antagonistic dimension

antagonistic dimension

• 1: A and B are in conflict
• 2: (A+B) and C are in conflict
• 3: ((A+B)+C) and D are in conflict
  • Here the number of dimensions is not enough so that A and B become identical in the 2-dimensional PCA.
  • Nonlinear dimensionality reduction (UMAP, etc.) should split

Experiment. py

A = np.array([-1, 0, 0])
B = np.array([1, 0, 0])
C = np.array([0, 2, 0])
D = np.array([0, 0, 4])

• 
• 
  • SD=0.1
  • Lack of dimensionality causes A and B, which have the least separation in PCA, to mix and become one.
  • The UMAP is clearly divided
• 
  • SD=0.5
  • They are also placed in close proximity in UMAP by A and B data becoming inseparable in the first place.
• 
  • SD=0.75
  • A, B, and C cannot be separated and become connected.
• 
  • SD=1
• 
  • SD=1.5
  • It's all in one piece.
  • string artifact is occurring.
  • Because of a lack of data?
  • You can't increase it by a factor of 10.
    • 

It looks like Variational Bayesian is needed to distinguish between them

• Implemented EM algorithm for mixed Gaussian distribution in Numpy - Yasukazu Nishio's Hatena Diary
• Estimating clusters of mixed Gaussian distribution model by k-means method, EM algorithm and variational Bayesian respectively - Yasukazu Nishio's Hatena Diary
• But it's not a good idea to assume a normal distribution for real data in the first place, so it's not a good idea.

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