Questions tagged [linear-algebra]

For questions about the use/aspects/implementation/intuition/mathematical proofs of various Linear Algebra methods used in Machine Learning and AI algorithms.

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7
votes
1answer
214 views

What does it mean to do multi-dimensional processing with tensors in tensor cores?

In some tweets about NeurIPS 2018, this video from NVIDIA appeared. At around 0.37, she says: If you think about the current computations in our deep learning systems, they are all based on Linear ...
5
votes
3answers
360 views

How does neural network classifier classify from just drawing a decision plane?

I understand that a neural network basically distorts(non-linear transformation) and changes the perspective(linear transformations) of input space to draw a plane to classify data. How does the ...
4
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1answer
55 views

Why MLP cannot approximate a closed shape function?

[TL;DR] I generated two classes Red and Blue on a 2D space. Red are points on Unit Circle and Blue are points on a Circle Ring with radius limits (3,4). I tried to train a Multi Layer Perceptron ...
2
votes
1answer
85 views

How do you find the homography matrix given 4 points in both images?

I want to understand the process of finding a homography matrix given 4 points in both images. I am able to do that in python OpenCV, but I wonder how it works behind the scenes. Suppose I have ...
2
votes
1answer
172 views

Using reinforcement learning to find a preconditioner for linear systems of the form Ax = b

Sparse linear systems are normally solved by using solvers like MINRES, Conjugate gradient, GMRES. Efficient preconditioning, i.e., finding a matrix P such that PAx = Pb is easier to solve than the ...
1
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2answers
92 views

The math behind PCA

I am trying to understand the math behind PCA. I can only solve it in the case of mapping vectors to 1 Dimensional space. How to solve the math in the case we reduce the number of dimension is greater ...
1
vote
1answer
58 views

Is there any way to apply linear transformations on a vector other than matrix multiplication?

I am trying to optimize the cost function calculation in regression analysis using a non-matrix multiplication based approach. More specifically, I have a point $x = (1, 1, 2, 3)$, to which I want to ...
1
vote
1answer
303 views

Does k consistency always imply (k - 1) consistency?

From Russell-Norvig: A CSP is strongly k-consistent if it is k-consistent and is also (k − 1)-consistent, (k − 2)-consistent, . . . all the way down to 1-consistent. How can a CSP be k-consistent ...
1
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0answers
27 views

How to find distance between 2 points when dimensions are all of different nature?

I have a dataset with four features: the x coordinate the y coordinate the velocity magnitude angle Now, I want to measure the distance between two points in the dataset, taking into account the ...
1
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0answers
14 views

Human intuition behind SVD in case of recommendation system

This does not answer my question. I struggled very hard to understand the SVD from a linear-algebra point of view. But in some cases I failed to connect the dots. So, I started to see all the ...
1
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0answers
43 views

Simplifying Log Loss

I am reading through a paper (https://www.mitpressjournals.org/doi/pdf/10.1162/0891201053630273) where they describe logloss as a ranking function and can be simplified to the margin of the training ...
1
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0answers
28 views

CSP Formulation of an algebraic problem

Is anyone able to explain how to do this? I'm not looking for the complete answer, I would settle for a "how to for dummies" explanation of how this is supposed to be solved. I understand ...
1
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0answers
16 views

Estimating Baselines using ALS

I am trying to figure out how ALS works when minimizing the following formula: $\\ \\$ $\text{min}_{\lbrace b_u,b_i \rbrace} \sum_{(u,i)\in \mathcal{K}} (r_{ui} - \bar{r} - b_u - b_i )^2 + \lambda_{...
0
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0answers
21 views

How can I calibrate 3 cameras and track the object using only synchronized cameras feeds from all the cameras?

I have camera feed (in the form of RGB images) from 3 cameras with partially overlapping Field-of-view i.e. for the time stamp 0 to 100, I have total 300 frames or say synchronized 100 RGB frames for ...
0
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0answers
25 views

How can I calibrate 3 cameras without knowing global pose of the object & camera locations? How can I find the pose of each camera wrt the first one?

I have camera feed (in the form of RGB images) from 3 cameras with overlapping FOV e.g. for the time stamp 0 to 100, I have synchronized RGB frames for each camera. The object (Robot) is moving from ...
0
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0answers
11 views

How to decompose a non-positive definite matrix in the same manner as Cholseky decomposition?

I want to make a covariance matrix that incorporates my belief of how correlated the various dimensions are. The reason why I want to incorporate my belief is that in my modelling, the dimensions are ...
0
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1answer
46 views

What do you mean by 'Principal Angle between subspaces'

I came across the term 'Principal angle between Subspaces' as a tool for comparing objects in images. All material that I found on the internet seem to deal with this idea in a highly mathematical way ...