Weighted subsymbolic data encoding

A device for language processing that represents both sematic and orientation content within a text, the device comprising:

• circuitry configured to
• receive ordered data elements representing respective words in a text, the ordered data elements including a first data element and a second data element, which is sequential with the first data element;
• generate, based on a plurality of semantic classes corresponding respectively to blades of a graded vector space representing clusters of semantic meaning, a first subspace formed within the graded vector space by the first data element, a second subspace within the graded vector space by the second data element, a first set of data elements corresponding to one or more first semantic classes that include the first data element, and a second set of data elements corresponding to one or more second semantic classes that include the second data element;
• encode, when the one or more first semantic classes is non-degenerate with the one or more second semantic classes, the first data element with respect to the second data element such that the an encoded subspace formed by encoding the first data element with respect to the second data element is oriented with respect to an order of the first data element with respect to the second data element, the encoding being performed by computing one of a left contraction and a right contraction of the first set of data elements with respect to the second set of data elements;
• compute respective components of a weight distribution of the first data element with respect to the second data element, the components of the weight distribution corresponding to respective ordered pairs for each of the one or more first semantic classes with respect to the one or more second semantic classes;
• and
• determine a dominant semantic class of to an ordered sequence of the first data element and the second data element, the dominant semantic class representing an oriented semantic context of the ordered sequence of the first and second data elements, and the dominant semantic class being determined as a semantic class corresponding to a component having a maximum magnitude of the weight distribution, wherein
• the left contraction is one of a Clifford Algebra left contraction and a Geometric Algebra left contraction, and the right contraction is one of a Clifford Algebra right contraction and a Geometric Algebra right contraction.

A method of image analysis that represents both structure and orientation content within an image, the method being performed by circuitry included in a computing device, the method comprising:

• receiving, by the circuitry, ordered data elements representing respective pixels in an image, the ordered data elements including a first data element including one or more pixel values and a second data element, which is adjacent to the first data element and includes another one or more pixel values;
• generating, based on a plurality of semantic classes corresponding respectively to blades of a graded vector space representing clusters of semantic meaning, a first subspace formed within the graded vector space by the first data element, a second subspace within the graded vector space by the second data element, a first set of data elements corresponding to one or more first semantic classes that include the first data element, and a second set of data elements corresponding to one or more second semantic classes that include the second data element;
• encoding by the circuitry, when the one or more first semantic classes is non-degenerate with the one or more second semantic classes, the first data element with respect to the second data element such that the an encoded subspace formed by encoding the first data element with respect to the second data element is oriented with respect to an order of the first data element with respect to the second data element, the encoding being performed by computing one of a left contraction and a right contraction of the first set of data elements with respect to the second set of data elements;
• computing by the circuitry, respective components of a weight distribution of the first data element with respect to the second data element, the components of the weight distribution corresponding to respective ordered pairs for each of the one or more first semantic classes with respect to each of the one or more second semantic classes;
• and
• determining a dominant semantic class of an ordered sequence of the first data element and the second data element, the dominant semantic class representing an oriented semantic context of the ordered sequence of the first and second data elements, and the dominant semantic class being determined as a semantic class corresponding to a component having a maximum magnitude of the weight distribution, wherein
• the left contraction is one of a Clifford Algebra left contraction and a Geometric Algebra left contraction, and the right contraction is one of a Clifford Algebra right contraction and a Geometric Algebra right contraction.

A method of medical data processing that represents both content and orientation among medical information, the method being performed by circuitry included in a computing device, the method comprising:

• receiving, by the circuitry, ordered data elements representing respective parts of medical data, the ordered data elements including a first data element and a second data element, which is sequential with the first data element;
• generating, based on a plurality of semantic classes corresponding respectively to blades of a graded vector space representing clusters of semantic meaning, a first subspace formed within the graded vector space by the first data element, a second subspace within the graded vector space by the second data element, a first set of data elements corresponding to one or more first semantic classes that include the first data element, and a second set of data elements corresponding to one or more second semantic classes that include the second data element;
• encoding by the circuitry, when the one or more first semantic classes is non-degenerate with the one or more second semantic classes, the first data element with respect to the second data element such that an encoded subspace formed by encoding the first data element with respect to the second data element is oriented with respect to an order of the first data element with respect to the second data element, the encoding being performed by computing one of a left contraction and a right contraction of the first set of data elements with respect to the second set of data elements;
• computing by the circuitry, respective components of a weight distribution of the first data element with respect to the second data element, the components of the weight distribution corresponding to respective ordered pairs for each of the one or more first semantic classes with respect to each of the one or more second semantic classes;
• and
• determining a dominant semantic class of an ordered sequence of the first data element and the second data element, the dominant semantic class representing an oriented semantic context of the ordered sequence of the first and second data elements, and the dominant semantic class being determined as a semantic class corresponding to a component having a maximum magnitude of the weight distribution, wherein
• the left contraction is one of a Clifford Algebra left contraction and a Geometric Algebra left contraction, and the right contraction is one of a Clifford Algebra right contraction and a Geometric Algebra right contraction.

A device for medical data processing that represents both content and orientation among medical information, the device comprising:

• circuitry configured to
• receive ordered data elements representing respective parts of medical data, the ordered data elements including a first data element and a second data element, which is sequential with the first data element;
• generate, based on a plurality of semantic classes corresponding respectively to blades of a graded vector space representing clusters of semantic meaning, a first subspace formed within the graded vector space by the first data element, a second subspace within the graded vector space by the second data element, a first set of data elements corresponding to one or more first semantic classes that include the first data element, and a second set of data elements corresponding to one or more second semantic classes that include the second data element;
• encode, when the one or more first semantic classes is non-degenerate with the one or more second semantic classes, the first data element with respect to the second data element such that an encoded subspace formed by encoding the first data element with respect to the second data element is oriented with respect to an order of the first data element with respect to the second data element, the encoding being performed by computing one of a left contraction and a right contraction of the first set of data elements with respect to the second set of data elements;
• compute respective components of a weight distribution of the first data element with respect to the second data element, the components of the weight distribution corresponding to respective ordered pairs for each of the one or more first semantic classes with respect to the one or more second semantic classes;
• and
• determine a dominant semantic class of to an ordered sequence of the first data element and the second data element, the dominant semantic class representing an oriented semantic context of the ordered sequence of the first and second data elements, and the dominant semantic class being determined as a semantic class corresponding to a component having a maximum magnitude of the weight distribution, wherein
• the left contraction is one of a Clifford Algebra left contraction and a Geometric Algebra left contraction, and the right contraction is one of a Clifford Algebra right contraction and a Geometric Algebra right contraction.

A device for image analysis that represents both structure and orientation content within an image, the device comprising:

• circuitry configured to
• receive ordered data elements representing respective pixels in an image, the ordered data elements including a first data element including one or more pixel values and a second data element, which is adjacent to the first data element and includes another one or more pixel values;
• generate, based on a plurality of semantic classes corresponding respectively to blades of a graded vector space representing clusters of semantic meaning, a first subspace formed within the graded vector space by the first data element, a second subspace within the graded vector space by the second data element, a first set of data elements corresponding to one or more first semantic classes that include the first data element, and a second set of data elements corresponding to one or more second semantic classes that include the second data element;
• encode, when the one or more first semantic classes is non-degenerate with the one or more second semantic classes, the first data element with respect to the second data element such that an encoded subspace formed by encoding the first data element with respect to the second data element is oriented with respect to an order of the first data element with respect to the second data element, the encoding being performed by computing one of a left contraction and a right contraction of the first set of data elements with respect to the second set of data elements;
• compute respective components of a weight distribution of the first data element with respect to the second data element, the components of the weight distribution corresponding to respective ordered pairs for each of the one or more first semantic classes with respect to the one or more second semantic classes;
• and
• determine a dominant semantic class of to an ordered sequence of the first data element and the second data element, the dominant semantic class representing an oriented semantic context of the ordered sequence of the first and second data elements, and the dominant semantic class being determined as a semantic class corresponding to a component having a maximum magnitude of the weight distribution, wherein
• the left contraction is one of a Clifford Algebra left contraction and a Geometric Algebra left contraction, and the right contraction is one of a Clifford Algebra right contraction and a Geometric Algebra right contraction.