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147 | 147 | "because in the initial phase you want to explore the phase space as much as possible.\n", |
148 | 148 | "The downside of placing states in areas of low density is that we will have poor statistics on these states. \n", |
149 | 149 | "\n", |
150 | | - "Another advantage of regular space clustering is that it is very fast in comparison to $k$-means:\n", |
| 150 | + "Another advantage of regular space clustering is that it is fast in comparison to $k$-means:\n", |
151 | 151 | "regspace clustering runs in linear time while $k$-means is superpolynomial in time.\n", |
152 | 152 | "\n", |
153 | | - "⚠️ For very large datasets we also offer a mini batch version of $k$-means which has the same semantics as the original method but trains the centers on subsets of your data.\n", |
| 153 | + "⚠️ For large datasets we also offer a mini batch version of $k$-means which has the same semantics as the original method but trains the centers on subsets of your data.\n", |
154 | 154 | "This tutorial does not cover this case, but you should keep in mind that $k$-means requires your low dimensional space to fit into your main memory.\n", |
155 | 155 | "\n", |
156 | 156 | "The main result of a discretization for Markov modeling, however,\n", |
|
347 | 347 | "cell_type": "markdown", |
348 | 348 | "metadata": {}, |
349 | 349 | "source": [ |
350 | | - "In this very simple example, we clearly see a significant correlation between the $y$ component of the input data and the first independent component.\n", |
| 350 | + "In this simple example, we clearly see a significant correlation between the $y$ component of the input data and the first independent component.\n", |
351 | 351 | "\n", |
352 | 352 | "## Case 2: low-dimensional molecular dynamics data (alanine dipeptide)\n", |
353 | 353 | "\n", |
|
596 | 596 | "cell_type": "markdown", |
597 | 597 | "metadata": {}, |
598 | 598 | "source": [ |
599 | | - "This is not very helpful as it only shows that some of our $x, y, z$-coordinates correlate with the TICA components.\n", |
| 599 | + "This is not helpful as it only shows that some of our $x, y, z$-coordinates correlate with the TICA components.\n", |
600 | 600 | "Since we rather expect the slow processes to happen in backbone torsion space, this comes to no surprise. \n", |
601 | 601 | "\n", |
602 | 602 | "To understand what the TICs really mean, let us do a more systematic approach and scan through some angular features.\n", |
|
1259 | 1259 | "name": "python", |
1260 | 1260 | "nbconvert_exporter": "python", |
1261 | 1261 | "pygments_lexer": "ipython3", |
1262 | | - "version": "3.6.5" |
| 1262 | + "version": "3.6.6" |
1263 | 1263 | }, |
1264 | 1264 | "toc": { |
1265 | 1265 | "base_numbering": 1, |
|
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