Classifiers

This section provides definitions for the various classifiers used by the hm software and shows how to save a classification to a comma-separated-value text file. There are two kinds of classifiers: archaeological classifiers that reflect observations and inferences made by an archaeologist familiar with the stratigraphic situation represented by the sequence diagram; and graph theoretical classifiers that take advantage of the DAG representation to deduce structural relations that might prove useful to the archaeologist tasked with interpreting the sequence diagram.

The hm software currently implements the following classifiers:

(show-classifiers)

units
levels
phases
periods
adjacent
distance
reachable

Archaeological Classifiers

The hm software currently provides three ways to integrate archaeological observations about contexts into the sequence diagram, which it calls units, phases, and periods. Some preliminary discussion is in order because archaeologists define these terms more or less precisely and have achieved more or less consensus on their definitions. Also, there are very many other terms in use that attempt to capture the practice of classifying and grouping archaeological contexts.

Steve Roskams discusses this situation on pages 257–258 of Excavation in the context of assigning “basic units to higher-order categories.”

This raises the question of how such groups are to be defined—what is the point where one stops and another begins? Should there be a single type of group or a whole hierarchy of entities? How should each be named? Or are the potential configurations so diverse that it is impossible to make useful comparisons between sites?

This issue has been approached by a variety of specialists who have produced different schemes and terminology. To some extent the differences are a function of the great variety of sites with which they are dealing, and are thus entirely legitimate. Equally, they come, in part, from merely giving a different name to the same concept … This profusion of terminology is to be expected, given that thoughts on such matters are at a very formative stage, and it is probably right to retain some diversity in any case, given the variety of sites and associated stratigraphic sequences, and types of analytical procedures applied to them.

The units classification offered by the hm software is more precisely defined and widely appreciated by archaeologists than either periods or phases. The hm software recognizes the basic distinction of depositional from interfacial units of stratification and hard-wires this distinction into the software, while leaving to the hm user the choice of how it might be represented in the sequence diagram.

The hm software takes no such confident stand with periods and phases, leaving their definitions (if not their names within the software) completely up to the user. From the software’s point of the view, there is no difference between a period and a phase and there is no relationship between them. The hm user is best served by viewing them as ways to incorporate any kind of classification of contexts whatsoever. The classifications might be based on statistical analysis of the finds collected from each context, presence or absence of one or more index fossils, physical characteristics of the contexts themselves, etc.

In a sense, the crucial question from the software’s point of view is how many different kinds of classification might be useful on a single sequence diagram? Are two kinds sufficient? The answer to this question does not involve judgments about how many or few analyses are best carried out on excavation materials. Rather, it involves how many classifications it might be useful to plot on the same graphic. If there are a dozen classifications that need to be investigated, then the way forward is to use the hm software to make 6–12 sequence diagrams, each one showing one or two classifications, as appropriate.

Units

The units classifier is designed for use with excavation data, where both depositional and interfacial units are identified and recorded. Archaeologists universally identify and record depositional units (often as `layers’) but are somewhat ambivalent about interfaces, typically choosing to record interfaces that appear to be important and ignoring others.

This practice is potentially problematic for the hm software because it assumes that interfaces that are not identified and recorded do not themselves represent chunks of time that might be important in a chronological model. In an ideal sense, the stratigraphic sequence represents a continuous record of time from some point in the past represented by the base of excavation up through to the modern surface. Neglecting to identify and record interfaces potentially yields a discontinuous model of that continuous record, with gaps introduced by the time spans represented by the excluded interfaces.

The default configuration file uses node shape to distinguish deposits from interfaces. Deposits are shaped like a rectangular box and interfaces are shaped like a trapezium, as in this snippet from a configuration file:

[Graphviz sequence unit node shape]
deposit = box
interface = trapezium

Individual deposits and interfaces are identified in the input file for contexts (see Section ).

Periods and Phases

The stratigraphic DAG for this example shows the Figure 12 section divided into four periods (fig. 1). The oldest period includes the Natural ground and its surface. The next oldest period includes Context 9 and its surfaces. Next is the once-whole deposit represented by Contexts 7 and 8, the surfaces of those contexts, and all of the various contexts related to construction of the wall stub, Context 5. The youngest period is represented by the Context 1 deposit and its surface.

On a Linux system, Figure 1 can be reproduced with the following function call:

(run-project/example :fig-12-periods)

Graph Theoretical Classifiers

The graph theoretical classifiers are defined in the context of a general definition of a directed graph. The definition used here is paraphrased from the book, Structural Models in Anthropology written by Per Hage and Frank Harary. This book is the first in a remarkable trilogy that also includes Exchange in Oceania: A Graph Theoretic Analysis and Island Networks: Communication, Kinship, and Classification Structures in Oceania.

One of the challenges presented by the literature on graph theory is the number of synonyms for the basic elements of a graph (table 1), what this document and the hm software try to label consistently as nodes and arcs. Hage and Harary typically use point and arc for directed graphs, and point and line for graphs. The definitions given below and in the following sections are quoted verbatim, so it is up to the reader to translate synonyms appropriately.

node	arc
point	line
vertex	edge
junction	branch
0-simplex	1-simplex
element	element

Hage and Harary define a directed graph on page 68 of Structural Models in Anthropology as follows.

A directed graph or digraph D consists of a finite set V of points and a collection of ordered pairs of distinct points. Any such pair (u, v) is called an arc or directed line and will usually be denoted uv. The arc uv goes from u to v and is incident with u and v.

Adjacent

The adjacency classification is the simplest among the graph theoretical classifications. Following on the definition of directed graph, quoted above, Hage and Harary define adjacency as follows.

The arc uv goes from u to v and is incident with u and v. We also say that u is adjacent to v and v is adjacent from u.

It is important to note that the sequence diagram represents chronological adjacency, rather than physical adjacency. Two contexts that are in contact with one another can be said to be physically adjacent, but they might be chronologically separated by one or more other contexts.

This can be seen in the following example, which is based on the stratigraphic section shown on Figure .

The sequence diagram can be drawn to highlight the relationship of Context 2 to the others. When the sequence diagram is classified so nodes, node labels, and edges are colored according to adjacency from Context 2, such that the origin node is violet, adjacent nodes are cyan, and nodes not adjacent to Context 2 are orange, the graph in Figure 2 results.

The graph was produced on a Linux system with the following function call:

(run-project/example :roskams-h-solarized-dark)

The important sections in the initialization file include the following.

[Graph analysis configuration]
distance-from =
adjacent-from = 2
...

[Graphviz sequence classification]
node-fillcolor-by =
node-fontcolor-by = adjacent
node-shape-by =
node-color-by = adjacent
node-penwidth-by =
node-style-by =
node-polygon-distortion-by =
node-polygon-image-by =
node-polygon-orientation-by =
node-polygon-sides-by =
node-polygon-skew-by =
edge-color-by = adjacent
...

[Graphviz sequence graph attributes]
colorscheme = solarized
bgcolor = base02
fontname = Helvetica
fontsize = 14.0
fontcolor = base1
label = Roskams\' H-structure (corrected)
labelloc = t
style = filled
size =
ratio = 0.618034
...

[Graphviz sequence node attributes]
shape = box
colorscheme = solarized
style = filled
color = base01
fontsize = 14.0
fontsize-min = 6.0
fontsize-max = 22.0
fontcolor = base01
fillcolor = base03
...

[Graphviz sequence adjacent node colors]
origin = violet
adjacent = cyan
not-adjacent = orange
colorscheme = solarized

[Graphviz sequence adjacent node fontcolors]
origin = violet
adjacent = cyan
not-adjacent = orange
colorscheme = solarized

[Graphviz sequence adjacent edge colors]
origin = violet
adjacent = cyan
not-adjacent = orange
colorscheme = solarized

Note that Context 2 is in physical contact with Contexts 3 and 5. The sequence diagram (fig. 2) shows Context 2 adjacent to Context 3, but because the Context 2 pit cut into Context 3, which itself was cut into Context 5, Context 2 is not chronologically adjacent to Context 5.

Reachable

The graph theoretic definition of reachability requires definitions for directed walk and path. Hage and Harary define reachability this way on pages 68–69 of Structural Models in Anthropology, where they use digraph as a synonym for directed graph.

A (directed) walk in a digraph is an alternating sequence of points and arcs, v₀, x₁, v₁, …, xₙ, vₙ in which each arc xᵢ is vᵢ₋₁vᵢ. For brevity, we may write the sequence of points v₀, v₁, …, vₙ to indicate the same walk. The length of such a walk is n, the number of occurrences of arcs in it. A closed walk has the same first and last points, and open walk does not, and a spanning walk contains all the points. A path is a walk in which all points are distinct; a cycle is a nontrivial closed walk with all points distinct except the first and last. If there is a path from u to v, then v is said to be reachable from u …

Compare this definition with Roskams’ description of reachability as it is conceptualized by users of the Harris matrix on page 158 of the book, Excavation:

if one travels from a particular unit via the strands running up from it, all units through which one passes are provably later than that unit; if one travels down, every unit en route is provably earlier; any unit which cannot be reached in one of these two ways has no proven relationship with the unit in question.

This describes all the nodes from which the “particular unit” is reachable—”the strands running up from it”—and all the nodes reachable from “the particular unit” that are encountered when one “travels down”.

One key to dating Çatalhöyük has been identifying residual materials in the deposits. A good example of this is Context 1332+, where several seeds were recovered and dated. Initially, the seeds were thought to be associated with the Context 1332+ deposit, but four of them were subsequently determined to be residual. The effect of these different residuality determinations on the dating project at Çatalhöuyük is discussed by Dye and Buck.

The importance of Context 1332+ in the stratigraphy of Çatalhöyük is indicated by a graph classified by reachability (fig. 3). This graph assigns dark blue fills to nodes from which Context 1332+ is reachable and nodes reachable from Context 1332+. The node for Context 1332+ is filled light blue. Nodes from which Context 1332+ is not reachable and nodes not reachable from Context 1332+ are filled green. The colors are taken from the Brewer color paired palette.

A stratigraphic DAG for the information displayed on Figure 3 might be drawn on a Linux system with the hm software as follows:

(run-project/example :catal-hoyuk-reachable)

The important sections of the configuration file include the following.

[Graph analysis configuration]
distance-from =
adjacent-from =
reachable-from = 1332+
reachable-limit =

[Graphviz sequence classification]
node-fillcolor-by = reachable
...

[Graphviz sequence reachability node fillcolors]
origin = 0
reachable = 1
not-reachable = 2
colorscheme = paired

Classification by reachability is potentially important for decisions on what materials to date. Contexts that are reachable from many contexts or from which many contexts are reachable might be thought of as having relatively great potential influence in a chronological model.

Distance

The graph theoretic definition of distance follows directly on the definition of reachability. Hage and Harary define distance this way on page 69 of Structural Models in Anthropology.

If there is a path from u to v, then v is said to be reachable from u, and the distance d (u,v) from u to v is the length of any shortest such path.

An example of a graph classified by distance is Figure 4. This graph assigns node fills based on distance from Context 1332+. The node for Context 1332+ is the lightest blue. Nodes not reachable from Context 1332+ are the darkest blue. All other nodes have intermediate shades of blue based on their distance from Context 1332+, the farther the node the darker the color.

This graph was produced on a Linux system with the following function call:

(run-project/example :catal-hoyuk-distance :draw-chronology nil)

The interesting parts of the configuration file follow.

[Graph analysis configuration]
distance-from = 1332+

[Graphviz sequence classification]
node-fillcolor-by = distance

[Graphviz sequence node fill color schemes]
levels =
distance = cet-blues

Levels

The graph theoretic concept of level is closely tied to the stratigraphic concept of level. Hage and Harary define level on page 82 of Structural Models in Anthropology.

An acyclic digraph D has no cycles … [and] is said to have a level assignment, which assigns a positive integer n for each point v, called its level, if for each arc vᵢ vⱼ of D, the corresponding integers satisfy nᵢ < nⱼ. Thus each arc of D is directed from a lower to a higher level. If a digraph D has a cycle, then it cannot have a level assignment.

An example of a levels classification can be seen in the stratigraphic DAG of Çatalhöyük (fig. 5).

The graph was produced on a Linux system with the following function call:

(run-project/example :catal-hoyuk-levels :draw-chronology nil)

The interesting parts of the configuration file follow.

[Graphviz sequence classification]
node-fillcolor-by = levels

[Graphviz sequence node fill color schemes]
levels = cet-bgyw

Write a Classification to a File

In addition to creating graphical output, the hm software can write a classification to a comma-separated-value file to communicate with other software. The name of the output file is specified in the configuration file; this protocol insures that the user of an hm project created by someone else can be certain of a CSV file’s contents.

In the example below, the file names for distance, reachable, and adjacent classifications are helpfully descriptive, while the name given the phases classification is not too helpful.

[Output files]
sequence-dot = fig-12-polygon-1.dot
chronology-dot =
distance = fig-12-distance.csv
reachable = fig-12-reachable.csv
adjacent = fig-12-adjacent.csv
phases = foobar.csv
periods = fig-12-periods.csv
...

The following transcript writes the periods classifier for the :fig-12-polygon example to the fig-12-periods.csv file.

(defvar *seq*)
(setq *seq* (run-project/example :fig-12-polygon))
(write-classifier :periods *seq*)

The file fig-12-periods.csv file looks like this:

head ../examples/fig-12-chronology/fig-12-periods.csv