Principal Component Analysis: Math and Code

Principal Component Analysis(PCA) is a method for compressing a lot of data into something that captures the essence of data in a meaningful way. PCA has found a lot of application in the area on dimensionality reduction. Let’s see what dimensionality reduction is: Consider this graph: This graph can be mapped to: This approach can […]

Logistic Regression with Math and Code

Logistic regression a function that models the relationship between input space X and categorical output space Y which estimates probability P(Y/X) from data. Let’s define a two class classification model for linear regression( Two classes here are 0 or 1) y=mTx+b We all are familiar with this age old equation of a straight line.What looks different here […]

How to train Google’s Inception Model to build an Image Classifier

Let us learn what is tensorflow and what actually tensors are: Traditionally there are two ways to represent data by: Scalar: Contains a singular value. Vector: can be imagined as an array of values. Tensors are special types of directional vectors that possess the properties of both scalars and vectors. Tensorflow is a library by […]

More Gradient Optmization Techniques

SIMUlATED ANNEALING As in conventional hill climbing algorithm, with the tweak, R, is better than standard candidate solution,S,we replace S by R, But if R is worse than S ,we replace S with R with certain probability, P(t, R, S) = e Quality(R) – Quality(S) / t Algorithm is interesting in two ways: If […]

Gradient-based Optimization

Gradient-based Optimization works in a manner in which the parameters of a function are studied to achieve minimum possible loss. Consider a situation where we drop a marble inside the bowl shown above.The marble would overshoot the bottom many times and would finally stop at the bottom eventually. Gradient Descent works in a manner similar […]

CLUSTERING:BASICS

Clustering is the process of dividing a set of random data points into a fixed number of clusters. Clusters can be imagined as the set of similar data. Consider the set of random data points given in the image below: We can see from naked eye that there are two distinct clusters.But if we do […]

HASH ALGORITHMS:SECURITY THREAT?

Suppose you want to send a file from one computer to another, and you want to make sure that the file is intact, what you could do is send the file multiple times and compare them or you could use a Hash function. A hash code of a file is basically a code which can be considered […]

Neural Networks: Introduction

To really understand neural networks,we first need to see what the how the most fundamental biological unit of our brain: Neuron works. Each neuron is connected in one after the other with axon termina connected to the dendrite of the next neuron having a synaptic gap in between.These connections act as a transmission line.Human brain is […]

PUBLIC KEY CRYPTOGRAPHY(snippet)

The basic idea of cryptography is you convert some meaningful information into essentially garbage(random noise) and send across to somebody else and they try to decrypt or make sense out of it. MOTIVE:The main motivation behind doing this is to not let anyone who would eavesdrop on your communication get the data. The OLD Approach: […]

LAMBDA CALCULUS

HISTORY Lets have a sneak peek into the history of computational mathematics. Alonso Church who was a mathematician at princeton university, and he was interested in what was the notion of a function from a computational perspective,he was the PhD supervisor of the famous scientist Dr.Alan Turing whose work involved notion of function from a […]