K-Nearest Neighbor Classifier

By:
Neha Kulkarni (5201)
Pune Institute of Computer Technology,
Pune
K Nearest Neighbour Classifier

Contents
 Eager learners vs Lazy learners
 What is KNN?
 Discussion about categorical attributes
 Discussion about missing values
 How to choose k?
 KNN algorithm – choosing distance measure and k
 Solving an Example
 Weka Demonstration
 Advantages and Disadvantages of KNN
 Applications of KNN
 Comparison of various classifiers
 Conclusion
 References

Eager Learners vs Lazy Learners
 Eager learners, when given a set of training tuples,
will construct a generalization model before receiving
new (e.g., test) tuples to classify.
 Lazy learners simply stores data (or does only a little
minor processing) and waits until it is given a test
tuple.
 Lazy learners store the training tuples or “instances,”
they are also referred to as instance based learners,
even though all learning is essentially based on
instances.
 Lazy learner: less time in training but more in
predicting.
-k- Nearest Neighbor Classifier
-Case Based Classifier

k- Nearest Neighbor Classifier
 History
• It was first described in the early 1950s.
• The method is labor intensive when given large
training sets.
• Gained popularity, when increased computing
power became available.
• Used widely in area of pattern recognition and
statistical estimation.

What is k- NN??
 Nearest-neighbor classifiers are based on
learning by analogy, that is, by comparing a given
test tuple with training tuples that are similar to it.
 The training tuples are described by n attributes.
 When k = 1, the unknown tuple is assigned the
class of the training tuple that is closest to it in
pattern space.

Remarks!!
 Similarity Function Based.
 Choose an odd value of k for 2 class problem.
 k must not be multiple of number of classes.

Closeness
 The Euclidean distance between two points or
tuples, say,
X1 = (x11,x12,...,x1n) and X2 =(x21,x22,...,x2n), is
 Min-max normalization can be used to transform
a value v of a numeric attribute A to v0 in the
range [0,1] by computing

What if attributes are categorical??
 How can distance be computed for attribute
such as colour?
-Simple Method: Compare corresponding value of
attributes
-Other Method: Differential grading

What about missing values ??
 If the value of a given attribute A is missing in
tuple X1 and/or in tuple X2, we assume the
maximum possible difference.
 For categorical attributes, we take the difference
value to be 1 if either one or both of the
corresponding values of A are missing.
 If A is numeric and missing from both tuples X1
and X2, then the difference is also taken to be 1.

How to determine a good value for
k?
 Starting with k = 1, we use a test set to estimate
the error rate of the classifier.
 The k value that gives the minimum error rate
may be selected.

Distance Measures
Which distance measure to use?
We use Euclidean Distance as it treats each feature as
equally important.
𝐸𝑢𝑐𝑙𝑖𝑑𝑒𝑎𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∶ 𝑑 𝑥, 𝑦 = 𝑥𝑖 − 𝑦𝑖 2
𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝐸𝑢𝑐𝑙𝑖𝑑𝑒𝑎𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∶ 𝑑 𝑥, 𝑦 = 𝑥𝑖 − 𝑦𝑖 2
𝑀𝑎𝑛ℎ𝑎𝑡𝑡𝑎𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∶ 𝑑 𝑥, 𝑦 = |(𝑥𝑖 − 𝑦𝑖)|

How to choose K?
 If infinite number of samples available, the larger
is k, the better is classification.
 k = 1 is often used for efficiency, but sensitive to
“noise”

 Larger k gives smoother boundaries, better for generalization,
but only if locality is preserved. Locality is not preserved if end
up looking at samples too far away, not from the same class.
 Interesting relation to find k for large sample data : k =
sqrt(n)/2 where n is # of examples
 Can choose k through cross-validation

Example
 We have data from the questionnaires survey and
objective testing with two attributes (acid durability and
strength) to classify whether a special paper tissue is good
or not. Here are four training samples :
X1 = Acid Durability
(seconds)
X2 = Strength
(kg/square meter)
Y = Classification
7 7 Bad
7 4 Bad
3 4 Good
1 4 Good
Now the factory produces a new paper tissue that passes the
laboratory test with X1 = 3 and X2 = 7. Guess the classification of
this new tissue.

 Step 1 : Initialize and Define k.
Lets say, k = 3
(Always choose k as an odd number if the number of
attributes is even to avoid a tie in the class prediction)
 Step 2 : Compute the distance between input sample and
training sample
- Co-ordinate of the input sample is (3,7).
- Instead of calculating the Euclidean distance, we
calculate the Squared Euclidean distance.
X1 = Acid Durability
(seconds)
X2 = Strength
(kg/square meter)
Squared Euclidean distance
7 7 (7-3)2 + (7-7)2 = 16
7 4 (7-3)2 + (4-7)2 = 25
3 4 (3-3)2 + (4-7)2 = 09
1 4 (1-3)2 + (4-7)2 = 13

 Step 3 : Sort the distance and determine the nearest
neighbours based of the Kth minimum distance :
X1 = Acid
Durability
(seconds)
X2 = Strength
(kg/square
meter)
Squared
Euclidean
distance
Rank
minimum
distance
Is it included
in 3-Nearest
Neighbour?
7 7 16 3 Yes
7 4 25 4 No
3 4 09 1 Yes
1 4 13 2 Yes

 Step 4 : Take 3-Nearest Neighbours:
 Gather the category Y of the nearest neighbours.
X1 = Acid
Durability
(seconds)
X2 =
Strength
(kg/square
meter)
Squared
Euclidean
distance
Rank
minimum
distance
Is it
included in
3-Nearest
Neighbour?
Y =
Category of
the nearest
neighbour
7 7 16 3 Yes Bad
7 4 25 4 No -
3 4 09 1 Yes Good
1 4 13 2 Yes Good

 Step 5 : Apply simple majority
 Use simple majority of the category of the nearest
neighbours as the prediction value of the query instance.
 We have 2 “good” and 1 “bad”. Thus we conclude that
the new paper tissue that passes the laboratory test with
X1 = 3 and X2 = 7 is included in the “good” category.

Iris Dataset Example using Weka
 Iris dataset contains 150 sample instances belonging
to 3 classes. 50 samples belong to each of these 3
classes.
 Statistical observations :
 Let's denote the true value of interest as 𝜃 (𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑)
and the value estimated using some algorithm as
𝜃. (𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑)
 Kappa Statistics : The kappa statistic measures the
agreement of prediction with the true class -- 1.0
signifies complete agreement. It measures the
significance of the classification with respect to the
observed value and expected value.
 Mean absolute error :

 Root Mean Square Error :
 Relative Absolute Error :
 Root Relative Squared Error :

Complexity
 Basic kNN algorithm stores all examples
 Suppose we have n examples each of dimension
d
 O(d) to compute distance to one examples
 O(nd) to computed distances to all examples
 Plus O(nk) time to find k closest examples
 Total time: O(nk+nd)
 Very expensive for a large number of samples
 But we need a large number of samples for kNN
to to work well!!

 Advantages of KNN classifier :
 Can be applied to the data from any distribution for
example, data does not have to be separable with a
linear boundary
 Very simple and intuitive
 Good classification if the number of samples is large
enough
 Disadvantages of KNN classifier :
 Choosing k may be tricky
 Test stage is computationally expensive
 No training stage, all the work is done during the test
stage
 This is actually the opposite of what we want. Usually we
can afford training step to take a long time, but we want

Applications of KNN Classifier
 Used in classification
 Used to get missing values
 Used in pattern recognition
 Used in gene expression
 Used in protein-protein prediction
 Used to get 3D structure of protein
 Used to measure document similarity

Comparison of various classifiers
Algorithm Features Limitations
C4.5
Algorithm
- Models built can be easily
interpreted
- Easy to implement
- Can use both discrete and
continuous values
- Deals with noise
- Small variation in data can lead
to different decision trees
- Does not work very well on
small training dataset
- Over-fitting
ID3
Algorithm
- It produces more accuracy
than C4.5
- Detection rate is increased
and space consumption is
reduced
- Requires large searching time
- Sometimes it may generate
very long rules which are
difficult to prune
- Requires large amount of
memory to store tree
K-Nearest
Neighbour
Algorithm
- Classes need not be linearly
separable
- Zero cost of the learning
process
- Sometimes it is robust with
regard to noisy training data
- Well suited for multimodal
- Time to find the nearest
neighbours in a large training
dataset can be excessive
- It is sensitive to noisy or
irrelevant attributes
- Performance of the algorithm
depends on the number of

Naïve Bayes
Algorithm
- Simple to implement
- Great computational efficiency
and classification rate
- It predicts accurate results for
most of the classification and
prediction problems
- The precision of the
algorithm decreases if the
amount of data is less
- For obtaining good results,
it requires a very large
number of records
Support vector
machine
Algorithm
- High accuracy
- Work well even if the data is
not linearly separable in the
base feature space
- Speed and size
requirement both in training
and testing is more
- High complexity and
extensive memory
requirements for
classification in many
cases
Artificial Neural
Networks
Algorithm
- It is easy to use with few
parameters to adjust
- A neural network learns and
reprogramming is not needed.
- Easy to implement
- Applicable to a wide range of
problems in real life.
- Requires high processing
time if neural network is
large
- Difficult to know how many
neurons and layers are
necessary
- Learning can be slow

Conclusion
 KNN is what we call lazy learning (vs. eager
learning)
 Conceptually simple, easy to understand and
explain
 Very flexible decision boundaries
 Not much learning at all!
 It can be hard to find a good distance measure
 Irrelevant features and noise can be very
detrimental
 Typically can not handle more than a few dozen
attributes
 Computational cost: requires a lot computation

References
 “Data Mining : Concepts and Techniques”, J. Han, J.
Pei, 2001
 “A Comparative Analysis of Classification Techniques
on Categorical Data in Data Mining”, Sakshi, S.
Khare, International Journal on Recent and Innovation
Trends in Computing and Communication, Volume: 3
Issue: 8, ISSN: 2321-8169
 “Comparison of various classification algorithms on
iris datasets using WEKA”, Kanu Patel et al, IJAERD,
Volume 1 Issue 1, February 2014, ISSN: 2348 - 4470

K-Nearest Neighbor Classifier

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