Multi-Attribute Classification

Conjunctive. Wind requires seven attributes and one is present. Bile requires six and one is present. Phlegm requires seven and one is present. No class is assigned.

Disjunctive. Wind has dry, so wind. Bile has sour, so bile. Phlegm has heavy, so phlegm. All three classes are assigned, which is no answer at all.

Weighted, all weights one. Wind scores 1, bile 1, phlegm 1. A three-way tie, and the honest output is that the description does not discriminate.

Three rules, three different behaviours, and the third one is the only one that says something true: this description carries one attribute of each class and therefore decides nothing.

Worked example: a description that does decide

The description. Dry, unstable, subtile, keen.

Weighted, all weights one. Wind 4, bile 1, phlegm 0.

And the margin is what matters. Wind leads by three. Compare a case scoring wind 2 and bile 1: the same winner, a much weaker result, and a system that reports only the winner has thrown the difference away.

So a weighted rule should report the scores, not just the maximum. That is the practical conclusion of this chapter and it is what the program in [Ayurvedic Classification as a Rule-Based Expert System] does.

About weights

Nothing in Charaka assigns weights to attributes. The lists are lists; no quality is said to count for more than another in classifying.

So the weights used in this book are all one, which is a declared choice and not a finding. Any other weighting would have to come from somewhere, and inventing weights and presenting them as the text's would be a fabrication.

How weights are obtained in modern practice, for completeness, since a question may ask.

From an expert, by asking. Cheap, and it records what the expert believes rather than what is true.

From data, by fitting. Requires labelled examples, which for this scheme do not exist.

From information content. An attribute unique to one class is more informative than one shared by two, and the information gain of [Decision Trees] measures exactly that. This is the only one of the three available here, and [A Decision Tree Built From the Tridoṣa Attributes] shows what it yields on three rows, which is less than you would hope.

What multi-attribute classification is NOT

It is not the same as having many attributes. It is about the rule that combines them. A system with a hundred attributes and no stated combination rule has an unstated one.

It is not solved by a threshold. Choosing a threshold for a weighted sum is another modelling decision, and moving it trades false positives against false negatives. [Multi-Class Classification, and How It Is Scored] is where that trade is measured.

It does not require the attributes to be independent. They usually are not, and the weighted rule quietly assumes they are. Two attributes that always occur together contribute twice and should contribute once, which is a real defect of the simple weighted rule.

Quick revision

• With more than one attribute, a combination rule is required, and a system without a stated one has an unstated one.
• Conjunctive, all: precise and almost never satisfied. Disjunctive, any: permissive and produces multiple answers. Weighted: always ranks, and can tie.
• On dry, sour, heavy the three rules give no class, all three classes, and a three-way tie. The tie is the only true answer.
• A weighted rule should report the scores, because the margin matters and the maximum alone discards it.
• No weights are in Charaka, so this book uses one for every attribute and says so.
• The weighted rule assumes the attributes are independent, and two attributes that always co-occur are counted twice.

Test yourself

1. Name the three combination rules and give a setting where each is right.

Conjunctive, requiring all attributes: right where a false positive is very costly, as in a safety interlock. Disjunctive, requiring any: right where a false negative is very costly and further checking follows, as in a screening test. Weighted, summing contributions: right where a ranking is wanted and some evidence is better than none.

2. Classify a description of dry, sour and heavy under all three rules.

Conjunctive assigns nothing, since no class has all its attributes present. Disjunctive assigns all three classes, since each has one attribute present. Weighted with equal weights gives a three-way tie at one each, which correctly reports that the description does not discriminate.

3. Why should a weighted rule report the scores rather than only the winner?

Because the margin carries information. A win by three attributes to none is a different result from a win by two to one, and reporting only the maximum discards the difference.

4. Why are all the weights in this book equal to one?

Because Charaka assigns no weights to attributes, so any other weighting would have to be invented. Using one for every attribute is a declared choice, and attributing invented weights to the text would be a fabrication.