates their bag of words representation and displays an alert with the appropriate result

Complete Code

import SwiftUI

struct ContentView: View {
    @State private var title: String = ""
    @State private var headline: String = ""
    
    @State private var alertTitle = ""
    @State private var alertText = ""
    @State private var showingAlert = false
    
    var body: some View {
        NavigationView {
            VStack(alignment: .leading) {
                Text("Headline").font(.headline)
                TextField("Please Enter Headline", text: $title)
                    .lineLimit(nil)
                Text("Body").font(.headline)
                TextField("Please Enter the content", text: $headline)
                .lineLimit(nil)
            }
                .navigationBarTitle("Fake News Checker")
            .navigationBarItems(trailing:
                Button(action: classifyFakeNews) {
                    Text("Check")
                })
            .padding()
                .alert(isPresented: $showingAlert){
                    Alert(title: Text(alertTitle), message: Text(alertText), dismissButton: .default(Text("OK")))
            }
        }
        
    }
    
    func classifyFakeNews(){
        let model = FakeNews()
        let myTitle = bow(text: title)
        let myText = bow(text: headline)
        do {
            let prediction = try model.prediction(title: myTitle, text: myText)
            alertTitle = prediction.label
            alertText = "It is likely that this piece of news is \(prediction.label.lowercased())."
            print(alertText)
        } catch {
            alertTitle = "Error"
            alertText = "Sorry, could not classify if the input news was fake or not."
        }
        
        showingAlert = true
    }
    func bow(text: String) -> [String: Double] {
        var bagOfWords = [String: Double]()
        
        let tagger = NSLinguisticTagger(tagSchemes: [.tokenType], options: 0)
        let range = NSRange(location: 0, length: text.utf16.count)
        let options: NSLinguisticTagger.Options = [.omitPunctuation, .omitWhitespace]
        tagger.string = text
        
        tagger.enumerateTags(in: range, unit: .word, scheme: .tokenType, options: options) { _, tokenRange, _ in
            let word = (text as NSString).substring(with: tokenRange)
            if bagOfWords[word] != nil {
                bagOfWords[word]! += 1
            } else {
                bagOfWords[word] = 1
            }
        }
        
        return bagOfWords
    }
}

struct ContentView_Previews: PreviewProvider {
    static var previews: some View {
        ContentView()
    }
}

In this tutorial you will learn about polynomial regression and how you can implement it in Tensorflow.

In this, we will be performing polynomial regression using 5 types of equations -

• Linear
• Quadratic
• Cubic
• Quartic
• Quintic

Regression

What is Regression?

Regression is a statistical measurement that is used to try to determine the relationship between a dependent variable (often denoted by Y), and series of varying variables (called independent variables, often denoted by X ).

What is Polynomial Regression

This is a form of Regression Analysis where the relationship between Y and X is denoted as the nth degree/power of X. Polynomial regression even fits a non-linear relationship (e.g when the points don't form a straight line).

Imports

import tensorflow.compat.v1 as tf
tf.disable_v2_behavior()
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

Dataset

Creating Random Data

Even though in this tutorial we will use a Position Vs Salary datasset, it is important to know how to create synthetic data

To create 50 values spaced evenly between 0 and 50, we use NumPy's linspace funtion

linspace(lower_limit, upper_limit, no_of_observations)

x = np.linspace(0, 50, 50)
y = np.linspace(0, 50, 50)

We use the following function to add noise to the data, so that our values

x += np.random.uniform(-4, 4, 50)
y += np.random.uniform(-4, 4, 50)

Position vs Salary Dataset

We will be using https://drive.google.com/file/d/1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9/view (Salary vs Position Dataset)

!wget --no-check-certificate 'https://docs.google.com/uc?export=download&id=1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9' -O data.csv

df = pd.read_csv("data.csv")

df # this gives us a preview of the dataset we are working with

| Position          | Level | Salary  |
|-------------------|-------|---------|
| Business Analyst  | 1     | 45000   |
| Junior Consultant | 2     | 50000   |
| Senior Consultant | 3     | 60000   |
| Manager           | 4     | 80000   |
| Country Manager   | 5     | 110000  |
| Region Manager    | 6     | 150000  |
| Partner           | 7     | 200000  |
| Senior Partner    | 8     | 300000  |
| C-level           | 9     | 500000  |
| CEO               | 10    | 1000000 |

We convert the salary column as the ordinate (y-cordinate) and level column as the abscissa

abscissa = df["Level"].to_list() # abscissa = [1,2,3,4,5,6,7,8,9,10]
ordinate = df["Salary"].to_list() # ordinate = [45000,50000,60000,80000,110000,150000,200000,300000,500000,1000000]

n = len(abscissa) # no of observations
plt.scatter(abscissa, ordinate)
plt.ylabel('Salary')
plt.xlabel('Position')
plt.title("Salary vs Position")
plt.show()

Defining Stuff

X = tf.placeholder("float")
Y = tf.placeholder("float")

Defining Variables

We first define all the coefficients and constant as tensorflow variables haveing a random intitial value

a = tf.Variable(np.random.randn(), name = "a")
b = tf.Variable(np.random.randn(), name = "b")
c = tf.Variable(np.random.randn(), name = "c")
d = tf.Variable(np.random.randn(), name = "d")
e = tf.Variable(np.random.randn(), name = "e")
f = tf.Variable(np.random.randn(), name = "f")

Model Configuration

learning_rate = 0.2
no_of_epochs = 25000

Equations

deg1 = a*X + b
deg2 = a*tf.pow(X,2) + b*X + c
deg3 = a*tf.pow(X,3) + b*tf.pow(X,2) + c*X + d
deg4 = a*tf.pow(X,4) + b*tf.pow(X,3) + c*tf.pow(X,2) + d*X + e
deg5 = a*tf.pow(X,5) + b*tf.pow(X,4) + c*tf.pow(X,3) + d*tf.pow(X,2) + e*X + f

Cost Function

We use the Mean Squared Error Function

mse1 = tf.reduce_sum(tf.pow(deg1-Y,2))/(2*n)
mse2 = tf.reduce_sum(tf.pow(deg2-Y,2))/(2*n)
mse3 = tf.reduce_sum(tf.pow(deg3-Y,2))/(2*n)
mse4 = tf.reduce_sum(tf.pow(deg4-Y,2))/(2*n)
mse5 = tf.reduce_sum(tf.pow(deg5-Y,2))/(2*n)

Optimizer

We use the AdamOptimizer for the polynomial functions and GradientDescentOptimizer for the linear function

optimizer1 = tf.train.GradientDescentOptimizer(learning_rate).minimize(mse1)
optimizer2 = tf.train.AdamOptimizer(learning_rate).minimize(mse2)
optimizer3 = tf.train.AdamOptimizer(learning_rate).minimize(mse3)
optimizer4 = tf.train.AdamOptimizer(learning_rate).minimize(mse4)
optimizer5 = tf.train.AdamOptimizer(learning_rate).minimize(mse5)

init=tf.global_variables_initializer()

Model Predictions

For each type of equation first we make the model predict the values of the coefficient(s) and constant, once we get these values we use it to predict the Y values using the X values. We then plot it to compare the actual data and predicted line.

Linear Equation

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(no_of_epochs):
      for (x,y) in zip(abscissa, ordinate):
        sess.run(optimizer1, feed_dict={X:x, Y:y})
      if (epoch+1)%1000==0:
        cost = sess.run(mse1,feed_dict={X:abscissa,Y:ordinate})
        print("Epoch",(epoch+1), ": Training Cost:", cost," a,b:",sess.run(a),sess.run(b))

        training_cost = sess.run(mse1,feed_dict={X:abscissa,Y:ordinate})
        coefficient1 = sess.run(a)
        constant = sess.run(b)

print(training_cost, coefficient1, constant)

Epoch 1000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 2000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 3000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 4000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 5000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 6000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 7000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 8000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 9000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 10000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 11000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 12000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 13000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 14000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 15000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 16000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 17000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 18000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 19000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 20000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 21000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 22000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 23000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 24000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
Epoch 25000 : Training Cost: 88999125000.0  a,b: 180396.42 -478869.12
88999125000.0 180396.42 -478869.12

predictions = []
for x in abscissa:
  predictions.append((coefficient1*x + constant))
plt.plot(abscissa , ordinate, 'ro', label ='Original data')
plt.plot(abscissa, predictions, label ='Fitted line')
plt.title('Linear Regression Result')
plt.legend()
plt.show()

Quadratic Equation

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(no_of_epochs):
      for (x,y) in zip(abscissa, ordinate):
        sess.run(optimizer2, feed_dict={X:x, Y:y})
      if (epoch+1)%1000==0:
        cost = sess.run(mse2,feed_dict={X:abscissa,Y:ordinate})
        print("Epoch",(epoch+1), ": Training Cost:", cost," a,b,c:",sess.run(a),sess.run(b),sess.run(c))

        training_cost = sess.run(mse2,feed_dict={X:abscissa,Y:ordinate})
        coefficient1 = sess.run(a)
        coefficient2 = sess.run(b)
        constant = sess.run(c)

print(training_cost, coefficient1, coefficient2, constant)

Epoch 1000 : Training Cost: 52571360000.0  a,b,c: 1002.4456 1097.0197 1276.6921
Epoch 2000 : Training Cost: 37798890000.0  a,b,c: 1952.4263 2130.2825 2469.7756
Epoch 3000 : Training Cost: 26751185000.0  a,b,c: 2839.5825 3081.6118 3554.351
Epoch 4000 : Training Cost: 19020106000.0  a,b,c: 3644.56 3922.9563 4486.3135
Epoch 5000 : Training Cost: 14060446000.0  a,b,c: 4345.042 4621.4233 5212.693
Epoch 6000 : Training Cost: 11201084000.0  a,b,c: 4921.1855 5148.1504 5689.0713
Epoch 7000 : Training Cost: 9732740000.0  a,b,c: 5364.764 5493.0156 5906.754
Epoch 8000 : Training Cost: 9050918000.0  a,b,c: 5685.4067 5673.182 5902.0728
Epoch 9000 : Training Cost: 8750394000.0  a,b,c: 5906.9814 5724.8906 5734.746
Epoch 10000 : Training Cost: 8613128000.0  a,b,c: 6057.3677 5687.3364 5461.167
Epoch 11000 : Training Cost: 8540034600.0  a,b,c: 6160.547 5592.3022 5122.8633
Epoch 12000 : Training Cost: 8490983000.0  a,b,c: 6233.9175 5462.025 4747.111
Epoch 13000 : Training Cost: 8450816500.0  a,b,c: 6289.048 5310.7583 4350.6997
Epoch 14000 : Training Cost: 8414082000.0  a,b,c: 6333.199 5147.394 3943.9294
Epoch 15000 : Training Cost: 8378841600.0  a,b,c: 6370.7944 4977.1704 3532.476
Epoch 16000 : Training Cost: 8344471000.0  a,b,c: 6404.468 4803.542 3120.2087
Epoch 17000 : Training Cost: 8310785500.0  a,b,c: 6435.365 4628.1523 2709.1445
Epoch 18000 : Training Cost: 8277482000.0  a,b,c: 6465.5493 4451.833 2300.2783
Epoch 19000 : Training Cost: 8244650000.0  a,b,c: 6494.609 4274.826 1894.3738
Epoch 20000 : Training Cost: 8212349000.0  a,b,c: 6522.8247 4098.1733 1491.9915
Epoch 21000 : Training Cost: 8180598300.0  a,b,c: 6550.6567 3922.7405 1093.3868
Epoch 22000 : Training Cost: 8149257700.0  a,b,c: 6578.489 3747.8362 698.53357
Epoch 23000 : Training Cost: 8118325000.0  a,b,c: 6606.1973 3573.2742 307.3541
Epoch 24000 : Training Cost: 8088001000.0  a,b,c: 6632.96 3399.878 -79.89219
Epoch 25000 : Training Cost: 8058094600.0  a,b,c: 6659.793 3227.2517 -463.03156
8058094600.0 6659.793 3227.2517 -463.03156

predictions = []
for x in abscissa:
  predictions.append((coefficient1*pow(x,2) + coefficient2*x + constant))
plt.plot(abscissa , ordinate, 'ro', label ='Original data')
plt.plot(abscissa, predictions, label ='Fitted line')
plt.title('Quadratic Regression Result')
plt.legend()
plt.show()

Cubic

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(no_of_epochs):
      for (x,y) in zip(abscissa, ordinate):
        sess.run(optimizer3, feed_dict={X:x, Y:y})
      if (epoch+1)%1000==0:
        cost = sess.run(mse3,feed_dict={X:abscissa,Y:ordinate})
        print("Epoch",(epoch+1), ": Training Cost:", cost," a,b,c,d:",sess.run(a),sess.run(b),sess.run(c),sess.run(d))

        training_cost = sess.run(mse3,feed_dict={X:abscissa,Y:ordinate})
        coefficient1 = sess.run(a)
        coefficient2 = sess.run(b)
        coefficient3 = sess.run(c)
        constant = sess.run(d)

print(training_cost, coefficient1, coefficient2, coefficient3, constant)

Epoch 1000 : Training Cost: 4279814000.0  a,b,c,d: 670.1527 694.4212 751.4653 903.9527
Epoch 2000 : Training Cost: 3770950400.0  a,b,c,d: 742.6414 666.3489 636.94525 859.2088
Epoch 3000 : Training Cost: 3717708300.0  a,b,c,d: 756.2582 569.3339 448.105 748.23956
Epoch 4000 : Training Cost: 3667464000.0  a,b,c,d: 769.4476 474.0318 265.5761 654.75525
Epoch 5000 : Training Cost: 3620040700.0  a,b,c,d: 782.32324 380.54272 89.39888 578.5136
Epoch 6000 : Training Cost: 3575265800.0  a,b,c,d: 794.8898 288.83356 -80.5215 519.13654
Epoch 7000 : Training Cost: 3532972000.0  a,b,c,d: 807.1608 198.87044 -244.31102 476.2061
Epoch 8000 : Training Cost: 3493009200.0  a,b,c,d: 819.13513 110.64169 -402.0677 449.3291
Epoch 9000 : Training Cost: 3455228400.0  a,b,c,d: 830.80255 24.0964 -553.92804 438.0652
Epoch 10000 : Training Cost: 3419475500.0  a,b,c,d: 842.21594 -60.797424 -700.0123 441.983
Epoch 11000 : Training Cost: 3385625300.0  a,b,c,d: 853.3363 -144.08699 -840.467 460.6356
Epoch 12000 : Training Cost: 3353544700.0  a,b,c,d: 864.19135 -225.8125 -975.4196 493.57703
Epoch 13000 : Training Cost: 3323125000.0  a,b,c,d: 874.778 -305.98932 -1104.9867 540.39465
Epoch 14000 : Training Cost: 3294257000.0  a,b,c,d: 885.1007 -384.63474 -1229.277 600.65607
Epoch 15000 : Training Cost: 3266820000.0  a,b,c,d: 895.18823 -461.819 -1348.4417 673.9051
Epoch 16000 : Training Cost: 3240736000.0  a,b,c,d: 905.0128 -537.541 -1462.6171 759.7118
Epoch 17000 : Training Cost: 3215895000.0  a,b,c,d: 914.60065 -611.8676 -1571.9058 857.6638
Epoch 18000 : Training Cost: 3192216800.0  a,b,c,d: 923.9603 -684.8093 -1676.4642 967.30475
Epoch 19000 : Training Cost: 3169632300.0  a,b,c,d: 933.08594 -756.3582 -1776.4275 1088.2198
Epoch 20000 : Training Cost: 3148046300.0  a,b,c,d: 941.9928 -826.6257 -1871.9355 1219.9702
Epoch 21000 : Training Cost: 3127394800.0  a,b,c,d: 950.67896 -895.6205 -1963.0989 1362.1665
Epoch 22000 : Training Cost: 3107608600.0  a,b,c,d: 959.1487 -963.38116 -2050.0586 1514.4026
Epoch 23000 : Training Cost: 3088618200.0  a,b,c,d: 967.4355 -1029.9625 -2132.961 1676.2717
Epoch 24000 : Training Cost: 3070361300.0  a,b,c,d: 975.52875 -1095.4292 -2211.854 1847.4485
Epoch 25000 : Training Cost: 3052791300.0  a,b,c,d: 983.4346 -1159.7922 -2286.9412 2027.4857
3052791300.0 983.4346 -1159.7922 -2286.9412 2027.4857

predictions = []
for x in abscissa:
  predictions.append((coefficient1*pow(x,3) + coefficient2*pow(x,2) + coefficient3*x + constant))
plt.plot(abscissa , ordinate, 'ro', label ='Original data')
plt.plot(abscissa, predictions, label ='Fitted line')
plt.title('Cubic Regression Result')
plt.legend()
plt.show()

Quartic

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(no_of_epochs):
      for (x,y) in zip(abscissa, ordinate):
        sess.run(optimizer4, feed_dict={X:x, Y:y})
      if (epoch+1)%1000==0:
        cost = sess.run(mse4,feed_dict={X:abscissa,Y:ordinate})
        print("Epoch",(epoch+1), ": Training Cost:", cost," a,b,c,d:",sess.run(a),sess.run(b),sess.run(c),sess.run(d),sess.run(e))

        training_cost = sess.run(mse4,feed_dict={X:abscissa,Y:ordinate})
        coefficient1 = sess.run(a)
        coefficient2 = sess.run(b)
        coefficient3 = sess.run(c)
        coefficient4 = sess.run(d)
        constant = sess.run(e)

print(training_cost, coefficient1, coefficient2, coefficient3, coefficient4, constant)

Epoch 1000 : Training Cost: 1902632600.0  a,b,c,d: 84.48304 52.210594 54.791424 142.51952 512.0343
Epoch 2000 : Training Cost: 1854316200.0  a,b,c,d: 88.998955 13.073557 14.276088 223.55667 1056.4655
Epoch 3000 : Training Cost: 1812812400.0  a,b,c,d: 92.9462 -22.331177 -15.262934 327.41858 1634.9054
Epoch 4000 : Training Cost: 1775716000.0  a,b,c,d: 96.42522 -54.64535 -35.829437 449.5028 2239.1392
Epoch 5000 : Training Cost: 1741494100.0  a,b,c,d: 99.524734 -84.43976 -49.181057 585.85876 2862.4915
Epoch 6000 : Training Cost: 1709199600.0  a,b,c,d: 102.31984 -112.19895 -56.808075 733.1876 3499.6199
Epoch 7000 : Training Cost: 1678261800.0  a,b,c,d: 104.87324 -138.32709 -59.9442 888.79626 4146.2944
Epoch 8000 : Training Cost: 1648340600.0  a,b,c,d: 107.23536 -163.15173 -59.58964 1050.524 4798.979
Epoch 9000 : Training Cost: 1619243400.0  a,b,c,d: 109.44742 -186.9409 -56.53944 1216.6432 5454.9463
Epoch 10000 : Training Cost: 1590821900.0  a,b,c,d: 111.54233 -209.91287 -51.423084 1385.8513 6113.5137
Epoch 11000 : Training Cost: 1563042200.0  a,b,c,d: 113.54405 -232.21953 -44.73371 1557.1084 6771.7046
Epoch 12000 : Training Cost: 1535855600.0  a,b,c,d: 115.471565 -253.9838 -36.851135 1729.535 7429.069
Epoch 13000 : Training Cost: 1509255300.0  a,b,c,d: 117.33939 -275.29697 -28.0714 1902.5308 8083.9634
Epoch 14000 : Training Cost: 1483227000.0  a,b,c,d: 119.1605 -296.2472 -18.618649 2075.6094 8735.381
Epoch 15000 : Training Cost: 1457726700.0  a,b,c,d: 120.94584 -316.915 -8.650095 2248.3247 9384.197
Epoch 16000 : Training Cost: 1432777300.0  a,b,c,d: 122.69806 -337.30704 1.7027153 2420.5771 10028.871
Epoch 17000 : Training Cost: 1408365000.0  a,b,c,d: 124.42179 -357.45245 12.33499 2592.2983 10669.157
Epoch 18000 : Training Cost: 1384480000.0  a,b,c,d: 126.12332 -377.39734 23.168756 2763.0933 11305.027
Epoch 19000 : Training Cost: 1361116800.0  a,b,c,d: 127.80568 -397.16415 34.160156 2933.0452 11935.669
Epoch 20000 : Training Cost: 1338288100.0  a,b,c,d: 129.4674 -416.72803 45.259155 3101.7727 12561.179
Epoch 21000 : Training Cost: 1315959700.0  a,b,c,d: 131.11403 -436.14285 56.4436 3269.3142 13182.058
Epoch 22000 : Training Cost: 1294164700.0  a,b,c,d: 132.74377 -455.3779 67.6757 3435.3833 13796.807
Epoch 23000 : Training Cost: 1272863600.0  a,b,c,d: 134.35779 -474.45316 78.96117 3600.264 14406.58
Epoch 24000 : Training Cost: 1252052600.0  a,b,c,d: 135.9583 -493.38254 90.268616 3764.0078 15010.481
Epoch 25000 : Training Cost: 1231713700.0  a,b,c,d: 137.54753 -512.1876 101.59372 3926.4897 15609.368
1231713700.0 137.54753 -512.1876 101.59372 3926.4897 15609.368

predictions = []
for x in abscissa:
  predictions.append((coefficient1*pow(x,4) + coefficient2*pow(x,3) + coefficient3*pow(x,2) + coefficient4*x + constant))
plt.plot(abscissa , ordinate, 'ro', label ='Original data')
plt.plot(abscissa, predictions, label ='Fitted line')
plt.title('Quartic Regression Result')
plt.legend()
plt.show()

Quintic

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(no_of_epochs):
      for (x,y) in zip(abscissa, ordinate):
        sess.run(optimizer5, feed_dict={X:x, Y:y})
      if (epoch+1)%1000==0:
        cost = sess.run(mse5,feed_dict={X:abscissa,Y:ordinate})
        print("Epoch",(epoch+1), ": Training Cost:", cost," a,b,c,d,e,f:",sess.run(a),sess.run(b),sess.run(c),sess.run(d),sess.run(e),sess.run(f))

        training_cost = sess.run(mse5,feed_dict={X:abscissa,Y:ordinate})
        coefficient1 = sess.run(a)
        coefficient2 = sess.run(b)
        coefficient3 = sess.run(c)
        coefficient4 = sess.run(d)
        coefficient5 = sess.run(e)
        constant = sess.run(f)

Epoch 1000 : Training Cost: 1409200100.0  a,b,c,d,e,f: 7.949472 7.46219 55.626034 184.29028 484.00223 1024.0083
Epoch 2000 : Training Cost: 1306882400.0  a,b,c,d,e,f: 8.732181 -4.0085897 73.25298 315.90103 904.08887 2004.9749
Epoch 3000 : Training Cost: 1212606000.0  a,b,c,d,e,f: 9.732249 -16.90125 86.28379 437.06552 1305.055 2966.2188
Epoch 4000 : Training Cost: 1123640400.0  a,b,c,d,e,f: 10.74851 -29.82692 98.59997 555.331 1698.4631 3917.9155
Epoch 5000 : Training Cost: 1039694300.0  a,b,c,d,e,f: 11.75426 -42.598194 110.698326 671.64355 2085.5513 4860.8535
Epoch 6000 : Training Cost: 960663550.0  a,b,c,d,e,f: 12.745439 -55.18337 122.644936 786.00214 2466.1638 5794.3735
Epoch 7000 : Training Cost: 886438340.0  a,b,c,d,e,f: 13.721028 -67.57168 134.43822 898.3691 2839.9958 6717.659
Epoch 8000 : Training Cost: 816913100.0  a,b,c,d,e,f: 14.679965 -79.75113 146.07385 1008.66895 3206.6692 7629.812
Epoch 9000 : Training Cost: 751971500.0  a,b,c,d,e,f: 15.62181 -91.71608 157.55713 1116.7715 3565.8323 8529.976
Epoch 10000 : Training Cost: 691508740.0  a,b,c,d,e,f: 16.545347 -103.4531 168.88321 1222.6348 3916.9785 9416.236
Epoch 11000 : Training Cost: 635382000.0  a,b,c,d,e,f: 17.450052 -114.954254 180.03932 1326.1565 4259.842 10287.99
Epoch 12000 : Training Cost: 583477250.0  a,b,c,d,e,f: 18.334944 -126.20821 191.02948 1427.2095 4593.8 11143.449
Epoch 13000 : Training Cost: 535640400.0  a,b,c,d,e,f: 19.198917 -137.20206 201.84718 1525.6926 4918.5327 11981.633
Epoch 14000 : Training Cost: 491722240.0  a,b,c,d,e,f: 20.041153 -147.92719 212.49709 1621.5496 5233.627 12800.468
Epoch 15000 : Training Cost: 451559520.0  a,b,c,d,e,f: 20.860966 -158.37456 222.97133 1714.7141 5538.676 13598.337
Epoch 16000 : Training Cost: 414988960.0  a,b,c,d,e,f: 21.657421 -168.53406 233.27422 1805.0874 5833.1978 14373.658
Epoch 17000 : Training Cost: 381837920.0  a,b,c,d,e,f: 22.429693 -178.39536 243.39914 1892.5883 6116.847 15124.394
Epoch 18000 : Training Cost: 351931300.0  a,b,c,d,e,f: 23.176882 -187.94789 253.3445 1977.137 6389.117 15848.417
Epoch 19000 : Training Cost: 325074400.0  a,b,c,d,e,f: 23.898485 -197.18741 263.12512 2058.6716 6649.8037 16543.95
Epoch 20000 : Training Cost: 301073570.0  a,b,c,d,e,f: 24.593851 -206.10497 272.72385 2137.1797 6898.544 17209.367
Epoch 21000 : Training Cost: 279727000.0  a,b,c,d,e,f: 25.262104 -214.69217 282.14642 2212.6372 7135.217 17842.854
Epoch 22000 : Training Cost: 260845550.0  a,b,c,d,e,f: 25.903376 -222.94969 291.4003 2284.9844 7359.4644 18442.408
Epoch 23000 : Training Cost: 244218030.0  a,b,c,d,e,f: 26.517094 -230.8697 300.45532 2354.3003 7571.261 19007.49
Epoch 24000 : Training Cost: 229660080.0  a,b,c,d,e,f: 27.102589 -238.44817 309.35342 2420.4185 7770.5728 19536.19
Epoch 25000 : Training Cost: 216972400.0  a,b,c,d,e,f: 27.660324 -245.69016 318.10062 2483.3608 7957.354 20027.707
216972400.0 27.660324 -245.69016 318.10062 2483.3608 7957.354 20027.707

predictions = []
for x in abscissa:
  predictions.append((coefficient1*pow(x,5) + coefficient2*pow(x,4) + coefficient3*pow(x,3) + coefficient4*pow(x,2) + coefficient5*x + constant))
plt.plot(abscissa , ordinate, 'ro', label ='Original data')
plt.plot(abscissa, predictions, label ='Fitted line')
plt.title('Quintic Regression Result')
plt.legend()
plt.show()

Results and Conclusion

You just learnt Polynomial Regression using TensorFlow!

Notes

Overfitting

> Overfitting refers to a model that models the training data too well.Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.

Source: Machine Learning Mastery

Basically if you train your machine learning model on a small dataset for a really large number of epochs, the model will learn all the deformities/noise in the data and will actually think that it is a normal part. Therefore when it will see some new data, it will discard that new data as noise and will impact the accuracy of the model in a negative manner

This was tested on TF 2.x and works as of 2019-12-10

If you want to understand how to make your own custom image classifier, please refer to my previous post.

If you followed my last post, then you created a model which took an image of dimensions 50x50 as an input.

First we import the following if we have not imported these before

import cv2
import os

Then we read the file using OpenCV.

image=cv2.imread(imagePath)

The cv2. imread() function returns a NumPy array representing the image. Therefore, we need to convert it before we can use it.

image_from_array = Image.fromarray(image, 'RGB')

Then we resize the image

size_image = image_from_array.resize((50,50))

After this we create a batch consisting of only one image

p = np.expand_dims(size_image, 0)

We then convert this uint8 datatype to a float32 datatype

img = tf.cast(p, tf.float32)

Finally we make the prediction

print(['Infected','Uninfected'][np.argmax(model.predict(img))])

Infected

Done during Google Code-In. Org: Tensorflow.

Imports

%tensorflow_version 2.x #This is for telling Colab that you want to use TF 2.0, ignore if running on local machine

from PIL import Image # We use the PIL Library to resize images
import numpy as np
import os
import cv2
import tensorflow as tf
from tensorflow.keras import datasets, layers, models
import pandas as pd
import matplotlib.pyplot as plt
from keras.models import Sequential
from keras.layers import Conv2D,MaxPooling2D,Dense,Flatten,Dropout

Dataset

Fetching the Data

!wget ftp://lhcftp.nlm.nih.gov/Open-Access-Datasets/Malaria/cell_images.zip
!unzip cell_images.zip

Processing the Data

We resize all the images as 50x50 and add the numpy array of that image as well as their label names (Infected or Not) to common arrays.

data = []
labels = []

Parasitized = os.listdir("./cell_images/Parasitized/")
for parasite in Parasitized:
    try:
        image=cv2.imread("./cell_images/Parasitized/"+parasite)
        image_from_array = Image.fromarray(image, 'RGB')
        size_image = image_from_array.resize((50, 50))
        data.append(np.array(size_image))
        labels.append(0)
    except AttributeError:
        print("")

Uninfected = os.listdir("./cell_images/Uninfected/")
for uninfect in Uninfected:
    try:
        image=cv2.imread("./cell_images/Uninfected/"+uninfect)
        image_from_array = Image.fromarray(image, 'RGB')
        size_image = image_from_array.resize((50, 50))
        data.append(np.array(size_image))
        labels.append(1)
    except AttributeError:
        print("")

Splitting Data

df = np.array(data)
labels = np.array(labels)
(X_train, X_test) = df[(int)(0.1*len(df)):],df[:(int)(0.1*len(df))]
(y_train, y_test) = labels[(int)(0.1*len(labels)):],labels[:(int)(0.1*len(labels))]

s=np.arange(X_train.shape[0])
np.random.shuffle(s)
X_train=X_train[s]
y_train=y_train[s]
X_train = X_train/255.0

Model

Creating Model

By creating a sequential model, we create a linear stack of layers.

Note: The input shape for the first layer is 50,50 which corresponds with the sizes of the resized images

model = models.Sequential()
model.add(layers.Conv2D(filters=16, kernel_size=2, padding='same', activation='relu', input_shape=(50,50,3)))
model.add(layers.MaxPooling2D(pool_size=2))
model.add(layers.Conv2D(filters=32,kernel_size=2,padding='same',activation='relu'))
model.add(layers.MaxPooling2D(pool_size=2))
model.add(layers.Conv2D(filters=64,kernel_size=2,padding="same",activation="relu"))
model.add(layers.MaxPooling2D(pool_size=2))
model.add(layers.Dropout(0.2))
model.add(layers.Flatten())
model.add(layers.Dense(500,activation="relu"))
model.add(layers.Dropout(0.2))
model.add(layers.Dense(2,activation="softmax"))#2 represent output layer neurons 
model.summary()

Compiling Model

We use the adam optimiser as it is an adaptive learning rate optimization algorithm that's been designed specifically for training deep neural networks, which means it changes its learning rate automaticaly to get the best results

model.compile(optimizer="adam",
              loss="sparse_categorical_crossentropy", 
             metrics=["accuracy"])

Training Model

We train the model for 10 epochs on the training data and then validate it using the testing data

history = model.fit(X_train,y_train, epochs=10, validation_data=(X_test,y_test))

Train on 24803 samples, validate on 2755 samples
Epoch 1/10
24803/24803 [==============================] - 57s 2ms/sample - loss: 0.0786 - accuracy: 0.9729 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 2/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0746 - accuracy: 0.9731 - val_loss: 0.0290 - val_accuracy: 0.9996
Epoch 3/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0672 - accuracy: 0.9764 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 4/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0601 - accuracy: 0.9789 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 5/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0558 - accuracy: 0.9804 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 6/10
24803/24803 [==============================] - 57s 2ms/sample - loss: 0.0513 - accuracy: 0.9819 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 7/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0452 - accuracy: 0.9849 - val_loss: 0.3190 - val_accuracy: 0.9985
Epoch 8/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0404 - accuracy: 0.9858 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 9/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0352 - accuracy: 0.9878 - val_loss: 0.0000e+00 - val_accuracy: 1.0000
Epoch 10/10
24803/24803 [==============================] - 58s 2ms/sample - loss: 0.0373 - accuracy: 0.9865 - val_loss: 0.0000e+00 - val_accuracy: 1.0000