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                     Machine Learning
Support Vector Machines
A Support Vector Machine (SVM) can be imagined as a surface that 
creates  a boundary between points of data plotted in multidimensional 
that represent examples and their feature values
 The goal of a SVM is to create a flat boundary called a hyperplane, which 
divides the space to create fairly homogeneous  partitions on either side
SVMs can be adapted for use with nearly any type of learning task, 
including both classification and numeric prediction
Classification with hyper planes
 For example, the following figure depicts hyperplanes that 
separate groups of circles and squares in two and three dimensions. 
Because the circles and squares can be separated perfectly by the 
straight line or flat surface, they are said to be linearly separable
Which is the “best” Fit!
In two dimensions, the task of the SVM algorithm is to identify a line 
that separates the two classes. As shown in the following figure, there 
is more than one choice of dividing line between the groups of circles 
and squares. How does the algorithm choose
Linear Hyperplane for 2-classes
SVM Objective
OBJECTIVE: CONSTRAINT:
Min
Nonlinearly separable data
A cost value (denoted as C) is applied to all points that violate the 
constraints, and rather than finding the maximum margin, the 
algorithm attempts to minimize the total cost. We can therefore revise 
the optimization problem to:
Using kernels for non-linear spaces 
 A key feature of SVMs is their ability to map the problem into a 
higher dimension space using a process known as the kernel trick. In 
doing so, a nonlinear relationship may suddenly appear to be quite 
linear.
After the kernel trick has been applied, we look at the 
data through the lens of a new dimension: altitude. With 
the addition of this feature, the classes are now perfectly 
linearly separable
Neural Networks
Understanding neural networks
An Artificial Neural Network (ANN) models the relationship between a 
set of input signals and an output signal using a model derived from our 
understanding of how a biological brain responds to stimuli from 
sensory inputs. Just as a brain uses a network of interconnected cells 
called neurons to create a massive parallel processor, ANN uses a 
network of artificial neurons or nodes to solve learning problems
The human brain is made up of about 85 billion neurons, 
resulting in a network capable of representing a tremendous 
amount of knowledge
For instance, a cat has roughly a billion neurons, a mouse has 
about 75 million neurons, and a cockroach has only about a 
million neurons. In contrast, many ANNs contain far fewer 
neurons, typically only several hundred, so we're in no danger of 
creating an artificial brain anytime in the near future
Biological to artificial neurons
 Incoming signals are received by the cell's dendrites through a biochemical 
process. The process allows the impulse to be weighted according to its relative 
importance or frequency. As the cell body begins accumulating the incoming signals, 
a threshold is reached at which the cell fires and the output signal is transmitted via 
an electrochemical process down the axon. At the axon's terminals, the electric 
signal is again processed as a chemical signal to be passed to the neighboring 
neurons.
This directed network diagram defines 
a relationship between the input A typical artificial neuron with n input dendrites 
signals received by the dendrites (x can be represented by the formula that follows. 
variables), and the output signal (y The w weights allow each of the n inputs 
variable). Just as with the biological (denoted by xi) to contribute a greater or lesser 
neuron, each dendrite's signal is amount to the sum of input signals. The net total 
weighted (w values) according to its is used by the activation function f(x), and the 
importance. The input signals are resulting signal, y(x), is the output axon
summed by the cell body and the 
signal is passed on according to an 
activation function denoted by f
In biological sense, the activation function could be imagined as a process 
that involves summing the total input signal and determining whether it 
meets the firing threshold. If so, the neuron passes on the signal; 
otherwise, it does nothing. In ANN terms, this is known as a threshold 
activation function, as it results in an output signal only once a specified 
input threshold has been attained
The following figure depicts a typical threshold function; in 
this case, the neuron fires when the sum of input signals is at 
least zero. Because its shape resembles a stair, it is 
sometimes called a unit step activation function
Network topology 
The ability of a neural network to learn is rooted in its 
topology, or the patterns and structures of interconnected 
neurons
 key characteristics
• The number of layers 
• Whether information in the network is allowed to travel backward 
• The number of nodes within each layer of the network
Number of layers 
The input and output nodes are arranged in groups known as layers
 Input nodes process the incoming data exactly as it is 
received, the network has  only one set of connection weights 
(labeled here as w1, w2, and w3). It is therefore termed a 
single-layer network
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