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Dimensionality reduction could be achieved by using an Autoencoder Network, which learns a representation (or Encoding) for the input data. While training, the reduction side (Encoder) reduces the data to a lower-dimension and a reconstructing side (Decoder) tries to reconstruct the original input from the intermediate reduced encoding. You could assign ...


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Some examples of dimensionality reduction techniques: Linear methods PCA CCA ICA SVD LDA NMF Non-linear methods Kernel PCA GDA Autoencoders t-SNE UMAP MVU Graph-based methods ("Network embedding") Diffusion maps Graph Autoencoders Graph-based kernel PCA Isomap LLE Hessian LLE Laplacian Eigenmaps Though there are many more.


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The principal components (eigenvectors) correspond to the direction (in the original n-dimensional space) with the greatest variance in the data. The corresponding eigenvalue is a number that indicates how much variance there is in the data along that eigenvector (or principal component). Thus, feature 2 is the most important (based on ...


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You might want to have a look at the wikipedia article of PCA, where it says: "The $k$th component can be found by subtracting the first $k − 1$ principal components from $\mathbf{X}$:" $$\hat{\mathbf{X}}_k = \mathbf{X} - \sum_{s=1}^{k-1}\mathbf{X}\mathbf{w}_s\mathbf{w}_s^T$$ Then you repeat the process to find the next component: $$\mathbf{w}_k = \...


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PCA works well where data sample space is linear. If data sample space is not linear or it is manifold data then model without PCA may perform better than model using PCA. In the given image you can see, data is manifold. In this type of data, PCA, which is based on projection technique does not work well. That's why we use manifold learning technique to ...


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PCA can make models worse, imagine data points scattered along two elongated parallel rectangles. The axis with the greatest variation will be parallel to the rectangles but doesn't provide any benefit in classifying the points.


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