https://github.com/petroniocandido/nde_tsc
Neural Density Estimation for Time Series Classification
https://github.com/petroniocandido/nde_tsc
autoencoder deep-learning density-estimation locality-sensitive-hashing neural-density-estimation neural-networks pytorch self-organizing-map siamese-network time-series-classification
Last synced: about 2 months ago
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Neural Density Estimation for Time Series Classification
- Host: GitHub
- URL: https://github.com/petroniocandido/nde_tsc
- Owner: petroniocandido
- License: mit
- Created: 2023-09-19T11:27:11.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2023-09-20T17:45:27.000Z (over 2 years ago)
- Last Synced: 2023-09-21T03:53:39.125Z (over 2 years ago)
- Topics: autoencoder, deep-learning, density-estimation, locality-sensitive-hashing, neural-density-estimation, neural-networks, pytorch, self-organizing-map, siamese-network, time-series-classification
- Language: Python
- Homepage:
- Size: 93.8 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Self Organized Neural Density Estimation for Complex Time Series Classification
[](https://www.python.org/) [](https://www.latex-project.org/) 
* Petrônio C. L. Silva 
* Omid Orang
* Felipe A. R. da Silva
* Fabricio J. E. Costa
* Frederico G. Guimarães
In case you have any questions, do not hesitate in contact us using the following e-mail: petronio.candido@ifnmg.edu.br
The Time Series Classification is posed such that given a set of $M$ instances of time series $Y = \{ Y_1, \ldots, Y_M \}$, where all instances are IID and have the same number $T$ of samples $y(t) \in \mathbb{R}^N, \; \forall t=1\ldots T$, with $N$ attributes, and a discrete set of labels $C = \{0, \ldots, k\}$, each time series $Y_i$ should be associated with a label $j \in C$.
The present proposal aims to investigate methods for computing both the unconditional probability distribution $P(Y_i)$ and the conditional probability distribution $P(Y_i | c)$, $\forall c \in C$ and $Y_i \in Y$. Representing the data space in terms of the $[0,1]$ probability space is a challenging task due to the high dimensionality of $Y$, with the order of $R^N \times T$ dimensions.
To allow the representation o $Y$ in probability space, the present research proposes an approach based in Neural Networks in two layers: a) the embedding layer implemented using AutoEncoders and b) the density layer implemented using Self Organizing Maps and k-Nearest-Neighbors.
The embedding layer aims to learn a function $f_\mathcal{E}: Y \rightarrow \mathcal{E}$ that maps the original data space $Y \in \mathbb{R}^{T \times N}$ to a smaller dimensional space $\mathcal{E} \in \mathbb{R}^D$ dimensions, where $D \ll T \times N$. The embedding space $\mathcal{E}$ should keep, as much as possible, the properties and topoloty of the original space $Y$ such as the distances $d(Y_i, Y_j)$ of each pair of instances $Y_i, Y_j \in Y$, where $d: Y \times Y \rightarrow \mathbb{R}^+$ is a distance function.
The density layer aims to learn a map $W$ that represent the topology of the embedding space using a square $L \times A$ grid of cells $w_{i,j} \in \mathbb{R}^D$, where each cell $w_{i,j} \in W$ represents a prototype or representative value of a region of the $\mathcal{E}$ space.
Our proposal learns two more discrete maps, $P$ and $P_k$, where $P[w_{i,j}]$ represents the unconditional probability mass of a the cell $w_{i,j}$ in $\mathcal{E}$ space and $P_k[w_{i,j}]$ represents the the conditional probability mass of a the cell $w_{i,j}$ in $\mathcal{E}$ space given the class label $k \in C$.
With the maps $W$, $P$ and $P_k$ it is possible to calculate the unconditional $P(Y_i)$ and conditional probabilities $P(Y_i|k)$ for any continuous time series in $Y$, by embedding $Y_i$ such that $e_i = f_\mathcal{E}(Y_i)$, finding the k-nearest-neighbors of $e_i$ using the square map $W$ and then interpolate its probabilities weighted by their distances.