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Dimensionality Reduct
t-SNE
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Stochastic neighborhood embedding (SNE)
“ t-SNE is a tool to visualize high-dimensional data.
It converts simila
between data points to joint probabilities and tries to minimize
the Ku
divergence between the joint probabilities of the
low-dimensional em
the high-dimensional data. ”
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Problems:with dimensionality reduction
● The curse of dimensionality
○ An exponential amount of information is being crushed into an
approximately
○ Distance functions are far less meaningful in high dimensional
space.
with t-SNE
● Optimising a non-convex loss function.
● Large data sets are computationally expensive. Calculating
pairwise relationships
operations. Thus it is just not possible to do t-SNE embeddings
for large datasets l
which has 14 million images (n) and 196608 dimensions (k).
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The Solution:
Soft dimensionality reduction
We plan to test the theory that:
Continuous or incremented (soft) dimensionality reduction will
help preserve more struct
when embedding data from a higher dimension.
Potential realisations of soft dimensionality reduction
● Punishing data points that lie in the higher dimensions (3D
and above) through the
function that we are optimising
● Continuiously transforming the data (through folding and
dekinking) into a 2D plan
● Iteratively using t-SNE to project downward only a small
number of fixed dimensio
2D
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Evaluation (actually it’s another problem)
● Benchmark datasets○ in machine learning. MNIST, CIFAR 10-100,
COIL 20-100, …
● Computational complexity
○ It is straightforward to compare the speed of two algorithms.
Thus any impro
can easily be evaluated.
● Visualisations are subjective○ Changes to the actual
visualisation are inherently subjective. This makes eva
● Autoencoders
○ Will also be used to help validate and generalise the soft dim
reduction techn
that it is not just a property of t-SNE.
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Details
Process
● Iterate○ Literature review and ideas
○ Model design/creation
○ Evaluation
● Write report(s) throughout the year
Timeline
● Important dates○ Prepare preliminary report 6/6/16. Finish
13/6/16.
○ Prepare final report 19/9/16. Finish 26/9/16.
