Research

My area of research varies mostly and you can find me digging deeper into the following areas:


Human Computer Interaction


I am currently trying to bridge the gap between human-machine and human-human through design, mathematics and programming. Hence I sometimes call HCI as Human computer integration closely engraved with interaction. Some completed and ongoing works are:


  • Intelligent user interfaces for people with (dis)abilities.
  • Gaze controlled applications for spastic children with adaptive dwell times.
  • Smart Algorithms using mediums like Deep learning and Numerical analysis for making more interactive and playful products.


Interactive Installations

There are some ideas in the world which remain unclear under the strong foots of science and technology. As a known philosopher, Wittgenstein would say, they are so simple that they are hidden almost in their simplicity. One such example is like your hands. While you believe that most of the labor is done by the body and it is how you experience the world but the first experience of proper sense comes from the hands.

So my research in Interactive installations is to find props from the real world and generate ideas from them and exhibit to people in a poetic way, to state it simply; in a form of a story.

Some works I plan to do in future:


  • Idea of death and its eeriness.
  • Transformations of ideas as a "self" when people travel through different mediums of transportation.
  • Fight between binaries. e.g racism (white v/s blacks), body (fat v/s slim), genders (many v/s many).


Numerical Linear Algebra (NLA)

NLA is a field which takes help from Linear Algebra, Probability and Statistics and tries to improve the performance of algorithms which involves matrix computations. It broadly helps either to reduce time or complexity of the algorithm. To be precise my area of research lies in understanding iterative methods used for solving equations and dig deeper, analyze and create magic out of them ! Some well known algorithms that I am trying out are CG, GMRES, Bi-CG, QMR etc.

Some problems I am working & looking forward to work on are:


  • Finding robust error estimators for iterative methods.
  • Studying large dense graphs using spectral properties of various matrices like Adjacency, Laplacian etc.
  • Applying Numerical Linear Algebra in some useful machine learning related algorithms like K-nearest neighbour, PCA etc and giving useful insights.
  • Studying structured matrices like Toeplitz, Tri-diagonal and finding crazy properties of them.
  • Eigenvalue problems.


Philosophical prototyping

This is a word coined by me recently which takes into account philosophical understanding of the world around us. Philosophical prototyping means making a product for the people not by the means of your understanding but putting yourself into their shoes by unlearning most of the stuff you already believe is true. This mostly helps in areas when you are dealing people with disabilities.

Let me explain you by a short example. Describe a triangle. What is a triangle? Most of the people will say it's a closed figure with three vertices. Because we have the power of vision, sight and in and out interpretation of the 3-D world. What about a blind person? Is a square and a triangle same to him? Both are closed figures? Can he only depict the difference when a tactile square or a triangle is placed before him ? Where are those points and vertices in space if their is no vision? Did you get any of that?

Try understanding this problem:

Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and of the same bigness, so as to tell, when he felt one and the other, which is the cube, which is the sphere. Suppose then the cube and the sphere placed on a table, and the blind man made to see: query, Whether by his sight, before he touched them, he could now distinguish and tell which is the globe, which the cube?

Source: Molyneux Problem

Dealing with all such problems requires this level of philosophical understanding. Obviously the encouragement for this kind of research comes from people like Satre, Nietzsche, Albert Camus etc.


Spectral Graph Theory


Spectral graph theory is a tool which helps people working in the field of graph theory to solve problems using matrix algebra. Any graph with finite number of edges and vertices can be represented in the form of a matrix. Various matrices are used for the same, some frequent ones are Adjacency, Incedence, Laplacian etc.

Now the matrices of such form are mostly square and thus have some important numbers associated with it. These numbers which are equal to the size of the matrix which is 'n', and are called eigen values. Eigen which is other meaning of 'characteristic', thus represent the properties of the matrix. Amazing part is these values can tell very important properties of the graph.

Maximum eigen value of the adjacency matrix gives the bound on the diameter of the graph. Number of connected components of the graph can be given by the multiplicity of 0 eigen values of the Laplacian matrix. And many other properties like girth, number of spanning trees are also given by eigen values of the graphs.


Areas I am interested to work in this area:


How are singular values important for a directed graph?

Can we say something about the eigenvector matrix after graph sparsification?

Can we decrease the computational cost of graph sparsification?