An introduction to machine learning for students in secondary education

Conference Paper (PDF Available) · February 2011with 1,332 Reads
DOI: 10.1109/DSP-SPE.2011.5739219 · Source: IEEE Xplore
Conference: Digital Signal Processing Workshop and IEEE Signal Processing Education Workshop (DSP/SPE), 2011 IEEE
We have developed a platform for exposing high school students to machine learning techniques for signal processing problems, making use of relatively simple mathematics and engineering concepts. Along with this platform we have created two example scenarios which give motivation to the students for learning the theory underlying their solutions. The first scenario features a recycling sorting problem in which the students must setup a system so that the computer may learn the different types of objects to recycle so that it may automatically place them in the proper receptacle. The second scenario was motivated by a high school biology curriculum. The students are to develop a system that learns the different types of bacteria present in a pond sample. The system will then group the bacteria together based on similarity. One of the key strengths of this platform is that virtually any type of scenario may be built upon the concepts conveyed in this paper. This then permits student participation from a wide variety of educational motivation.
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Steven D. Essinger, Gail L. Rosen
Drexel University
Department of Electrical & Computer Engineering
3141 Chestnut Street
Philadelphia, PA 19104
We have developed a platform for exposing high school stu-
dents to machine learning techniques for signal processing
problems, making use of relatively simple mathematics and
engineering concepts. Along with this platform we have cre-
ated two example scenarios which give motivation to the stu-
dents for learning the theory underlying their solutions. The
first scenario features a recycling sorting problem in which
the students must setup a system so that the computer may
learn the different types of objects to recycle so that it may au-
tomatically place them in the proper receptacle. The second
scenario was motivated by a high school biology curriculum.
The students are to develop a system that learns the different
types of bacteria present in a pond sample. The system will
then group the bacteria together based on similarity. One of
the key strengths of this platform is that virtually any type
of scenario may be built upon the concepts conveyed in this
paper. This then permits student participation from a wide
variety of educational motivation.
Index TermsMachine Learning, Pattern Recognition,
Secondary Education, Lab Modules
Machine learning (ML), a subfield of artificial intelligence,
has evolved out of the need to teach computers how to au-
tomatically learn a solution to a problem. In engineering this
field is referred to as pattern recognition, aptly named because
the computer is extracting patterns out of data and making a
decision based on the pattern identified. It is a rich field that
is broadly and inherently related to signal processing most
notably through data-driven learning methodologies [1, 2].
Our understanding of human learning has inspired many
of the ML methods currently available. For example, take a
look at the foundation of neural networks, which is based off
the structure of the interconnection of multiple neurons from
This research is based upon work supported by the National Science
Foundation under Grant Nos. #0733284 and #0845827.
the brain [3]. While this class of methods undoubtedly em-
ploys coarse approximations of actual neuron function, they
have shown tremendous success in several ML applications
A few examples of ML applications include speech recog-
nition aka natural language processing, image processing
such as face detection, DNA sequence classification, financial
analysis such as detecting credit card fraud, sports prediction
and search engine algorithms which have been put into use by
major household name search providers [5, 6, 7]. Many ML
techniques do require a moderate mathematical background.
Statistics, linear algebra, and calculus are commonplace in
many of the algorithms. Fortunately, simple mathematical
techniques have been shown to be quite successful on prac-
tical problems exploiting ML. With only an understanding
of means and Euclidean distances, students can be shown
how to instruct a computer to identify the difference between
a pen and pencil, albeit with the proper assumptions. The
simplicity of the math therefore permits accessibility of the
field of ML to the high school student.
ML not only employs mathematics for practical purposes,
but also demands problem-solving skill at a fundamental level
since each problem encountered requires proper tool selection
and then the interfacing of the tool to the problem. Through
the application of lab modules such as the one proposed in
this paper, students may be exposed to multi-interdisciplinary
fields simultaneously such as engineering, mathematics, com-
puter science and the field of the problem being addressed
such as biology, economics, photography, etc.
There are innumerable examples with which machine learn-
ing techniques may be employed to facilitate automatic prob-
lem solving. Suppose you wish to separate quarters, nickels
and dimes. What information would the computer need to dis-
tinguish between these three types of coins? Think about how
you would do the task yourself. It is easy to see that each type
of coin has a different size. So all we need to do is supervise
243978-1-61284-227-1/11/$26.00 ©2011 IEEE DSP/SPE 2011
or rather tell the computer the circumference of each type of
coin and then let the computer automatically do the sorting.
This problem is exceedingly easy and does not necessarily re-
quire any complex ML technique. Now let’s say that we have
a bag of unknown coins of several different currencies. We
wish the computer to sort the coins by type and currency au-
tomatically. In this case the computer must learn the types for
sorting and then classify each coin without our explicit input
as in the previous example. This problem requires an unsu-
pervised solution in that we do not know the types of coins
beforehand. This example will serve as the basis for delineat-
ing the basic steps involved in developing a machine learning
solution as depicted in figure 1.
The first step in any engineering design is to define the
problem. In our example our problem is to sort a bag of un-
known coins. To further motivate the use of ML techniques
lets say that the bag contains 1,000,000 coins so that a man-
ual solution of sorting is unrealistic for all practical purposes.
We cannot simply just feed the computer the bag of coins,
but must provide it with some information that it can use to
make a decision about each coins type or rather its class as its
known in the ML literature. This second step of the design is
known as feature extraction.
Feature extraction requires the user to provide the com-
puter with information that may be used to differentiate the
classes, which in our case is the types of coins. We need to
insure that our features contain enough discriminatory infor-
mation about the classes.
For example, shape would probably be a poor choice since
each coin is assumed to be round. However, if some coins
were non-circular than this could be one useful feature. Many
times we include multiple features to aid the algorithm. For
our example the diameter of the coin is probably a useful fea-
ture, but since we have coins of multiple currencies there is
a good chance that two different types of coins will have the
same diameter. Therefore we chose a second feature such
color of the coin. But since we are working with mathematics
and computation, we need to map color to a number. We can-
not simply say silver or copper, but instead find a numerical
quantity that furnishes the same discriminatory information,
say RGB value or perhaps luster. Let us choose luster since
its arguable easier and cheaper to obtain. Some of the coins
may be older than the others and therefore may not be as lus-
trous as those newer of the same class. This variation could
be viewed as each type of coin having a mean value of lus-
ter and a standard deviation of luster across all coins of that
type. Depending on the chosen algorithm, this information
could be of use for separating the coins. A third feature may
be added such as weight of the coin and a fourth, albeit ex-
treme example, such as the bacterial composition found on
each coin with the assumption that the composition varies de-
pending on the region of the world the coin originated from.
From this discussion, it is therefore no surprise that if poor
features are chosen, then the algorithm will perform poorly.
Fig. 1. This block diagram outlines the basic steps required to
be addressed when developing a machine learning solution.
This is known as the garbage-in, garbage-out theorem and is
why feature selection is one of the most important steps in
ML and is almost always carried out by the designer.
There are potentially hundreds, if not thousands of differ-
ent ML algorithms to choose from. In many instances, the
algorithms are modified to fit a particular problem resulting
in a new model, thereby growing the population of choices.
High school students should not have a problem comprehend-
ing Euclidean distance and mean so we suggest the use of the
K-means algorithm for solving our coin sorting example and
the subsequent lab activities. The details of the K-means al-
gorithm are discussed in the next section. Of course, more
advanced algorithms may be selected based on the students
mathematical aptitude resulting in a highly scalable ML lab
No matter which algorithm is chosen it must be properly
coded and executed on the computer. Many programming
options are available, but we suggest the use of Matlab for
rapid implementation ( This software
package already includes the K-means algorithm as a one-
line command thereby alleviating the students or teacher from
coding the algorithm from scratch. Alternatively, coding this
simple algorithm could be an excellent exercise for a student
in a computer science course using any language such as C,
Java, Perl, Python, etc. Weka is another great machine learn-
ing tool for algorithm implementation that is based on Java
[8, 9, 10]. The bottom line is that the coding part of the ML
activity can be kept as simple or scaled as complex as desired
by the educator without loss of generality.
Once the corresponding data has been captured based on
the features selected and the algorithm has run on the data
we evaluate the performance of the classifier on the dataset.
In our example we expect to have groups of coins with each
group containing one type of coin. In order to evaluate the
performance of our ML selection we need to know the ground
truth of the type of each coin. Here we may simply visually
inspect the coins in each group. Under other circumstances
this information could be recorded, set aside and kept un-
known to the algorithm until after it has run, upon which the
truth is compared to the algorithms output.
There are nearly as many evaluation metrics in ML as
there are algorithms. The most appropriate metric depends on
the specific application and problem being solved making the
selection another aspect of design. We could simply count the
number of misplaced coins and use that figure as our metric.
A metric known as the rand index would be suitable for our
ML design [11]. This metric shown in eqn. (1) essentially as-
sesses the similarity of the groupings between the algorithms
output and the ground truth. It is relatively straightforward to
implement the rand index in Matlab or an Excel spreadsheet.
a, the number of pairs of elements that are in the same
set in X and in the same set in Y
b, the number of pairs of elements that are in different
sets in X and in different sets in Y
c, the number of pairs of elements that are in the same
set in X and in different sets in Y
d, the number of pairs of elements that are in different
sets in X and in the same set in Y
X is referred to as the algorithm output and Y is the
ground truth
The K-means algorithm is a very simple yet effective ML
learning technique [12]. Besides the actual data (extracted
features) from our coin example all we need to provide is the
number of groups, K, we want the algorithm to produce. Ide-
ally, we would want the algorithm to determine this number
on its own, but in this case we would have to provide it with
some other piece of information. This is known as the no free
lunch theorem in that we must always specify at least one free
parameter for all ML techniques. There are additional meth-
ods available to assist us in estimating the number of groups
for this problem, but we will just assume that we now know
the number of different types of currency in the coin bag,
namely 3. We will chose the circumference and the luster of
the coins as our features and run the K-means algorithm with
The steps for the K-means algorithm are as follows with
a graphical depiction shown in figure 2:
1. Choose 3 staring points randomly. These are called the
2. Calculate the Euclidean distance between each point
and centroids.
3. Assign each point to its nearest centroid.
4. Calculate the mean of each centroid based on the points
assigned to it.
5. Move the centroid to the mean location.
6. Repeat steps 1-5 until centroids no longer move.
Each coin is represented as a 1×2vector, [x1,x
2], with
x1and x2corresponding to circumference and luster respec-
tively. Given a set of objects (x1,x
2...., xn), with each object
represented by a d-dimensional vector, the k-means algorithm
partitions the data into k sets S = {S1,S
3, ..., Sk}. The K-
means algorithm aims to minimize the within-cluster sum of
squares described by eqn. (2).
arg min
The students may perform the K-means algorithm by hand
on a few instances by following steps 1-6 above using their
knowledge of Euclidean distance (eqn. (3)) and mean (eqn.
d(x, y)=
The preceding information on ML and the K-means algorithm
has been provided as a framework for customized activities
for implementation in secondary education. There are essen-
tially an unlimited number of exemplary problems that may
Fig. 2. This figure identifies several key steps in the k-means
algorithm. Part A shows the objects represented by their fea-
tures. Part B show the randomization assignment of centroids.
Part C, displaying an intermediate step, depicts the movement
of centroids based on the euclidean distance of each point and
the centroids. Part D show the final location of the centroids
and the assignment of points to their respective centroid.
be proposed to students varying with level of depth and com-
plexity based on the student/teacher needs. The following ex-
amples are proposed as potential lab activities for implemen-
tation in the classroom.
4.1. Recycling Containers
The students have just been hired to design a container sorting
system at their local recycling center. The system must be
able to identify glass, plastic and cardboard drink containers
so that they may be automatically placed in their respective
bins. The students are to design and implement the artificial
intelligence portion of the system using the ML techniques as
delineated above.
A potential solution for this activity includes the layout of
the system as shown in figure 3. Here the containers move
along a conveyor belt where one by one their opacity is mea-
sured and then their weight is taken using the scale. These
two features are stored in the variables x and y respectively.
Once all of the containers have been analyzed the data is run
through the k-means algorithm with k set to 3. The algo-
rithm outputs three groups corresponding to the three differ-
ent types of containers. Now when each container reaches
the end of the conveyor belt the system automatically rotates
the appropriate bin under the container based on its grouping
as identified by the algorithm. The accuracy of this approach
could be evaluated using one of the metrics described such as
the rand index.
Fig. 3. This figure depicts a suggest solution for the recycling
problem. Glass, plastic and cardboard items are placed down
a conveyor belt towards the recycling bins. To extract their
features they each pass through an opacity meter and a scale.
The computer then runs the k-means algorithm to determine
the appropriate bin for each item and rotates the platform ac-
4.2. Bacterial Classification
Several water samples have been obtained from a local pond
as part of a biology lab series. The students in class have al-
ready been learning about plant and animal cells. Through
their lab activities they have developed an appreciation of the
labor involved with the identification and separation of the
plant from animal cells in the pond samples. Since this is go-
ing to be an ongoing project they decide to use their newfound
ML expertise to design a system to automatically identify the
plant and animal cells present in each sample. To increase the
difficulty of the problem we include a third type of bacteria in
the sample such as Euglena, which has both animal and plant
features (i.e. a chloroplast and flagellum).
A potential solution includes setting up a video monitor
that projects the image from a microscope viewing a particu-
lar pond sample as shown in figure 4. The bacteria are each
numerically labeled for tracking. The students decide to ex-
tract three features from each bacterium: shape, size and mo-
bility. The data is entered in spreadsheet form and is submit-
ted to the k-means algorithm. Since they know that there are
two groups of bacteria, plant and animal, they decided to set
k=2. The performance of the algorithm on this test dataset
may be evaluated using any of the metrics discussed such as
the rand index. It should be of interest to the students to see
how the Euglena cells are grouped.
There are several areas for post-lab discussion that are benefi-
cial regardless of the specific example and algorithm chosen.
For instance, perhaps the students ran each experiment multi-
ple times using different features. How did the features affect
performance? Are some superior to others? Could all of the
Fig. 4. This figure depicts a potential scenario for bacterial
classification. The pond sample is placed under a microscope
with a video sensor attached to the lens. This sensor is con-
nected to a large monitor that displays the magnified pond
sample. The data extraction from each object could be com-
pleted by the students or hypothetically by image processing
software. Either way this data is input to the k-means al-
gorithm. The output of the algorithm will specify to which
group each bacterium belongs.
features be used? What about using more than three features?
Can we visualize this data? Why or why not?
Each approach undoubtedly has its own strengths and
weaknesses to be highlighted. In the recycling example the
containers are all analyzed before each is deposited in its
appropriate bin. How does this fair on the design of the
conveyor belt? In the bacterial classification example the stu-
dents had to deal with a bacterium that has both animal and
plant features. How did this bacterium group? Was it consis-
tent? Could they infer whether it is more of one class over the
other? What about automating the feature extraction? Could
they develop a ML technique to automatically measure the
shape, size and motility of each bacterium?
Another important concept is that of generality. The stu-
dents can run their ML design with different datasets, but
remain using the same parameters and features. Based on
the evaluation criteria does each run perform similarity or
are some much better than others? What impact would this
have if they were to spend a large sum of money on an unpre-
dictable solution?
We propose a variety of methods for presenting the lab to the
students, although any combination of pedagogy may be cho-
sen for a particular classroom. Our past experience designing
and implementing signal processing labs on topics such as im-
age processing and bioinformatics have taught us that the stu-
dents tend to respond best to these topics when they are first
briefed on the lab and background followed by a short, open
class discussion [13]. In this ML lab we suggest class par-
ticipation when walking through the example exercise such
as the coin-sorting problem. The students may then break
off into small groups to work on another exercise such as the
bacterial classification problem. The results of each group’s
algorithm performance may then be compared and discussed
collectively as a class. The lab could then conclude with one
or more of the ideas from the suggested class discussion top-
The scalable nature of the proposed ML lab suggests that ad-
ditional lab modules may be developed that expand on the
basic concepts described here. We envision labs utilizing neu-
ral networks to highlight advanced ML techniques as well as
provide insight into biologically inspired algorithms. We also
intend to develop an activity for use in classrooms where stu-
dents have chosen to focus on fields stemming from the cre-
ative arts. We advocate student exposure to these topics dur-
ing secondary education because not only is this lab activity
an introduction to engineering, it is insight into how many de-
cisions are made on a daily basis across virtually all areas of
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