@@ -293,24 +293,24 @@ It requires ``n_neighbors > n_components * (n_components + 3) / 2``.
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294294.. dropdown :: Complexity
295295
296- The HLLE algorithm comprises three stages:
296+ The HLLE algorithm comprises three stages:
297297
298- 1. **Nearest Neighbors Search **. Same as standard LLE
298+ 1. **Nearest Neighbors Search **. Same as standard LLE
299299
300- 2. **Weight Matrix Construction **. Approximately
301- :math: `O[D N k^3 ] + O[N d^6 ]`. The first term reflects a similar
302- cost to that of standard LLE. The second term comes from a QR
303- decomposition of the local hessian estimator.
300+ 2. **Weight Matrix Construction **. Approximately
301+ :math: `O[D N k^3 ] + O[N d^6 ]`. The first term reflects a similar
302+ cost to that of standard LLE. The second term comes from a QR
303+ decomposition of the local hessian estimator.
304304
305- 3. **Partial Eigenvalue Decomposition **. Same as standard LLE.
305+ 3. **Partial Eigenvalue Decomposition **. Same as standard LLE.
306306
307- The overall complexity of standard HLLE is
308- :math: `O[D \log (k) N \log (N)] + O[D N k^3 ] + O[N d^6 ] + O[d N^2 ]`.
307+ The overall complexity of standard HLLE is
308+ :math: `O[D \log (k) N \log (N)] + O[D N k^3 ] + O[N d^6 ] + O[d N^2 ]`.
309309
310- * :math: `N` : number of training data points
311- * :math: `D` : input dimension
312- * :math: `k` : number of nearest neighbors
313- * :math: `d` : output dimension
310+ * :math: `N` : number of training data points
311+ * :math: `D` : input dimension
312+ * :math: `k` : number of nearest neighbors
313+ * :math: `d` : output dimension
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315315.. rubric :: References
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