# Questions tagged [linear-algebra]

A field of mathematics concerned with the study of finite dimensional vector spaces, including matrices and their manipulation, which are important in statistics.

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### Linear Discriminant Analysis (LDA) determining the class for test data after transforming with eigenvectors

Suppose we are given two classes class-1 and class-2 and the mean of the two classes are $μ_1$ and $μ_2$ respectively before projection. Both of their variance-covariance matrix is also provided ...
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### How to identify the basis?

I got this slide from the class lecture. My questions are: Q1. Why "there are enough vectors" are required for the linear span of vectors to satisfy 1st condition of basis? And why "...
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### What type of technique can be used to solve this question?

Apology for the ambiguous title, I do not know the term. I have data of some products which a few variables: origin, weight, brand. For example: Product A = "China, 100g, Brand X" Product ...
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### Outlier detection with elliptic envelope - unexpected error

I am trying to detect outliers with sklearn.covariance.EllipticEnvelope for a single variable, but it throws an unexpected error. Here is an example the reproduces ...
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### Affine 2D mapping in python

I have two sets of 2D data $A$ and $B$ (representing 2D positions on a 2D plane $x,y$) which are related (the first pair of $x,y$ of $A$ is related to the first pair of $x,y$ of $B$ for instance). I ...
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### What are some application of Google's PageRank Algorithm in Data Science

I came across a topic on computational linear algebra that talks about iterative algorithms to compute eigenvalues. I've worked with power method which is an iterative algorithm that converges a ...
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### Inverting a matrix using a convolutional neural network

Just for a fun exercise, I am trying to invert a matrix, say size 28x28 (or even 5x5) with a neural network. The way I approached this (quite naively) is as follows: I built a fully convolutional ...
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### Why do we use 'T' when we are to say matrix-vector product? [closed]

On the first picture author uses $T$ meaning matrix-vector product But other website do not use $T$, but says that $x$ is a vector, I do not understand if it is important or not
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### 3d input for Dense Layer Keras

Is there any example of how Keras Dense layer handles 3D input. The documentation explains the following: ...
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### Difference between FDA and LDA

I have asked this question in Mathematics Stackexchange, thought however that it might be more fit for here: I am currently taking a Data-Analysis course and I learned about both the terms LDA (Linear ...
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### What is the Intuition behind weight vector W which is normal to the plane? Is the weight vector W same as the W which is normal to the plane π?

In an interview, I was asked the intuition behind the weight vector. I told the weight vector is a vector which we try to minimize to a local minima with the help of regulariser so we don't overfit. ...
1 vote
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### How does the equation "dW = - (2 * (X^T ).dot(Y - Y_hat)) / m" comes in Linear Regression (using Matrix + Gradient Descent)?

I was trying to code the Linear Regression in Python using Matrix Multiplication method using Gradient Descent and followed a code where there was no mention what is the loss but just a code as Per ...
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### How does tree-based algorithms handle linearly combined features?

While I am aware that tree-based algorithms (e.g., DT, RF, XGBoost) are 'immune' to multi-collinearity, how do they handle linearly combined features? For example, is there is any additional value or ...
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### Geometric classification models

In class we have been presented with a Geometric classification model such that the goal is to construct a linear decision boundary $\bf{w} \cdot \bf{x} = t$; where $\bf{w}$ is the vector from the ...
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### Dot product and linear regression

I'm studying PCA and my professor said something about finding the linear regression by doing the dot product of both axis. Could someone explain to me why? The dot product returns a number. What's ...
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### Why do we usually have fully connected layers of same sizes in CNNs?

Is there any specific reason that we observe in CNNs, the fully connected layers usually have the same sizes? You can verify this for many CNNs. I'm aware that if, for instance, we have a vector of ...
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### Hypothesis vs Hyperplane in Machine Learning

I am finding it hard to understand the clear difference between Hypothesis and Hyperplane. I know that Hypothesis is a candidate model that maps inputs to outputs after training. And, Hyperplane is ...
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