v1 of intro docs

virtdata-lib-vectors/src/main/java/io/nosqlbench/virtdata/lib/vectors/dnn/package-info.java

@@ -16,12 +16,25 @@
 
 /**
  * <P>This package contains experimental support for new methods for testing vector stores.
- * projective simulation ... TBD
- * of vector spaces
- * within which provably correct KNN relationships can be derived from affine ordinal relationships.
- * In other words, vectors in some projective  space which are addressable by some ordinal identity
- * can be constructed with procedural generation methods, and provably correct KNN neighborhoods of
- * some size can be derived on the fly in a closed form calculation.</P>
+ * The primary method employed is functional mapping of ordinal spaces to vector spaces.
+ * In this way, closed-form functions can be used to synthesize vectors and provably correct neighborhoods
+ * as if they were defined in a static dataset. This allows for arbitrary testing scenarios to be
+ * created and used immediately and with no need to regenerate or compute any data beforehand.</P>
+ *
+ * <P>The original concept for this was derived by Shaunak Das, in the form of (Das) Direct Nearest Neighbor.
+ * Additional methods have been implemented using this technique to include additional space mappings
+ * for other vector distance functions.</P>
+ *
+ * <P>The testing methods enabled by this approach include:
+ * <OL>
+ * <LI>Generation of a population of vectors which are enumerable and stable with respect to their
+ * ordinal addresses.</LI>
+ * <LI>Generation of ordered subsets of this population which maintain a unique local ordering in
+ * terms of the selected distance function, otherwise known as rank for KNN queries.</LI>
+ * <LI>Validation of results for nearest neighborhood queries, using synthetic results computed on the fly as the
+ * basis for correctness.</LI>
+ * </OL>
+ * </P>
  *
  * <P>The vector spaces constructed in this way are not intended nor guaranteed to be dimensionally disperse.
  * They are meant to provide an algebraic basis for exercising vector storage systems with increasing
@@ -30,13 +43,22 @@
  *
  * <P>Each vector scheme in this method has the following properties:
  * <UL>
- *     <LI>All vectors within the space are enumerable. Each increasing ordinal value describes a new and distinct
- *     vector. The value of this vector is deterministic within the parameters of the space.</LI>
+ * <LI>Each virtual vector space is defined by a set of parameters which are used as inputs to the
+ * mapping functions. The space, and the definition of valid vectors in a neighborhood depend on these
+ * for stability and correctness. Thus each space is explicitly defined by and inseparable from its parameters.</LI>
+ * <LI>All vectors within the space are enumerable. Each increasing ordinal value describes a new and distinct
+ * vector. The value of this vector is deterministic within the parameters of the space.</LI>
+ * <LI>Each vector within a space is a valid query vector which implies a correct set of distance-ranked
+ * neighbors up to some neighborhood size for the related distance function.</LI>
+ * <LI>Nearest neighbors may have equal distance in some cases, for which ties are accommodated in testing
+ * assertions. Suppose the distance from v<sub>10</sub> to v<sub>5</sub> is the same as the distance from
+ * v<sub>10</sub> to v<sub>15</sub>, then both v<sub>5</sub> and v<sub>15</sub> should be interchangeable as
+ * correct elements in any KNN results for query vector v<sub>10</sub>, provided that their distances are within
+ * the top K results as otherwise expected.
+ * </LI>
  * </UL>
- * </P>
  *
- * <P>This work is largely inspired by the DNN or "Das/Direct Nearest Neighbor" method, pioneered by
- * Shaunak Das at DataStax. Additional implementations and ideas are contributed by the vector performance
- * team and our testing community.</P>
+ * <P>TBD: Explain the above in terms of specific implementations and parameters.</P>
+ * </P>
  */
 package io.nosqlbench.virtdata.lib.vectors.dnn;