PP: Deep r -th Root of Rank Supervised Joint Binary Embedding for Multivariate Time Series Retrieval

from: Dacheng Tao 悉尼大学

PROBLEM:

time series retrieval: given the current multivariate time series segment, how to obtain its relevant time series segments in the historical data.

Two challenging:

1. it requires a compact representation of the raw time series, which can explicitly encode the temporal dynamics as well as the correlations (interactions) between different pairs of time series.

2. 查询相似结果的快速性和准确性。

Compact representation: temporal dynamics + correlations 

INTRODUCTION:

问题定义： given the current multivariate time series segment, i.e., a slice of multivariate time series which lasts for a short period of time, we aim to find its most similar time series segments in the historical data (or database). 

A supervised multivariate time series retrieval problem. label information is available in historical data. 

other methods: discrete Fourier transform; discrete wavelet transform; piecewise aggregate approximation; 但是这些方法仅仅针对univariate time series representation and ignore the correlations between different pairs.

?? 不同序列间的相关性也要compact?? 由于是一个窗口内的multivariate time series, 需要衡量他们之间的correlation. 

time serie作为一个独立的个体，如果想研究他们之间的correlations：

1. time series ----> compact representation -----> correlations

2. time series ----> correlation -----> compact representation

To speed up the expensive similarity search。

purpose: multivariate time series retrieval. 

input: a raw multivariate time series segment

steps: 

1. employ lstm units to encode the temporal dynamics
2. use cnn to encode the correlations between different pairs of ts
3. generated two separate feature vectors from the first two steps.
4.  two separate feature vectors ----> a joint binary embedding
5. calculate the similarity between two multivariate ts segments in Hamming space.  
6. r-th root ranking loss to train the disciplined embedding functions.

DEEP r-TH ROOT OF RANK SUPERVISED JOINT BINARY EMBEDDING

1. multivariate time series ----> lstm -----> the last hidden state ht

2. multivariate time series ---> correlation matrix -----> cnn ------> fully connected layer, l

3. joint binary embedding: y = [ht, l]; hash function/ embedding ----> H^v

4. 相比于pairwise similarities,我们使用了segment similarities in the form of triplets. {(X_q,X_i,X_j)}

yq: a query segment, yi: similar segment; yj: dissimilar segment; 

就我目前看来，只是根据r-th ranking loss进行了训练，输入是{(X_q,X_i,X_j)}。但是最终如何检索的，还是不知道。

EXPERIMENTS

To measure the effectiveness of various binary embedding techniques for multivariate time series retrieval, we consider three evaluation metrics, i.e., Mean Average Precision (MAP), precision at top-k positions (Precision@k), and recall at top-k positions (Recall@k).

结果看起来很不错。

SUPPLEMENTARY KNOWLEDGE:

1. hamming distance: 是两个字符串对应位置的不同字符的个数。

例如：

• 1011101与1001001之间的汉明距离是2。
• 2143896与2233796之间的汉明距离是3。
• "toned"与"roses"之间的汉明距离是3。

2. triplet loss

Triplet loss is a loss function for artificial neural networks where a baseline (anchor) input is compared to a positive (truthy) input and a negative (falsy) input. The distance from the baseline (anchor) input to the positive (truthy) input is minimized, and the distance from the baseline (anchor) input to the negative (falsy) input is maximized.^[1][2]