<p>Because it selects both <code>Xtrain</code> and <code>Xtest</code> from the space of two selected principal components. Hence, the 90% accuracy is in that 2-D selected space. </p>

<p>This fact that the ratio in PCA stands the information, depends on the distribution of the data and it's not true at all. </p>

CC BY-SA 4.0
2019-01-05T10:36:46.887Z
2019-01-05T10:43:41.540Z
2019-01-05T10:43:41.540Z
OmG
<p>I'm learning machine learning by looking through other people's kernel on Kaggle, specifically this <a href="https://www.kaggle.com/raghuchaudhary/mushroom-classification/data" rel="nofollow noreferrer">Mushroom Classification kernel</a>.</p>
<p>The author first applied PCA to the transformed indicator matrix. He only used 2 principal components for visualization later. Then I checked how much variance it has maintained, and found out that only 16% variance is maintained.</p>
<pre><code>in [18]: pca.explained_variance_ratio_.cumsum()
out[18]: array([0.09412961, 0.16600686])
</code></pre>
<p>But the test result with 90% accuracy suggests it works well.</p>
<p>If variance stands for information, then how can the ML model work well when so much information is lost?</p>

<machine-learning><principal-component-analysis>
Why does PCA work well while the total variance retained is small?
Bicheng
# Why does PCA work well while the total variance retained is small?

(Asked by: username_0 on 2019-01-05)

I'm learning machine learning by looking through other people's kernel on Kaggle, specifically this Mushroom Classification kernel.
The author first applied PCA to the transformed indicator matrix. He only used 2 principal components for visualization later. Then I checked how much variance it has maintained, and found out that only 16% variance is maintained.
in [18]: pca.explained_variance_ratio_.cumsum()
out[18]: array([0.09412961, 0.16600686])

But the test result with 90% accuracy suggests it works well.
If variance stands for information, then how can the ML model work well when so much information is lost?

**Tags:** machine-learning, principal-component-analysis


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## 1 answers

### Answer by username_1 on 2019-01-05. Score: 0

Because it selects both `Xtrain` and `Xtest` from the space of two selected principal components. Hence, the 90% accuracy is in that 2-D selected space.

This fact that the ratio in PCA stands the information, depends on the distribution of the data and it's not true at all.


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