![](bg5.png)
for every set of chromosomes and the sub-sequences
that are formed are exchanged respectively. Then, we
randomly choose a small proportion of the chromo-
somes, based on the mutation rate which was set to
0.4, to undergo mutation, that is the random change
of some elements of a chromosome. In order to guar-
antee that the newly produced chromosomes will not
have been altered too much we perform mutation by
converting 1% of 0’s to 1’s and vice versa.
After the application of genetic operations to the
chromosomes, the new generation has been formed.
In order to perform spectral clustering (Section 2.2),
we need to reconstruct the k-nearest neighbour matrix
A, which will consist of binary digits, from the one-
dimensional vector chromosome. Then we apply the
similarity matrix S on A using the ⊙ operator, in or-
der to obtain the W as illustrated in Figure 1. Spectral
clustering (Ng et al., 2002) may now be performed on
L as in (3).
The next step is to calculate the fitness values of
all the newly produced chromosomes, and place them
along with the parent-chromosomes. Then, elitism is
performed: we sort all chromosomes, with the fittest
being on the top, and we keep only those chromo-
somes with the highest fitness value, so as the number
of the chromosomes kept to remain unchanged after
every generation.
The proposed algorithm terminates when a maxi-
mum of 50 generations has been reached, or when the
optimised criterion has not been altered for 5 consec-
utive generations.
3.4 Semi-supervised Learning
It is natural for many practical problems to con-
sider that we only possess a proportion of labels in a
dataset. Then, the problem of clustering can be trans-
formed into how this small proportion of labels can be
used in order to obtain a better clustering of the data.
Semi-supervised learning (Chapelle et al., 2006), in
machine learning, is a class of techniques which uses
both labeled and unlabeled data, usually a small set
of the former and a large set of the latter, in order to
obtain clusters. In this paper, semi-supervised learn-
ing has been used in clustering, in order to optimise
an external criterion.
In more detail, for some of the experiments, we
have assumed that we possess a small proportion of
labels l of the dataset, which are selected randomly
once and, then, the same labeled data are used in ev-
ery genetic cycle. Then, using only these l labels, we
have computed the fitness value f of the population,
by using one of the external criteria. The evaluation of
the algorithm is performed using only the rest of the
Table 1: Datasets used.
Dataset Duration Classes Size of # of
dataset features
Movie 1 02 : 06 : 21 21 1,222 152×152
Movie 2 01 : 44 : 31 41 1,435 150×150
Dataset Source Classes Size of # of
dataset features
Libras
Movement UCI 15 360 90
Iris UCI 3 150 4
folk dances 5 1012 1000
criteria (and not the one being optimised), which are
also being calculated during every experiment. The
overall value of a criterion is the value of an exter-
nal criterion calculated as if we possessed the labels
for the whole dataset. Thus, this technique uses both
labeled and unlabeled data in order to obtain clusters.
Essentially, only a small proportion of labels was used
in this method for obtaining the fitness values of chro-
mosomes, while the rest of the procedure remained
unchanged.
4 EXPERIMENTS
In order to evaluate the proposed algorithm, we
have conducted several experiments using 5 different
datasets and exploiting several input parameters. The
characteristics of the datasets used, are described in
Table 1.
Datasets “Movie 1” and “Movie 2” consist mainly
of facialimages originate from movies, detected using
a face detector. In the experiments the images were
scaled, in order to have the same size, considering all
the detected facial images of the movie clip and using
a mean bounding box, from all bounding boxes that
the face detector provided. A problem that might arise
is that of anisotropic scaling: the images returned by
the detector might have different height and width,
which is problematic when scaling towards a mean
bounding box, thus we calculate the bigger dimen-
sion of the bounding box and then we take the square
box that equals this dimension centered to the original
bounding box center. Datasets “Libras Movement”
and “Iris” originate from UCI (Newman and Merz,
1998) and consist of less data than the rest. Lastly, the
initial “Folk dances” dataset consists of videos of 5
different traditional dances: Lotzia, Capetan Loukas,
Ramna, Stankena and Zablitsena with 180, 220, 220
201 and 192 videos respectively, from which his-
tograms were extracted according to (Iosifidis et al.,
2013). An example of the dataset is illustrated in Fig-
ure 4.
The size of the populations remained unchanged
SpectralClusteringUsingEvolvingSimilarityGraphs
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