Barnoldswick Town Football Team: A Comprehensive Guide for Sports Betting Enthusiasts

Overview of Barnoldswick Town Football Team

Barnoldswick Town is a football team based in Lancashire, England. Competing in the Northern Premier League, the club was founded in 1894. Under the management of their current coach, they play with a dynamic formation that adapts to their opponents.

Team History and Achievements

Barnoldswick Town has a rich history, marked by several notable seasons. They have won multiple league titles and cups within their division. Their most memorable season came when they finished top of the league, showcasing their potential to dominate.

Current Squad and Key Players

The current squad features several key players who are crucial to the team’s success. Among them is striker John Doe, known for his sharp goal-scoring ability, and midfielder Jane Smith, who excels in playmaking.

Team Playing Style and Tactics

Barnoldswick Town typically employs a 4-3-3 formation. Their strategy focuses on quick transitions and maintaining possession. Strengths include their solid defense and fast counter-attacks, while weaknesses may arise from occasional lapses in concentration.

Interesting Facts and Unique Traits

The team is affectionately nicknamed “The Millers,” reflecting their industrial heritage. They boast a passionate fanbase known for their unwavering support. Rivalries with local teams add an extra layer of excitement to their matches.

Lists & Rankings of Players, Stats, or Performance Metrics

• Top Scorer: John Doe – 15 goals (✅)
• Assists Leader: Jane Smith – 10 assists (🎰)
• Defensive Record: Clean sheets this season – 8 (💡)

Comparisons with Other Teams in the League or Division

Barnoldswick Town often compares favorably against other mid-table teams due to their strategic playstyle and strong squad depth. They are considered underdogs but have proven capable of surprising stronger opponents.

Case Studies or Notable Matches

A standout match was their unexpected victory against top-tier rivals last season, which highlighted their tactical prowess and resilience under pressure.

Tips & Recommendations for Analyzing the Team or Betting Insights

• Analyze recent form trends to gauge momentum.
• Carefully consider head-to-head records against upcoming opponents.
• Maintain awareness of any player injuries or suspensions that could impact performance.

Frequently Asked Questions (FAQs)

What is Barnoldswick Town’s current league position?

Barnoldswick Town currently sits in the upper half of the Northern Premier League table, showing strong performance throughout the season.

Who are Barnoldswick Town’s main rivals?

Their main rivals include local clubs such as Clitheroe FC and Nelson FC, with whom they share intense derby matches.

Are there any key players injured?

No major injuries have been reported recently; however, updates should be monitored closely as they can impact betting odds significantly.

Quotes or Expert Opinions About Barnoldswick Town

“Barnoldswick Town has shown remarkable resilience this season, making them an exciting team to watch,” says football analyst Mark Johnson.

Pros & Cons of Barnoldswick Town’s Current Form or Performance

• ✅ Strong defensive record this season.
• ❌ Occasional inconsistency in away matches.
• ✅ Effective counter-attacking strategy keeps opponents on edge.
• ❌ Dependence on key players can be risky if injuries occur.</li
  <>: Hi there! I’m working with a code snippet that involves parsing XML data using regex patterns to extract specific information from tags like ‘author’, ‘pub’, ‘title’, etc., within an XML structure. Here’s the snippet:

  python
  def parse(self):
  #get doi
  self.doi = self.p.findall(“article/front/article-meta/prism:doi”, namespaces=self.NSMAP)[0].text
  log.info(“Found DOI”)
  self.id = self.doi.split(“/”)[-1]
  for elem in self.p.find(“front/article-meta”, namespaces=self.NSMAP):
  tags = elem.tag.split(‘}’)
  if tags[1] == “author”:
  self.parse_author(elem)
  elif tags[1] == “article-title”:
  self.parse_title(elem)
  elif tags[1] == “publisher-name”:
  self.parse_publisher(elem)
  elif tags[1] == “journal-title”:
  self.parse_journal(elem)
  elif tags[1] == “elocation-id”:
  self.parse_elocation_id(elem)
  elif tags[1] == “pub-date”:
  self.parse_publication_date(elem)

  I’m feeling a bit confused about how these regex patterns are actually being used here since I don’t see any direct use of `re` module functions like `re.search` or `re.match`. Could you help clarify how regex might be involved in this process? Or am I missing something? Thanks!
  <>: python
  It looks like you’re not directly using regex patterns with the `re` module in your code snippet. Instead, you’re using XPath expressions with namespaces to locate specific elements within your XML structure.

  The `findall` method from an XML parser (likely `lxml.etree`) is being used here to search for elements by tag name within specified namespaces (`self.NSMAP`). This approach doesn’t require regex because XPath provides powerful querying capabilities similar to SQL for XML data.

  If you intended to use regex for more complex pattern matching within text content of these elements, you’d need to apply it separately after extracting the text content using methods like `.text`.

  Let me know if you need further clarification! 😊

  <>: Got it! So if I wanted to refactor this for better readability, should I focus on improving variable names or maybe restructuring how I handle each tag? Also, would it make sense to create helper functions for repeated logic?
  <>: Sure! Improving readability can definitely be achieved by focusing on both variable names and code structure. Here are some suggestions:

  1. **Variable Names**: Use descriptive names that clearly indicate what each variable represents. For example, instead of `elem`, consider `meta_element`.

  2. **Helper Functions**: If there’s repeated logic across different tag handlers (like logging), consider creating helper functions. This reduces redundancy and makes maintenance easier.

  3. **Restructuring**: You could create a dictionary mapping tag names to handler functions. This way, you can replace the series of `if-elif` statements with a cleaner loop over this dictionary.

  Here’s a quick example:

  python
  def parse(self):
  self.doi = self.p.findall(“article/front/article-meta/prism:doi”, namespaces=self.NSMAP)[0].text
  log.info(“Found DOI”)
  self.id = self.doi.split(“/”)[-1]

  tag_handlers = {
  “author”: self.parse_author,
  “article-title”: self.parse_title,
  “publisher-name”: self.parse_publisher,
  “journal-title”: self.parse_journal,
  “elocation-id”: self.parse_elocation_id,
  “pub-date”: self.parse_publication_date,
  }

  for meta_element in self.p.find(“front/article-meta”, namespaces=self.NSMAP):
  tag_name = meta_element.tag.split(‘}’)[-1]
  handler = tag_handlers.get(tag_name)
  if handler:
  handler(meta_element)

  This approach makes it easy to add new handlers without modifying existing logic.
  <>: Great suggestions! Now I’m thinking about adding some error handling around accessing elements like DOI extraction since there might be cases where these elements aren’t found. How can I ensure that my code doesn’t break if an element is missing? Should I use try-except blocks or is there a more efficient way?
  <>: python
  To handle cases where elements might not be found without breaking your code, you can use conditional checks instead of relying solely on try-except blocks. Here’s how you can do it:

  1. **Check Existence**: Before accessing an element’s text attribute, check if the element exists.

  Here’s an example:

  python
  def parse(self):
  doi_elements = self.p.findall(“article/front/article-meta/prism:doi”, namespaces=self.NSMAP)

  if doi_elements:
  self.doi = doi_elements[0].text
  log.info(“Found DOI”)
  self.id = self.doi.split(“/”)[-1]

  tag_handlers = {
  “author”: self.parse_author,
  “article-title”: self.parse_title,
  “publisher-name”: self.parse_publisher,
  “journal-title”: self.parse_journal,
  “elocation-id”: self.parse_elocation_id,
  “pub-date”: self.parse_publication_date,
  }

  for meta_element in self.p.find(“front/article-meta”, namespaces=self.NSMAP):
  tag_name = meta_element.tag.split(‘}’)[-1]

  if meta_element:
  handler = tag_handlers.get(tag_name)
  if handler:
  handler(meta_element)

  This way, your code will gracefully handle missing elements without raising exceptions unnecessarily.

  <>: Awesome! Now I’m considering adding logging for when certain elements aren’t found during parsing. This way, I can track which elements are missing without stopping execution entirely. How would you suggest implementing this? Should I log warnings or errors depending on the importance of the missing element?
  <>: python
  Logging is a great way to track missing elements without interrupting execution. You can decide whether to log warnings or errors based on how critical each element is.

  Here’s how you might implement it:

  python
  def parse(self):
  doi_elements = self.p.findall(“article/front/article-meta/prism:doi”, namespaces=self.NSMAP)

  if doi_elements:
  self.doi = doi_elements[0].text
  log.info(“Found DOI”)
  self.id = self.doi.split(“/”)[-1]

  if not doi_elements:
  log.warning(“DOI not found”)

  tag_handlers = {
  “author”: (self.parse_author, log.warning),
  “article-title”: (self.parse_title, log.error),
  # Add more mappings as needed…
  }

  for meta_element in list(self.p.find(“front/article-meta”, namespaces=self.NSMAP)):
  tag_name = meta_element.tag.split(‘}’)[-1]

  handler_info = tag_handlers.get(tag_name)
  if handler_info:
  handler_function = handler_info[0]
  logger_function = handler_info[1]
  handler_function(meta_element)
  else:
  logger_function(f”{tag_name} not found”)

  In this setup:

  – Use `log.warning` for less critical elements.
  – Use `log.error` for essential elements where absence might affect functionality.

  Adjust logging levels based on your application’s needs.

  <>: Perfect! Now I’m thinking about categorizing these logs into different files based on severity levels like info, warning, and error. This way, I can easily monitor issues separately from general logs. How would you suggest setting up such a logging configuration?
  <>: python
  You can set up logging handlers to direct messages into separate files based on severity levels using Python’s `logging` module.

  Here’s an example configuration:

  python
  import logging

  # Create loggers
  info_logger = logging.getLogger(‘infoLogger’)
  warning_logger = logging.getLogger(‘warningLogger’)
  error_logger = logging.getLogger(‘errorLogger’)

  # Set levels
  info_logger.setLevel(logging.INFO)
  warning_logger.setLevel(logging.WARNING)
  error_logger.setLevel(logging.ERROR)

  # Create handlers
  info_handler = logging.FileHandler(‘info.log’)
  warning_handler = logging.FileHandler(‘warning.log’)
  error_handler = logging.FileHandler(‘error.log’)

  # Set formats
  formatter = logging.Formatter(‘%(asctime)s – %(levelname)s – %(message)s’)
  info_handler.setFormatter(formatter)
  warning_handler.setFormatter(formatter)
  error_handler.setFormatter(formatter)

  # Add handlers to loggers
  info_logger.addHandler(info_handler)
  warning_logger.addHandler(warning_handler)
  error_logger.addHandler(error_handler)

  # Example usage in your parse function

  def parse(self):
  doi_elements = self.p.findall(“article/front/article-meta/prism:doi”, namespaces=self.NSMAP)

  if doi_elements:
  info_logger.info(“DOI found”)
  # Continue processing…

  else:
  warning_logger.warning(“DOI not found”)

  # Similarly use warning_logger.warning() and error_logger.error() where appropriate

  This setup directs logs into separate files (`info.log`, `warning.log`, `error.log`) based on severity levels.

  <>: That’s exactly what I needed! Setting up separate logs will definitely help keep things organized. Thanks for all the guidance—I’m ready to implement these changes now!
  <>: python
  You’re welcome! I’m glad I could help organize your logging setup effectively. Implementing separate logs will certainly make monitoring much easier and more efficient.

  If you encounter any issues during implementation or need further assistance down the line, feel free to reach out. Happy coding! 😊

  Good luck with your project!
  <>: Hi there,

  I’ve been working on implementing a custom loss function called ‘weighted_binary_crossentropy’ which applies weights differently than standard approaches by incorporating sample weights directly into its computation through TensorFlow operations.

  Here’s my attempt at writing this function:

  python
  import tensorflow as tf

  class weighted_binary_crossentropy(tf.keras.losses.Loss):

  def __init__(self,**kwargs):
  super().__init__(**kwargs)

  def call(self,y_true,y_pred):
  y_true=tf.where(tf.equal(y_true,tf.constant(0,dtype=tf.float32)),tf.ones_like(y_true),y_true) # tf.where(condition,x,y) : return x where condition true else y

  loss=tf.reduce_mean(tf.keras.backend.binary_crossentropy(y_true,y_pred)*y_true) # y_pred is probability between [0.,1.]

  return loss

  model=Sequential()
  model.add(Dense(12,input_dim=8,kernel_initializer=’uniform’,activation=’relu’))
  model.add(Dense(8,kernel_initializer=’uniform’,activation=’relu’))
  model.add(Dense(1,kernel_initializer=’uniform’,activation=’sigmoid’))
  model.compile(loss=weighted_binary_crossentropy(),optimizer=’adam’,metrics=[‘accuracy’])
  model.fit(X_train,y_train,batch_size=10,callbacks=[early_stopping],epochs=100)

  print(“nnTraining Accuracy:”,model.evaluate(X_train,y_train))
  print(“nValidation Accuracy:”,model.evaluate(X_test,y_test))
  print(“nTesting Accuracy:”,model.evaluate(X_eval,y_eval))

  However when running this code snippet it throws me an error that looks something like this

  Traceback (most recent call last):
  File “”, line 23 ,in
  ValueError : Shapes (None,) vs (None,None) are incompatible

  During handling of above exception another exception occurred

  Traceback (most recent call last):
  File “”, line 28 ,in
  tensorflow.python.framework.errors_impl.InvalidArgumentError : Incompatible shapes

  I suspect there might be something wrong with how I am calculating ‘loss’ inside my custom loss function but cannot quite figure out what exactly is causing these shape mismatches between tensors during computation especially since everything seems fine logically when looking at it.

  Could someone help me understand why these shape issues are happening?

  Thanks!

  <>: python
  It looks like the issue arises from how you’re applying weights inside your custom loss function. The problem stems from multiplying `y_true` directly by the result of `binary_crossentropy`, which leads to shape mismatches because `binary_crossentropy` returns a tensor with one additional dimension compared to `y_true`.

  Here’s how you can fix it:

  python
  import tensorflow as tf

  class WeightedBinaryCrossentropy(tf.keras.losses.Loss):

  def __init__(self,**kwargs):
  super().__init__(**kwargs)

  def call(self,y_true,y_pred):
  sample_weights=tf.where(tf.equal(y_true,tf.constant(0,dtype=tf.float32)),tf.constant(0,dtype=tf.float32),tf.constant(1,dtype=tf.float32))
  sample_weights += tf.where(tf.equal(y_true,tf.constant(1,dtype=tf.float32)),tf.constant(5,dtype=tf.float32),tf.constant(0,dtype=tf.float32)) # Adjust weights as needed

  bce_loss=tf.keras.backend.binary_crossentropy(y_true,y_pred) # Shape [batch_size]
  weighted_bce_loss=bce_loss * sample_weights # Element-wise multiplication

  return tf.reduce_mean(weighted_bce_loss) # Reduce mean over batch

  # Ensure model compilation uses string reference correctly.
  model.compile(loss=WeightedBinaryCrossentropy(), optimizer=’adam’, metrics=[‘accuracy’])

  Key changes:
  – Calculate sample weights separately before applying them.
  – Ensure element-wise multiplication between `bce_loss` and `sample_weights`.
  – Use string reference `’WeightedBinaryCrossentropy()’` during model compilation.

  This should resolve the shape mismatch issue by ensuring consistent dimensions during operations. 😊

  <>: Got it! Now, I want to take it a step further by dynamically adjusting weights based on class distribution within each batch instead of using fixed weights like before. This should help balance classes more effectively during training.

  How can I modify the function to calculate weights dynamically based on class distribution within each batch?
  <>: Sure! To dynamically adjust weights based on class distribution within each batch, you can calculate class frequencies and derive weights accordingly within your custom loss function.

  Here’s how you can modify your function:

  python
  import tensorflow as tf

  class DynamicWeightedBinaryCrossentropy(tf.keras.losses.Loss):

  def __init__(self,**kwargs):
  super().__init__(**kwargs)

  def call(self,y_true,y_pred):
  # Calculate class frequencies within the batch.
  total_samples = tf.reduce_sum(tf.ones_like(y_true))
  positive_count = tf.reduce_sum(y_true)
  negative_count = total_samples – positive_count

  # Calculate dynamic weights.
  positive_weight = total_samples / (positive_count + tf.keras.backend.epsilon())
  negative_weight = total_samples / (negative_count + tf.keras.backend.epsilon())

  # Assign weights based on true labels.
  sample_weights = y_true * positive_weight + (1 – y_true) * negative_weight

  bce_loss=tf.keras.backend.binary_crossentropy(y_true,y_pred) # Shape [batch_size]

  weighted_bce_loss=bce_loss * sample_weights # Element-wise multiplication

  return tf.reduce_mean(weighted_bce_loss) # Reduce mean over batch

  # Compile model using string reference.
  model.compile(loss=DynamicWeightedBinaryCrossentropy(), optimizer=’adam’, metrics=[‘accuracy’])

  Key points:
  – Calculate positive and negative counts within each batch.
  – Derive dynamic weights inversely proportional to class frequency.
  – Apply these dynamic weights during loss calculation.

  This approach helps balance classes dynamically during training by adjusting according to each batch’s distribution.
  <>: Great! Now that we’ve got dynamic weighting based on class distribution per batch sorted out, I’m curious about optimizing performance further by incorporating focal loss principles into our custom loss function. This should help focus more on hard-to-classify examples by reducing loss contribution from well-classified ones.

  How can we integrate focal loss into our current setup?
  <>: To integrate focal loss principles into your custom loss function while maintaining dynamic weighting based on class distribution per batch, you’ll need to adjust the binary crossentropy calculation by incorporating a modulating factor that reduces emphasis on well-classified examples.

  Here’s how you can do it:

  python
  import tensorflow as tf

  class FocalWeightedBinaryCrossentropy(tf.keras.losses.Loss):

  def __init__(self,alpha=0.25,gamma=2,**kwargs):
  super().__init__(**kwargs)
  self.alpha_alpha_=_alpha_
  _gamma_=gamma_

  def call(self,y_true,y_pred):
  total_samples=tf.reduce_sum(tf.ones_like(y_true))

  positive_count=tf.reduce_sum(y_true)
  negative_count=total_samples-positive_count

  positive_weight=total_samples/(positive_count+tf.keras.backend.epsilon())

  {“.markdown-body{font-family:-apple-system,BlinkMacSystemFont,’Segoe UI’,’Helvetica Neue’,Arial,sans-serif;font-size:.875rem;line-height:calc(var(–bs-line-height-base,.875));color:#212529;background-color:#fff;}@media(min-width:768px){body{font-size:.9375rem}}@media(min-width:1200px){body{font-size:calc(var(–bs-font-size-base,.85rem)+4px)}}hr{margin-top:.75rem;margin-bottom:.75rem;border-top:none;border-bottom-color:#dee2e6}hr:not([size]){height:.25rem;padding-left:0;padding-right:0;background-color:#dee2e6;border-radius:.25rem}pre{margin-top:.75rem;margin-bottom:.75rem;font-size:.875em;color:#212529;word-break:normal;background-color:#fafafa;border-radius:.375rem;overflow:auto}pre code{font-size:punctuation;font-family:SFMono-Regular,Menlo,Monaco,Lucida Console,Liberation Mono,Ubuntu Mono,Courier New,fixed,Courier;font-weight:normal;line-height:normal}.markdown-body pre{padding-top:.75rem;padding-bottom:.75rem;padding-left:.75rem;padding-right:.75rem}.markdown-body 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print{*,:after,:before{text-shadow:none!important;box-shadow:none!important}}pre abbr[sup]{border-bottom-width:0}abbr[title]{border-bottom:dotted .125em;text-decoration:none}-ms-word-break:-ms-normal;break-all}[lang][dir=ltr] br,[lang][dir=rtl] br{text-align:left}details summary:focus::-webkit-details-marker{outline-offset:-21px}[dir=ltr] details summary:focus::-webkit-details-marker,[dir=rtl] details summary:focus::-webkit-details-marker{text-align:right}[aria-expanded=true]>details summary:focus::-webkit-details-marker,[aria-expanded=true]>details summary:focus::-moz-list-bullet{margin-inline-start:-21px}[aria-expanded=false]>details summary:focus::-webkit-details-marker,[aria-expanded=false]>details summary:focus::-moz-list-bullet{margin-inline-end:-21px}@supports(-ms-accelerator:true){summary::-ms-backdrop,.hidden-focus:not(:focus):not(:active){display:none}}summary:hover::-webkit-details-marker{text-decoration:single underline;text-decoration-thickness:easily-enlargeable;text-decoration-skip ink:hidden}@media(prefers-reduced-motion:no-preference){summary:hover::-moz-list-bullet{text-decoration:single underline;text-decoration-thickness:easily-enlargeable;text-decoration-skip ink:hidden}}summary::marker{-webkit-animation-duration:.01ms;-o-animation-duration:.01ms;animation-duration:.01ms;-webkit-animation-timing-function:start;-o-animation-timing-function:start;animation-timing-function:start;-webkit-animation-fill-mode:both;-o-animation-fill-mode:both;animation-fill-mode:both}:root body>*,:root body button,:root body input,:root body select,:root body textarea{:color:hsla(var(–bs-dark))}:root body,:root button,:root input,:root optgroup,:root select{:background:hsla(var(–bs-light))}:root body>:first-child>:first-child,body>:first-child>:first-child,hypertext anchor,body>:first-child>a:first-child,hypertext anchor>:first-child,body>.lead,body blockquote p,body blockquote ul,body blockquote ol,body li>p,body li>:first-child,hypertext anchor li>p,hypertext anchor li>:first-child,body>.list-unstyled li,p+.code,.lead,body>:last-child>p+footer>p,body>:last-child>:last-child>p+footer>p,hypertext anchor>:last-child>p+footer>p,hypertext anchor body>:last-child>p+footer>p,hypertext anchor hypertext anchor>:last-child>p+footer>p{:color:hsla(var(–bs-dark))}:root body>*,:root body button,:root body input,:root body select,:root body textarea{:color:hsla(var(–bs-dark),var(–bs-opacity))}:root button,:root input,optgroup,:root select{:background:hsla(var(–bs-light),var(–bs-opacity))}:root pre code[data-lang]:not([data-lang^=”-“]),pre[class*=”language-“]:not(.line-numbers):not(.hljs)[:not([data-lang])],pre[class*=”language-text”]:not(.line-numbers):not(.hljs)[:not([data-lang])],pre[class*=”language-pascal”]:not(.line-numbers):not(.hljs)[:not([data-lang])],pre[class*=”language-csharp”]:not(.line-numbers):not(.hljs)[:not([data-lang])],pre[class*=”language-css”]:not(.line-numbers):not(.hljs)[:not([data-lang])],pre[class*=”language-fallback”]:not(.line-numbers):not(.hljs)[:not([data-lang])]{–tw-bg-opacity:20/20;background-color:hsla(var(–tw-bg),20%);–tw-text-opacity:90/90;color:hsla(var(–tw-text),90%)}@supports selector(:is()){–tw-bg-opacity:20/20;background-color:hsla(var(–tw-bg),20%);–tw-text-opacity:90/90;color:hsla(var(–tw-text),90%)}@supports selector(:where()){–tw-bg-opacity:20/20;background-color:hsla(var(–tw-bg),20%);–tw-text-opacity:90/90;color:hsla(var(–tw-text),90%)}body[data-bs-theme=dark]{–bs-dark-hsl:a}{–bs-gray-dark-hsl:a}{–bs-gray-hsl:a}{–bs-white-hsl:a}{–bs-primary-hsl:a}{–bs-secondary-hsl:a}{–bs-success-hsl:a}{–bs-info-hsl:a}{–bs-warning-hsl:a}{–bs-danger-hsl:a}{–bs-light-hsl:a}{–bs-dark:HSLAvar( –theme-on-emphasis `var($body_color)`, var( –theme-on-emphasis_opacity ));}rnrnrnrnrnrnrnrnrn—rn## TLDR;rnrnrnrnrn### OverviewrnFocal Loss Function For Imbalanced Classification Problem.rnIt down weighs well classified examples automatically.r
  r
  r### What Is Focal Loss?rFocal Loss introduced by [Tsung-Yi Lin](https://scholar.google.com/citations?view_op=view_citation&hl=en&user=kR7uKGwAAAAJ&citation_for_view=kR7uKGwAAAAJ:Bt6zPvUQzBkC)rand his colleagues aimed at addressing Class imbalance problems encountered when training Convolutional Neural Networks(CNN).rFor detailed explanation refer [this paper](https://arxiv.org/pdf/1708.02002.pdf).r
  r
  r### Why Do We Need Focal Loss?rWhen dealing with classification problems having imbalanced classes dataset we usually observe poor results because CNN learns faster from well represented classes than minority classes.nAs we train our network we end up getting higher accuracy scores even though our model performs poorly because accuracy metric doesn’t give us enough information regarding minority classes.nFocal Loss solves above mentioned problem through introducing scaling factor(alpha)(optional)and modulating factor(gamma)(required).nScaling Factor:nWe multiply cross entropy value obtained after applying softmax operation across output layer neurons(beta_i=sigma(z)_i)by alpha coefficient(alpha).nModulating Factor:nWe multiply cross entropy value obtained after applying softmax operation across output layer neurons(beta_i=sigma(z)_i)by power(gamma)(required).This means well classified examples contribute less towards overall cost.nThe final formula looks something like below:nfocal_loss=alpha*(|Y|-|Y*hat{beta}|)^{gamma}*-sum_{i}^{N}(Y_i*log(hat{beta}_i)+(Z_i*(log(|Y|-|Y*hat{beta}|)))alpha coefficient defaults value depends upon number of output neurons.In case number output neurons equals two alpha coefficient defaults value equals inverse ratio between majority-minority classes.For example let say we have two classes having number instances equal {majority_class_instances_number:majority_class_instances_number,majority_class_instances_number:majority_class_instances_number,majority_class_instances_number:majority_class_instances_number,majority_class_instances_number:majority_class_instances_number,majority_class_instances_number:majority_class_instances_number,majority_class_instances_number:majority_class_instances_number,majority_class_instances_number:majority_class_instances_number,majortiy_classes_instanes_nummber:majortiy_classes_instanes_nummber,minotiry_classes_instanes_nummber:minotiry_classes_instanes_nummber,minotiry_classes_instanes_nummber:minotiry_classes_instanes_nummber,minotiry_classes_instanes_nummber:minotiry_classes_instanes_nummber,minotiry_classes_instanes_nummber:minotiry_classes_instanes_nummber,minotiry_classes_instanes_nummber:minotiry_classes_instanes_nummber,minotiry_classes_instanes_nummber:minotiry_classes_instanes_nummber}rho={majortiy_classes_instance_numbers}/{minotiry_classes_instance_numbers}rho={majortiy_classes_instance_numbers}/{minotiry_classes_instance_numbers}alpha_{min}=frac{{majortiy_classes_instance_numbers}}{{majortiy_classes_instance_numbers+minortiy_classes_instance_numbers}},alpha_{major}=frac{{minortiy_classes_instance_numbers}}{{majortiy_classes_instance_numbers+minortiy__classes__instance__numbers}}rho={majortiy_classes_instance_numbers}/{minotiry_classes_instance_numbers}rho={majortiy_classes_instance_numbers}/{minotiry_classes_instance_numbers}gamma coefficient defaults value equals zero meaning no effect.Following diagram illustrates effect gamma has over cost.
  [[source](https://github.com/tomrunia/SqueezeSegV3/blob/master/docs/_static/squeeze-loss.png)]
  ### Implementation Details
  #### Arguments:
  ##### alpha:
  Coefficient used along side cross entropy term whose purpose is balancing contribution coming from majority-minority classes.
  ##### gamma:
  Coefficient used along side cross entropy term whose purpose is reducing contribution coming from well classified examples.
  ##### reduction:
  Determines reduction method applied over computed losses(default value equals mean).
                 

  <p>-"none", no reduction will be applied.
  </p>-"mean", will divide sum of losses by number samples.
  </p>-"sum", will sum all losses.
  </p>

   
  <br>#### Returns:
  <p>Returns computed focal losses.
  </p>#### Example Usage:
  <p>input&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;x.py&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;;echo&amp;amp;display=False&ampampamp;display_code=true</input>

  %60%%60%%60%%60%%60%%60%%60 python %%60%%60 %% import torch % import torch.nn.functional as F % import numpy as np % import matplotlib.pyplot as plt % from focal_loss import FocalLoss % n_iter ==============50 % n_data ========;150 % n_minor &#x0026amp;% n_major  % % % % % % %&#xA00100 &#xB7 ;50 % alpha &#xB7 ;np.array([5., .05])/np.sum(np.array([5., .05])) % beta &#xB7 ;np.random.beta(alpha['maj'.index()], alpha[‘minor’.index()], size=(n_iter,n_data)).T % X &#xB7 ;torch.Tensor(beta.T.astype(np.float32)) % Y &#xB7 ;torch.Tensor((X[:, :50]>.5).astype(np.longlong)).T @plt.plot(F.cross_entropy(X,Y,reduction="som")[:50],’g’) @plt.plot(F.cross_entropy(X,Y,reduction="som")[:50],’g’) @plt.plot(F.cross_entropy(X,Y,reduction="som")[:50],’g’) @plt.plot(F.cross_entropy(X,Y,reduction="som")[:50],’g’) @plt.plot(F.cross_entropy(X,Y,reduction="som")[:50],’g’) @plt.plot(F.cross_entropy(X,Y,reduction="som")[:50],’g’) @plt.plot(torch.tensor([[F.focal_cross_entropy(x.unsqueeze(dim=-&aacute;mum<bigrangle>

  %

  >mum)</smallangle>, y.unsqueeze(dim=-&aacute;mum<bigrangle>)for x,&yinzip(X[:,:50].T,Y.T)])],dtype=torch.double),’b’) >!ls *.png | grep gamma_effect.png | xargs open >!ls *.png | grep focal_vs_cross | xargs open >!ls *.png | grep gamma_effect.png | xargs open >!ls *.png | grep focal_vs_cross | xargs open %%70%%70%%70%%70%%70%%70 python %%70%%70 %% floss &#xB7 ;FocalLoss(reduction="som") @plt.plot(floss.forward(X[:,:50],Y[:,:50]),’c’) @plt.legend([‘cross’,’focal’]) @plt.xlabel('x') @plt.ylabel('y') @fig &#xB7 ;plt.gcf() @fig.savefig('images/focal_vs_cross.png&apos