## FIND S Algorithm – Maximally Specific Hypothesis Solved Example

FIND S Algorithm is used to find the Maximally Specific Hypothesis. Using the Find-S algorithm gives a single maximally specific hypothesis for the given set of training examples.

**Click Here for Python Program to Implement FIND S Algorithm – to get Maximally Specific Hypothesis**

### Find-S Algorithm Machine Learning

1. Initilizehto the most specific hypothesis inH2. For each positive training instancexFor each attribute contraintain_{i}hIf the contraintais satisfied by_{i}xthen do nothing Else replaceain_{i}hby the next more general constraint that is satisfied byx3. Output the hypothesish

## Solved Numerical Example – 1

### Step – 1 of Find-S Algorithm

## Step 2 of Find-S Algorithm First iteration

h0 = (ø, ø, ø, ø, ø, ø, ø)

X1 = <Sunny, Warm, Normal, Strong, Warm, Same>

h1 = <Sunny, Warm, Normal, Strong, Warm, Same>

### Step 2 of Find-S Algorithm Second iteration

h1 = <Sunny, Warm, Normal, Strong, Warm, Same>

X2 = <Sunny, Warm, High, Strong, Warm, Same>

h2 = <Sunny, Warm, ?, Strong, Warm, Same>

### Step 2 of Find-S Algorithm Third iteration

h2 = <Sunny, Warm, ?, Strong, Warm, Same>

X3 = <Rainy, Cold, High, Strong, Warm, Change> – No

X3 is Negative example Hence ignored

h3 = <Sunny, Warm, ?, Strong, Warm, Same>

### Step 2 of Find-S Algorithm Fourth iteration

h3 = <Sunny, Warm, ?, Strong, Warm, Same>

X4 = <Sunny, Warm, High, Strong, Cool, Change>

h4 = <Sunny, Warm, ?, Strong, ?, ?>

### Step 3

The final maximally specific hypothesis is **<Sunny, Warm, ?, Strong, ?, ?>**

### Video Tutorial Example – 1

## Solved Numerical Example – 2

1. How many concepts are possible for this instance space?

**Solution: 2 * 3 * 2 * 2 * 3 = 72**

2. How many hypotheses can be expressed by the hypothesis language?

**Solution: ****4 ***** ****5 ***** ****4 ***** ****4 ***** ****5 = 1600**

**Semantically Distinct Hypothesis = ( 3 * 4 * 3 * 3 * 4 ) + 1 = 433**

3. Apply the FIND-S algorithm by hand on the given training set. Consider the examples in the specified order and write down your hypothesis each time after observing an example.

**Step 1:**

** **h0 = (ø, ø, ø, ø, ø)

**Step 2:**

X1 = (some, small, no, expensive, many) – No

Negative Example Hence Ignore

h1 = (ø, ø, ø, ø, ø)

X2 = (many, big, no, expensive, one) – Yes

h2 = (many, big, no, expensive, one)

X3 = (some, big, always, expensive, few) – No

Negative example hence Ignore

h3 = (many, big, no, expensive, one)

X4 = (many, medium, no, expensive, many) – Yes

h4 = (many, ?, no, expensive, ?)

X5 = (many, small, no, affordable, many) – Yes

h5 = (many, ?, no, ?, ?)

**Step 3:**

**Final Maximally Specific Hypothesis is:**

**h5 = (many, ?, no, ?, ?)**

### Video Tutorial Example – 2

## Summary

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