Experiment/Principle Components - Unsupervised Learning

  • Thread starter brojesus111
  • Start date
  • Tags
    Components
In summary, a researcher collected expression measurements for 1,000 genes in 100 tissue samples, represented as a 1,000 x 100 matrix. The samples were processed on different days and belong to two groups: control and treatment. Before comparing the two groups, the researcher performs a principal component analysis and finds that the first component has a strong linear trend and explains 10% of the variation. The researcher then replaces the (i,j)th element of X with a subtraction of the ith score and the jth loading for the first principal component, in order to perform a two-sample t-test on each gene and determine if there is a difference in expression between the two conditions. This approach may have some flaws and a better approach
  • #1
brojesus111
39
0

Homework Statement



A researcher collects expression measurements for 1,000 genes in 100 tissue samples. The data can be written as a 1, 000 × 100 matrix, which we call X, in which each row represents a gene and each column a tissue sample. Each tissue sample was processed on a different day, and the columns of X are ordered so that the samples that were processed earliest are on the left, and the samples that were processed later are on the right. The tissue samples belong to two groups: control (C) and treatment (T). The C and T samples were processed in a random order across the days. The researcher wishes to determine whether each gene’s expression measurements differ between the treatment and control groups.

As a pre-analysis (before comparing T versus C), the researcher performs a principal component analysis of the data, and finds that the first principal component (a vector of length 100) has a strong linear trend from left to right, and explains 10 % of the variation. The researcher now remembers that each patient sample was run on one of two machines, A and B, and machine A was used more often in the earlier times while B was used more often later. The researcher has a record of which sample was run on which machine.

(a) The researcher decides to replace the (i, j)th element of X with

x_ij − z_i1 φ_j1

where z_i1 is the ith score, and φ_j1 is the jth loading, for the first principal component. He will then perform a two-sample t-test on each gene in this new data set in order to determine whether its expression differs between the two conditions. Critique this idea, and suggest a better approach.

(b) Design and run a small simulation experiment to demonstrate the superiority of your idea.

The Attempt at a Solution



I'm just not sure what's going on in this problem. I'm pretty sure there's something wrong with how he decides to replace the (i,j)th element of X, but I'm not sure what. What is he accomplishing with his subtraction?

I'm assuming my simulation should be based on my approach from part a, but does that mean I have to make up some fake data? Will any fake data work?

I appreciate any help.
 
Physics news on Phys.org
  • #2
Anyone? :/
 

Related to Experiment/Principle Components - Unsupervised Learning

1. What is the purpose of unsupervised learning in experiments?

Unsupervised learning is a type of machine learning where the algorithm learns patterns and relationships in data without being given specific labels or categories. In experiments, unsupervised learning can help identify hidden patterns or clusters in the data that may not be apparent to the researcher. This can lead to new insights and help guide further research or experiments.

2. How does unsupervised learning differ from supervised learning in experiments?

In supervised learning, the algorithm is given labeled data and is trained to predict the correct label for new data. In contrast, unsupervised learning does not use labels and instead focuses on finding patterns and relationships in the data on its own. This makes it useful for exploring and understanding data without preconceived notions or biases.

3. What are some common applications of unsupervised learning in experiments?

Unsupervised learning has a wide range of applications in experiments, including data clustering, anomaly detection, and feature extraction. It can also be used for data preprocessing and exploratory data analysis to gain insights and inform further experiments or research.

4. What are the advantages of using unsupervised learning in experiments?

One of the main advantages of unsupervised learning is its ability to handle large and complex datasets without the need for labeled data. This makes it a valuable tool for discovering hidden patterns and relationships in experimental data. Additionally, unsupervised learning can help reduce bias and provide more objective insights compared to traditional manual analysis methods.

5. What are some challenges or limitations of unsupervised learning in experiments?

One challenge of unsupervised learning is that the results may be difficult to interpret, especially if the data is high-dimensional. It also requires careful selection and tuning of algorithms and parameters, which can be time-consuming. Additionally, since unsupervised learning does not use labels, the quality of the results may depend on the quality and structure of the data itself.

Similar threads

Principal component analysis and data compression in Machine Learning
    • Programming and Computer Science
Replies
6
Views
867
Principal Component Analysis related problem
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
The Higher Dimensional Analysis of Embryonic Development
    • Biology and Medical
Replies
10
Views
3K
MHB Test Equivalence: Med Student Seeking Help
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
Estimate the total harmonic distortion present
    • Engineering and Comp Sci Homework Help
Replies
6
Views
5K
Why is randomization necessary in ANOVA experiments?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Challenge Experimental Physics Challenge, June 2021
    • Classical Physics
Replies
8
Views
2K
B Exploring Relativistic Thermodynamics Experiments
    • Special and General Relativity
Replies
4
Views
946
Convert 1 phase to 3 phase by using an old washing machine
    • Electrical Engineering
Replies
19
Views
2K
Variance of 'concatenated' distributions
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top