added short feature description

visualization.ipynb

@@ -12,6 +12,38 @@
  "https://github.com/berylgithub"
  ]
  },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Feature Extraction\n",
+ "\n",
+ "The data is pre-processed to acquire the $D=\\{(y^{(n)}, \\vec{x}^{(n)})\\}^N_{n=1}$ array. By calculating the Heaviside step function that counts the contacts of atoms between proteins ($d_{cutoff}$) within 12 Angstrom. The formula to count the number of occurence between $j$ and $i$ atom is as follows:\n",
+ "<br>\n",
+ "$x_{Z(P_X(j)),Z(P_Y(i))}\\equiv\\sum^{K_j}_{k=1}\\sum^{L_i}_{l=1} \\odot (d_{cutoff} - d_{kl})$\n",
+ "<br>\n",
+ "\n",
+ "Here $P_X(j)$ corresponds to the protein atoms within the first chain of the protein pairing combination, and $P_Y(i)$ corresponds to the protein atoms within the second one, where four atom types are considered respectively as follows:\n",
+ "<br>\n",
+ "$\\{P_N(j)\\}_{j=1}^{4} = \\{C,N,O,S\\}$, $N \\in Z^+$,<br>\n",
+ "The hydrophobic patches and acid patches interactions respectively are also considered: \n",
+ "<br>\n",
+ "- hydrophobic patch : $\\{C\\alpha_H\\}$\n",
+ "<br>\n",
+ "- acid patch : $\\{C\\alpha_A\\}$,\n",
+ "<br>\n",
+ "\n",
+ "where $C\\alpha_H$ and $C\\alpha_A$ is the total interactions between carbon-alpha on Hydrophobic and Acid patch respectively.\n",
+ "\n",
+ "Therefore the total atomic interaction features used are $|\\{P_N(j)\\}_{j=1}^{4}|^2 + |\\{C\\alpha_H\\}| + |\\{C\\alpha_A\\}| = 18$\n",
+ "\n",
+ "Suppose there are four chains of protein $S = \\{P_1, P_2, P_3, P_4 \\}$, the interaction is the combinations of two chains, hence the total of interactions between two chains for this case is $c^{|S|}_2$=6 (where $c$ here refers to combination formula), the list of chains combination are as follows:\n",
+ "<br>\n",
+ "$\\sum interaction = interaction(P_1, P_2) + interaction(P_1,P_3) + interaction(P_1,P_4) + interaction(P_2,P_3) + interaction(P_2,P_4) + interaction(P_3,P_4)$\n",
+ "\n",
+ "The script used for data preprocessing and feature extraction is available at https://github.com/berylgithub/ppbap."
+ ]
+ },
  {
  "cell_type": "code",
  "execution_count": 1,