HyperblockParser

A Hyperblock (HB) is mathematically defined as an n-orthotope by a set of n-dimensional (n-D) points $\{ \mathbf{x} = (x_1, x_2, \ldots, x_n) \} $, with center n-D point $\mathbf{c} = (c_1, c_2, \ldots, c_n)$, and side lengths $\mathbf{L} = (L_1, L_2, \ldots, L_n)$, such that $\forall_i \| x_i - c_i \| \leq \frac{L_i}{2}$.

We can write this in mathematical notation as a conjunctive normal form (CNF) statement of variables, inequalities, and logical operators; such as here are the three Fisher Iris data flower species HB statements in the form of a CNF statement which are combined by the + operator to one PC graph:

[(4.30 <= sepal_length <= 5.80) & (2.30 <= sepal_width <= 4.40) & (1.00 <= petal_length <= 1.90) & (0.10 <= petal_width <= 0.60)] + [(4.90 <= sepal_length <= 7.00) & (2.00 <= sepal_width <= 3.40) & (3.00 <= petal_length <= 5.10) & (1.00 <= petal_width <= 1.80)] + [(4.90 <= sepal_length <= 7.90) & (2.20 <= sepal_width <= 3.80) & (4.50 <= petal_length <= 6.90) & (1.40 <= petal_width <= 2.50)]

This project parses the statement into a list of bounds for each variable or attribute and visualizes the resultant HB as a graph in parallel coordinates (PC) where the graph is a upper and lower bound for each attribute connected by polylines by the logical operators.

The current project reads all statements in the statements.txt file and visualizes them sequentially with Matplotlib as PC n-D graphs.

Parsing

The parser supports CNF HB statements in the following format:

Basic Syntax

• Variables: Any alphanumeric variable name (case insensitive)
• Inequalities: < (strict, open circle) or <= (non-strict, closed circle)
• Values: Decimal numbers
• Logical operators:
  • & for AND
  • v for OR
  • + to combine multiple hyperblocks
• Parentheses: () to group expressions
• Brackets: [] to group disjunctions

The lower and upper bounds of the HB PC graph are determined by the global min and max of all the bounds in the statement.

Statement Structure

1. Single bounds: (0.2 < temperature <= 0.4)
2. Conjunctions: (0.2 < temp <= 0.4) & (0.3 <= pressure <= 0.5)
3. Disjunctions: [(0.2 < humidity <= 0.4) v (0.6 <= humidity <= 0.8)]
4. Combined hyperblocks: <hyperblock1> + <hyperblock2>

Please see the statements.txt file for more indepth examples.

Todo

1. Count cases per class label within HB statements for some given CSV data
2. Interactive REPL interface alongside static statement loading

License

HyperblockParser is licensed under the MIT License, free to use and modify, commercially and non-commercially, see the LICENSE file for more details.