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Gives introduction to a machine learning algorithm: Logistic Regression. First, we describe the theoretical background of regression analysis using simple linear regression and the Generalized Linear Model. Then, we describe the Logistic Regression algorithm itself, and its solution using gradient descent. Finally, we provide an intuitive demonstration of how it works in a classification application with figures (including the MATLAB code used to generate the figures), and links to learn about more real-world applications.


This is an introductory module on using Logistic Regression to solve large-scale classification tasks. In the first section, we will digress into the statistical background behind the generalized linear modeling for regression analysis, and then proceed to describe logistic regression, which has become something of a workhorse in industry and academia. This module assumes basic exposure to vector/matrix notation, enough to understand

M = 2 2 1 0 , x = 3 - 1 , x 1 = ? , M * x = ?

What is all this about?

Regression Analysis is in essence the minimization of a cost function J that models the squared difference between the exact values y of a dataset, and one's estimate h of that dataset . Often, it is referred to as fitting a curve (the estimate) to a set of points based on some quantified measure of how well the curve fits the data. Formally, the most general form of the equation to model this process is:

minimize x J ( θ ) subject to h θ ( x )

This minimization function models all regression analysis, but for the sake of understanding, this general form is not the most useful. How exactly do we model the estimate? How exactly do we minimize? To answer these questions and to be more specific, we shall begin by considering the simplest regression form, linear regression.

Linear regression

In linear regression, we model the cost function's equation as:

J ( θ ) = 1 2 m i = 1 m ( h θ ( x i ) - y i ) 2

What does this mean? Essentially, h θ ( x ) is a vector that models one's hypothesis, the initial guess, of every point of the dataset. y is the exact value of every point in the dataset. Taking the squared difference between these two at every point creates a new vector that quantifies the error between one's guess and the actual value. We then seek to minimize the average value of this vector, because if this is minimized, then we have gotten our estimate to be as close as possible to the actual value for as many points as possible, given our choice of hypothesis.

As the above module demonstrates, linear regression is simply about fitting to a line, whether that line is straight or contains an arbitrary number of polynomial features. But that hasn't quite gotten us to where we wanted to get, which is classification, so we may need more tools.

Generalized linear model

As was stated in the beginning, there are many ways to describe the cost function. In the above description, we used the simplest linear model that can describe the hypothesis, but there are a range of values that can go into the hypothesis, and they can be grouped into families of functions. We can construct a Generalized Linear Model to model these extensions systematically. We can describe the value of the estimate and the actual points by incorporating them inside of an exponential function. In our example, we shall use the sigmoid function, which is the following:

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Introductory survey and applications of machine learning methods. OpenStax CNX. Dec 22, 2011 Download for free at http://legacy.cnx.org/content/col11400/1.1
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