BACKGROUND

Technical Field

The present disclosure relates to the field of data compression, and more particularly to lossy compression of data based on statistical properties, e.g., for storage and communication of sensor data.

Description of the Related Art

In order to continuously transfer machine data time series between computers (e.g., from an edge device that is collecting one or more machine's data and sending to one or more cloud servers) one computer typically transfers all of the sensor data values collected from the machine(s) at each timestamp along with timestamp data and optionally position data (e.g., GPS location) or other context information, to another computer, which may be in the cloud. This communication burden is one of the main challenges in Internet of things (IoT) data transfer, due of the cost of transferring the large volume of data. Further, latency may increase and communication reliability may decrease with increasing data volume.

The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding; encoding done at the source of the data before it is stored or transmitted.

In signal processing, data compression, source coding, or bit-rate reduction typically involves encoding information using fewer bits than the original representation. Compression can be either lossy or lossless. Lossless compression reduces bits by identifying and eliminating redundancy. This reduction may be deterministic, i.e., reduction in bits is assured, or statistical, i.e., a particular type of redundancy reduction under most circumstances leads to a net reduction in bit required for encoding. No information is lost in lossless compression.

Lossless data compression algorithms usually exploit statistical redundancy to represent data without losing any information, so that the process is reversible. Lossless compression relies on the fact that real world data typically has redundancy (lack of entropy). Therefore, by reencoding the data to increase the entropy of the expression, the amount of data (bits) may be reduced. The Lempel-Ziv (LZ) compression methods employ run-length encoding. For most LZ methods, a table of previous strings is generated dynamically from earlier data in the input. The table itself is often Huffman encoded. Grammar-based codes like this can compress highly repetitive input extremely effectively, for instance, a biological data collection of the same or closely related species, a huge versioned document collection, internet archival, etc. The basic task of grammar-based codes is constructing a context-free grammar deriving a single string. Other practical grammar compression algorithms include Sequitur and Re-Pair.

Some lossless compressors use probabilistic models, such as prediction by partial matching. The Burrows-Wheeler transform can also be viewed as an indirect form of statistical modeling. In a further refinement of the direct use of probabilistic modeling, statistical estimates can be coupled to an algorithm called arithmetic coding, which uses the mathematical calculations of a finite-state machine to produce a string of encoded bits from a series of input data symbols. It uses an internal memory state to avoid the need to perform a one-to-one mapping of individual input symbols to distinct representations that use an integer number of bits, and it clears out the internal memory only after encoding the entire string of data symbols. Arithmetic coding applies especially well to adaptive data compression tasks where the statistics vary and are context-dependent, as it can be easily coupled with an adaptive model of the probability distribution of the input data.

Lossy compression typically reduces the number of bits by removing unnecessary or less important information. This can involve predicting which signal aspects may be considered noise, and/or which signal aspects have low importance for the ultimate use of the data. Lossy data compression is, in one aspect, the converse of lossless data compression, which loses information. However, subject to loss of information, the techniques of lossless compression may also be employed with lossy data compression.

There is a close connection between machine learning and compression: a system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression (by using arithmetic coding on the output distribution) while an optimal compressor can be used for prediction (by finding the symbol that compresses best, given the previous history).

Compression algorithms can implicitly map strings into implicit feature space vectors, and compression-based similarity measures used to compute similarity within these feature spaces. For each compressor C(.) we define an associated vector space ϰ, such that C(.) maps an input string x, corresponds to the vector norm ∥˜x∥.

In lossless compression, and typically lossy compression as well, information redundancy is reduced, using methods such as coding, pattern recognition, and linear prediction to reduce the amount of information used to represent the uncompressed data. Due to the nature of lossy algorithms, quality suffers when a file is decompressed and recompressed (digital generation loss). (Lossless compression may be achieved through loss of non-redundant information, so increase in entropy is not assured.)

In lossy compression, the lost information is, or is treated as, noise. One way to filter noise is to transform the data to a representation where the supposed signal is concentrated in regions of the data space, to form a sparse distribution. The sparse regions of the distribution may be truncated, e.g., by applying a threshold, and the remaining dense regions of the distribution may be further transformed or encoded. Multiple different methods may be employed, to reduce noise based on different criteria.

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Wireless Sensor Networks (WSN) typically consist of a large number of sensors distributed in a sensing area to serve different tasks, such as continuous environmental monitoring. These networks are intended to continuously sense an area of interest and transmit the sensed data to a sink node. Due to the power consumption constraints, it is inefficient to directly transmit the raw sensed data to the sink, as they often exhibit a high correlation in the spatial and temporal domains and can be efficiently compressed to reduce power and bandwidth requirements, and reduce latency, and provide greater opportunity for error detection and correction (EDC) encoding. See:

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Spatial correlation in WSN refers to, e.g., the correlation between the sensed data at spatially adjacent sensor nodes. On the other hand, temporal correlation usually refers to the slow varying nature of the sensed data. Compressive sensing (CS) is a tool that provides a means to process and transport correlated data in an efficient manner by exploring the sparsity of these data. Temporal correlation can be modeled in the form of a multiple measurement vector (MMV), where it models the source as an auto regressive (AR) process and then incorporates such information into the framework of sparse Bayesian learning for sparse signal recovery and converts MMV to block single measurement vector (SMV) model. Compressive sensing theory provides an elegant mathematical framework to compress and recover signals using a small number of linear measurements. Under certain conditions on the measurement matrix, the acquired signal can be perfectly reconstructed from these measurements.

A mean is a commonly used measure of central tendency, and is influenced by every value in a sample according to the formula:

μ=∑XN

where μ is population mean, andXis sample mean.

A standard deviation is a measure of variability, according to the formula:

σ=∑(X-μ)2N

(if μ is unknown, useX)

A small sample bias may be corrected by dividing by n−1, where n is the number of samples, i.e.:

σ=∑(X-X¯)2n-1

A normal distribution has a bell shaped curve, and is a reasonably accurate description of many (but not all) natural distributions introduced by a random process. It is unimodal, symmetrical, has points of inflection at μ±σ, has tails that approach x-axis, and is completely defined by its mean and standard deviation.

The standard error of the mean, is a standard deviation of sampling error of different samples of a given sample size. For a sampling error of (X−μ), as n increases, variability decreases:

σX_-=σn

“File Compression Possibilities”. A Brief guide to compress a file in 4 different ways.

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