> What I mean by contradiction is different orderings of an entire set of data, not points of contrast within a set of data That's not what people usually mean by contradiction, definitely not in a general sense.
You are talking about reframing dataset (subset) of multivariate items along the spectrum of one or several most predictive variable in items. This is basically a PCA, closely related to Spectral Clustering I mentioned in the first section of my readme: "Initial frame of reference here is space-time, but higher levels will reorder the input along all sufficiently predictive derived dimensions, similar to spectral clustering <https://en.wikipedia.org/wiki/Spectral_clustering>." >Claude 3.5: Yes, there is indeed a relationship between Principal Component Analysis (PCA) and spectral clustering. Both techniques involve eigenvalue decomposition and can be used for dimensionality reduction, but they have different primary purposes and methodologies. Let me explain the connection: 1. Similarity: - Both PCA and spectral clustering use eigenvalue decomposition of a matrix derived from the data. - Both can be used for dimensionality reduction before applying other algorithms. 2. Key Differences: - PCA focuses on variance maximization, while spectral clustering focuses on graph partitioning. - PCA operates on the covariance matrix, while spectral clustering typically uses the graph Laplacian matrix. 3. Spectral Clustering Overview: - Spectral clustering is a technique that treats the data clustering as a graph partitioning problem. - It uses the eigenvalues of the similarity matrix to perform dimensionality reduction before clustering in fewer dimensions. 4. Connection: - The eigenvectors used in spectral clustering can be seen as a nonlinear generalization of the principal components in PCA. - In some cases, when the data lies on a linear manifold, spectral clustering can reduce to PCA. 5. Laplacian Eigenmaps: - This is a technique that bridges PCA and spectral clustering. - It's similar to PCA but preserves local neighborhoods, making it more suitable for nonlinear manifolds. 6. Use Cases: - PCA is often used for general dimensionality reduction and feature extraction. - Spectral clustering is particularly effective for clustering data that isn't linearly separable in the original space. I can't give you any demonstration because my algo is far from complete. It would be like like demostrating how ANN works before you figure out how single-node perceptron works. Except that my scheme is hundreds of times more complex than perceptron. You just have to decide for yourself if it makes sense from the first principles. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T682a307a763c1ced-Ma97988eb78fb8750ac41ec53 Delivery options: https://agi.topicbox.com/groups/agi/subscription
